From 28bf4ef1893786e50d0b39f32aaaf002eb7de786 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 16 Sep 2024 15:13:09 +0000 Subject: [PATCH] build based on c0fa8ad --- dev/.documenter-siteinfo.json | 2 +- dev/assets/documenter.js | 985 ++++++++------- dev/assets/themes/catppuccin-frappe.css | 1 + dev/assets/themes/catppuccin-latte.css | 1 + dev/assets/themes/catppuccin-macchiato.css | 1 + dev/assets/themes/catppuccin-mocha.css | 1 + dev/assets/themes/documenter-dark.css | 4 +- dev/assets/themes/documenter-light.css | 2 +- dev/examples/index.html | 6 +- dev/index.html | 2 +- dev/interface/index.html | 28 +- dev/library/index.html | 2 +- dev/objects.inv | Bin 0 -> 1429 bytes dev/search_index.js | 2 +- stable | 2 +- v1 | 2 +- v1.3.0/.documenter-siteinfo.json | 2 +- v1.3.0/examples/index.html | 6 +- v1.3.0/index.html | 2 +- v1.3.0/interface/index.html | 28 +- v1.3.0/library/index.html | 2 +- v1.4 | 1 + v1.4.0/.documenter-siteinfo.json | 1 + v1.4.0/assets/documenter.js | 889 ++++++++++++++ v1.4.0/assets/themes/documenter-dark.css | 7 + v1.4.0/assets/themes/documenter-light.css | 9 + v1.4.0/assets/themeswap.js | 84 ++ v1.4.0/assets/warner.js | 52 + v1.4.0/examples/index.html | 48 + v1.4.0/index.html | 2 + v1.4.0/interface/index.html | 75 ++ v1.4.0/library/index.html | 2 + v1.4.0/search_index.js | 3 + v1.4.0/siteinfo.js | 1 + v1.4.1/.documenter-siteinfo.json | 1 + v1.4.1/assets/documenter.js | 889 ++++++++++++++ v1.4.1/assets/themes/documenter-dark.css | 7 + v1.4.1/assets/themes/documenter-light.css | 9 + v1.4.1/assets/themeswap.js | 84 ++ v1.4.1/assets/warner.js | 52 + v1.4.1/examples/index.html | 48 + v1.4.1/index.html | 2 + v1.4.1/interface/index.html | 75 ++ v1.4.1/library/index.html | 2 + v1.4.1/search_index.js | 3 + v1.4.1/siteinfo.js | 1 + v1.4.2/.documenter-siteinfo.json | 1 + v1.4.2/assets/documenter.js | 1050 ++++++++++++++++ v1.4.2/assets/themes/documenter-dark.css | 7 + v1.4.2/assets/themes/documenter-light.css | 9 + v1.4.2/assets/themeswap.js | 84 ++ v1.4.2/assets/warner.js | 52 + v1.4.2/examples/index.html | 48 + v1.4.2/index.html | 2 + v1.4.2/interface/index.html | 75 ++ v1.4.2/library/index.html | 2 + v1.4.2/objects.inv | Bin 0 -> 1420 bytes v1.4.2/search_index.js | 3 + v1.4.2/siteinfo.js | 1 + v1.4.3/.documenter-siteinfo.json | 1 + v1.4.3/assets/documenter.js | 1050 ++++++++++++++++ v1.4.3/assets/themes/documenter-dark.css | 7 + v1.4.3/assets/themes/documenter-light.css | 9 + v1.4.3/assets/themeswap.js | 84 ++ v1.4.3/assets/warner.js | 52 + v1.4.3/examples/index.html | 48 + v1.4.3/index.html | 2 + v1.4.3/interface/index.html | 75 ++ v1.4.3/library/index.html | 2 + v1.4.3/objects.inv | Bin 0 -> 1420 bytes v1.4.3/search_index.js | 3 + v1.4.3/siteinfo.js | 1 + v1.4.4/.documenter-siteinfo.json | 1 + v1.4.4/assets/documenter.js | 1050 ++++++++++++++++ v1.4.4/assets/themes/documenter-dark.css | 7 + v1.4.4/assets/themes/documenter-light.css | 9 + v1.4.4/assets/themeswap.js | 84 ++ v1.4.4/assets/warner.js | 52 + v1.4.4/examples/index.html | 48 + v1.4.4/index.html | 2 + v1.4.4/interface/index.html | 75 ++ v1.4.4/library/index.html | 2 + v1.4.4/objects.inv | Bin 0 -> 1420 bytes v1.4.4/search_index.js | 3 + v1.4.4/siteinfo.js | 1 + v1.5 | 1 + v1.5.0/.documenter-siteinfo.json | 1 + v1.5.0/assets/documenter.js | 1059 +++++++++++++++++ v1.5.0/assets/themes/catppuccin-frappe.css | 1 + v1.5.0/assets/themes/catppuccin-latte.css | 1 + v1.5.0/assets/themes/catppuccin-macchiato.css | 1 + v1.5.0/assets/themes/catppuccin-mocha.css | 1 + v1.5.0/assets/themes/documenter-dark.css | 7 + v1.5.0/assets/themes/documenter-light.css | 9 + v1.5.0/assets/themeswap.js | 84 ++ v1.5.0/assets/warner.js | 52 + v1.5.0/examples/index.html | 48 + v1.5.0/index.html | 2 + v1.5.0/interface/index.html | 75 ++ v1.5.0/library/index.html | 2 + v1.5.0/objects.inv | Bin 0 -> 1429 bytes v1.5.0/search_index.js | 3 + v1.5.0/siteinfo.js | 1 + v1.5.1/.documenter-siteinfo.json | 1 + v1.5.1/assets/documenter.js | 1059 +++++++++++++++++ v1.5.1/assets/themes/catppuccin-frappe.css | 1 + v1.5.1/assets/themes/catppuccin-latte.css | 1 + v1.5.1/assets/themes/catppuccin-macchiato.css | 1 + v1.5.1/assets/themes/catppuccin-mocha.css | 1 + v1.5.1/assets/themes/documenter-dark.css | 7 + v1.5.1/assets/themes/documenter-light.css | 9 + v1.5.1/assets/themeswap.js | 84 ++ v1.5.1/assets/warner.js | 52 + v1.5.1/examples/index.html | 48 + v1.5.1/index.html | 2 + v1.5.1/interface/index.html | 75 ++ v1.5.1/library/index.html | 2 + v1.5.1/objects.inv | Bin 0 -> 1429 bytes v1.5.1/search_index.js | 3 + v1.5.1/siteinfo.js | 1 + versions.js | 4 +- 121 files changed, 9677 insertions(+), 452 deletions(-) create mode 100644 dev/assets/themes/catppuccin-frappe.css create mode 100644 dev/assets/themes/catppuccin-latte.css create mode 100644 dev/assets/themes/catppuccin-macchiato.css create mode 100644 dev/assets/themes/catppuccin-mocha.css create mode 100644 dev/objects.inv create mode 120000 v1.4 create mode 100644 v1.4.0/.documenter-siteinfo.json create mode 100644 v1.4.0/assets/documenter.js create mode 100644 v1.4.0/assets/themes/documenter-dark.css create mode 100644 v1.4.0/assets/themes/documenter-light.css create mode 100644 v1.4.0/assets/themeswap.js create mode 100644 v1.4.0/assets/warner.js create mode 100644 v1.4.0/examples/index.html create mode 100644 v1.4.0/index.html create mode 100644 v1.4.0/interface/index.html create mode 100644 v1.4.0/library/index.html create mode 100644 v1.4.0/search_index.js create mode 100644 v1.4.0/siteinfo.js create mode 100644 v1.4.1/.documenter-siteinfo.json create mode 100644 v1.4.1/assets/documenter.js create mode 100644 v1.4.1/assets/themes/documenter-dark.css create mode 100644 v1.4.1/assets/themes/documenter-light.css create mode 100644 v1.4.1/assets/themeswap.js create mode 100644 v1.4.1/assets/warner.js create mode 100644 v1.4.1/examples/index.html create mode 100644 v1.4.1/index.html create mode 100644 v1.4.1/interface/index.html create mode 100644 v1.4.1/library/index.html create mode 100644 v1.4.1/search_index.js create mode 100644 v1.4.1/siteinfo.js create mode 100644 v1.4.2/.documenter-siteinfo.json create mode 100644 v1.4.2/assets/documenter.js create mode 100644 v1.4.2/assets/themes/documenter-dark.css create mode 100644 v1.4.2/assets/themes/documenter-light.css create mode 100644 v1.4.2/assets/themeswap.js create mode 100644 v1.4.2/assets/warner.js create mode 100644 v1.4.2/examples/index.html create mode 100644 v1.4.2/index.html create mode 100644 v1.4.2/interface/index.html create mode 100644 v1.4.2/library/index.html create mode 100644 v1.4.2/objects.inv create mode 100644 v1.4.2/search_index.js create mode 100644 v1.4.2/siteinfo.js create mode 100644 v1.4.3/.documenter-siteinfo.json create mode 100644 v1.4.3/assets/documenter.js create mode 100644 v1.4.3/assets/themes/documenter-dark.css create mode 100644 v1.4.3/assets/themes/documenter-light.css create mode 100644 v1.4.3/assets/themeswap.js create mode 100644 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create mode 100644 v1.5.0/assets/documenter.js create mode 100644 v1.5.0/assets/themes/catppuccin-frappe.css create mode 100644 v1.5.0/assets/themes/catppuccin-latte.css create mode 100644 v1.5.0/assets/themes/catppuccin-macchiato.css create mode 100644 v1.5.0/assets/themes/catppuccin-mocha.css create mode 100644 v1.5.0/assets/themes/documenter-dark.css create mode 100644 v1.5.0/assets/themes/documenter-light.css create mode 100644 v1.5.0/assets/themeswap.js create mode 100644 v1.5.0/assets/warner.js create mode 100644 v1.5.0/examples/index.html create mode 100644 v1.5.0/index.html create mode 100644 v1.5.0/interface/index.html create mode 100644 v1.5.0/library/index.html create mode 100644 v1.5.0/objects.inv create mode 100644 v1.5.0/search_index.js create mode 100644 v1.5.0/siteinfo.js create mode 100644 v1.5.1/.documenter-siteinfo.json create mode 100644 v1.5.1/assets/documenter.js create mode 100644 v1.5.1/assets/themes/catppuccin-frappe.css create mode 100644 v1.5.1/assets/themes/catppuccin-latte.css create mode 100644 v1.5.1/assets/themes/catppuccin-macchiato.css create mode 100644 v1.5.1/assets/themes/catppuccin-mocha.css create mode 100644 v1.5.1/assets/themes/documenter-dark.css create mode 100644 v1.5.1/assets/themes/documenter-light.css create mode 100644 v1.5.1/assets/themeswap.js create mode 100644 v1.5.1/assets/warner.js create mode 100644 v1.5.1/examples/index.html create mode 100644 v1.5.1/index.html create mode 100644 v1.5.1/interface/index.html create mode 100644 v1.5.1/library/index.html create mode 100644 v1.5.1/objects.inv create mode 100644 v1.5.1/search_index.js create mode 100644 v1.5.1/siteinfo.js diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 4ae2e527..0e900569 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-09T14:49:43","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-16T15:13:05","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js index f5311607..82252a11 100644 --- a/dev/assets/documenter.js +++ b/dev/assets/documenter.js @@ -4,7 +4,6 @@ requirejs.config({ 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', - 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', @@ -78,48 +77,54 @@ require(['jquery'], function($) { let timer = 0; var isExpanded = true; -$(document).on("click", ".docstring header", function () { - let articleToggleTitle = "Expand docstring"; - - debounce(() => { - if ($(this).siblings("section").is(":visible")) { - $(this) - .find(".docstring-article-toggle-button") - .removeClass("fa-chevron-down") - .addClass("fa-chevron-right"); - } else { - $(this) - .find(".docstring-article-toggle-button") - .removeClass("fa-chevron-right") - .addClass("fa-chevron-down"); +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); - articleToggleTitle = "Collapse docstring"; - } + articleToggleTitle = "Collapse docstring"; + } - $(this) - .find(".docstring-article-toggle-button") - .prop("title", articleToggleTitle); - $(this).siblings("section").slideToggle(); - }); -}); + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); -$(document).on("click", ".docs-article-toggle-button", function () { +$(document).on("click", ".docs-article-toggle-button", function (event) { let articleToggleTitle = "Expand docstring"; let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; debounce(() => { if (isExpanded) { $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); - $(".docstring-article-toggle-button") + $("a.docstring-article-toggle-button") .removeClass("fa-chevron-down") .addClass("fa-chevron-right"); isExpanded = false; - $(".docstring section").slideUp(); + $(".docstring section").slideUp(animationSpeed); } else { $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); - $(".docstring-article-toggle-button") + $("a.docstring-article-toggle-button") .removeClass("fa-chevron-right") .addClass("fa-chevron-down"); @@ -127,7 +132,7 @@ $(document).on("click", ".docs-article-toggle-button", function () { articleToggleTitle = "Collapse docstring"; navArticleToggleTitle = "Collapse all docstrings"; - $(".docstring section").slideDown(); + $(".docstring section").slideDown(animationSpeed); } $(this).prop("title", navArticleToggleTitle); @@ -224,224 +229,474 @@ $(document).ready(function () { }) //////////////////////////////////////////////////////////////////////////////// -require(['jquery', 'minisearch'], function($, minisearch) { - -// In general, most search related things will have "search" as a prefix. -// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc +require(['jquery'], function($) { -let results = []; -let timer = undefined; +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); -let data = documenterSearchIndex["docs"].map((x, key) => { - x["id"] = key; // minisearch requires a unique for each object - return x; + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } }); -// list below is the lunr 2.1.3 list minus the intersect with names(Base) -// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) -// ideally we'd just filter the original list but it's not available as a variable -const stopWords = new Set([ - "a", - "able", - "about", - "across", - "after", - "almost", - "also", - "am", - "among", - "an", - "and", - "are", - "as", - "at", - "be", - "because", - "been", - "but", - "by", - "can", - "cannot", - "could", - "dear", - "did", - "does", - "either", - "ever", - "every", - "from", - "got", - "had", - "has", - "have", - "he", - "her", - "hers", - "him", - "his", - "how", - "however", - "i", - "if", - "into", - "it", - "its", - "just", - "least", - "like", - "likely", - "may", - "me", - "might", - "most", - "must", - "my", - "neither", - "no", - "nor", - "not", - "of", - "off", - "often", - "on", - "or", - "other", - "our", - "own", - "rather", - "said", - "say", - "says", - "she", - "should", - "since", - "so", - "some", - "than", - "that", - "the", - "their", - "them", - "then", - "there", - "these", - "they", - "this", - "tis", - "to", - "too", - "twas", - "us", - "wants", - "was", - "we", - "were", - "what", - "when", - "who", - "whom", - "why", - "will", - "would", - "yet", - "you", - "your", -]); - -let index = new minisearch({ - fields: ["title", "text"], // fields to index for full-text search - storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results - processTerm: (term) => { - let word = stopWords.has(term) ? null : term; - if (word) { - // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names - word = word - .replace(/^[^a-zA-Z0-9@!]+/, "") - .replace(/[^a-zA-Z0-9@!]+$/, ""); - } +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { - return word ?? null; - }, - // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification - tokenize: (string) => string.split(/[\s\-\.]+/), - // options which will be applied during the search - searchOptions: { - boost: { title: 100 }, - fuzzy: 2, +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results processTerm: (term) => { let word = stopWords.has(term) ? null : term; if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names word = word .replace(/^[^a-zA-Z0-9@!]+/, "") .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); } return word ?? null; }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification tokenize: (string) => string.split(/[\s\-\.]+/), - }, -}); + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } -index.addAll(data); + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } -let filters = [...new Set(data.map((x) => x.category))]; -var modal_filters = make_modal_body_filters(filters); -var filter_results = []; + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div -$(document).on("keyup", ".documenter-search-input", function (event) { - // Adding a debounce to prevent disruptions from super-speed typing! - debounce(() => update_search(filter_results), 300); + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } }); +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + $(document).on("click", ".search-filter", function () { if ($(this).hasClass("search-filter-selected")) { - $(this).removeClass("search-filter-selected"); + selected_filter = ""; } else { - $(this).addClass("search-filter-selected"); + selected_filter = $(this).text().toLowerCase(); } - // Adding a debounce to prevent disruptions from crazy clicking! - debounce(() => get_filters(), 300); + // This updates search results and toggles classes for UI: + update_search(); }); -/** - * A debounce function, takes a function and an optional timeout in milliseconds - * - * @function callback - * @param {number} timeout - */ -function debounce(callback, timeout = 300) { - clearTimeout(timer); - timer = setTimeout(callback, timeout); -} - /** * Make/Update the search component - * - * @param {string[]} selected_filters */ -function update_search(selected_filters = []) { - let initial_search_body = ` -
Type something to get started!
- `; - +function update_search() { let querystring = $(".documenter-search-input").val(); if (querystring.trim()) { - results = index.search(querystring, { - filter: (result) => { - // Filtering results - if (selected_filters.length === 0) { - return result.score >= 1; - } else { - return ( - result.score >= 1 && selected_filters.includes(result.category) - ); - } - }, - }); + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } let search_result_container = ``; + let modal_filters = make_modal_body_filters(); let search_divider = `
`; if (results.length) { @@ -449,19 +704,23 @@ function update_search(selected_filters = []) { let count = 0; let search_results = ""; - results.forEach(function (result) { - if (result.location) { - // Checking for duplication of results for the same page - if (!links.includes(result.location)) { - search_results += make_search_result(result, querystring); - count++; - } - + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; links.push(result.location); } - }); + } - let result_count = `
${count} result(s)
`; + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; search_result_container = `
@@ -490,125 +749,37 @@ function update_search(selected_filters = []) { $(".search-modal-card-body").html(search_result_container); } else { - filter_results = []; - modal_filters = make_modal_body_filters(filters, filter_results); - if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { $(".search-modal-card-body").addClass("is-justify-content-center"); } - $(".search-modal-card-body").html(initial_search_body); + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); } } /** * Make the modal filter html * - * @param {string[]} filters - * @param {string[]} selected_filters * @returns string */ -function make_modal_body_filters(filters, selected_filters = []) { - let str = ``; - - filters.forEach((val) => { - if (selected_filters.includes(val)) { - str += `${val}`; - } else { - str += `${val}`; - } - }); +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); - let filter_html = ` + return `
Filters: ${str} -
- `; - - return filter_html; -} - -/** - * Make the result component given a minisearch result data object and the value of the search input as queryString. - * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult - * - * @param {object} result - * @param {string} querystring - * @returns string - */ -function make_search_result(result, querystring) { - let search_divider = `
`; - let display_link = - result.location.slice(Math.max(0), Math.min(50, result.location.length)) + - (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div - - if (result.page !== "") { - display_link += ` (${result.page})`; - } - - let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); - let text = - textindex !== null - ? result.text.slice( - Math.max(textindex.index - 100, 0), - Math.min( - textindex.index + querystring.length + 100, - result.text.length - ) - ) - : ""; // cut-off text before and after from the match - - let display_result = text.length - ? "..." + - text.replace( - new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence - '$&' - ) + - "..." - : ""; // highlights the match - - let in_code = false; - if (!["page", "section"].includes(result.category.toLowerCase())) { - in_code = true; - } - - // We encode the full url to escape some special characters which can lead to broken links - let result_div = ` - -
-
${result.title}
-
${result.category}
-
-

- ${display_result} -

-
- ${display_link} -
- - ${search_divider} - `; - - return result_div; -} - -/** - * Get selected filters, remake the filter html and lastly update the search modal - */ -function get_filters() { - let ele = $(".search-filters .search-filter-selected").get(); - filter_results = ele.map((x) => $(x).text().toLowerCase()); - modal_filters = make_modal_body_filters(filters, filter_results); - update_search(filter_results); +
`; } }) @@ -635,103 +806,107 @@ $(document).ready(function () { //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { -let search_modal_header = ` -
-
-

- - - - -

-
-
- -
-
-`; - -let initial_search_body = ` -
Type something to get started!
-`; - -let search_modal_footer = ` - -`; - -$(document.body).append( - ` - diff --git a/dev/library/index.html b/dev/library/index.html index 0d9bd205..7adc60c3 100644 --- a/dev/library/index.html +++ b/dev/library/index.html @@ -1,2 +1,2 @@ -Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
+Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
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z8yOnR-!A8G7hZg)QW3-)%8*#`j4grByqC=0k=vI|+M2=o<4WWrh!bvx6R(gHS#Jf} zSeHX_M7u-tt*R&J2*WcO(myH31nxA+Ga3{|&vGMbw`0CRXoqcZrUJc6GZy699&q?) zp<{^S1Jj+P@z2R++G#1J-fX@i3;FcirJ`a47G}aME)OGT6Ls1_2Ao&d>hrskJptUtEaQJNGh!ZB4QWDSgXr7q zPJVvew*gB=1m1AJ)b%h;2OvFnR<4>^*(*f54>ev7(ABU3+Tq-pn5(0S+20Xdi?T8J zV{|oej0z3+hirVgCXIpvk^R@H#ZCB>6U(vBaYvR@c^-OP>8<9%Yq~@AcB9~~QjS8r zeXZM`GZf(uyt#d3h1PI*A6~xcZ9Zq=lrB49gm*K20NcJ3<$RChxi*<}RZrh4`%BIU zV%z~SzD#K56L|?*ok|hSafBK^ ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +[{"location":"interface/#interface","page":"Interface","title":"The ExponentialFamilyDistribution Interface","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.","category":"page"},{"location":"interface/#Notation","page":"Interface","title":"Notation","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the context of the package, exponential family distributions are represented in the form:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"f_X(xmideta) = h(x) cdot expleft eta cdot T(x) - A(eta) right","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Here:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"h(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the following discussion we also use the following convention","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"η corresponds to the distribution's natural parameters in the natural parameter space.\nθ corresponds to the distribution's mean parameters in the mean parameter space.","category":"page"},{"location":"interface/#ExponentialFamilyDistribution-structure","page":"Interface","title":"ExponentialFamilyDistribution structure","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamilyDistribution\nExponentialFamilyDistributionAttributes\nlogpdf(ef::ExponentialFamilyDistribution, x)\npdf(ef::ExponentialFamilyDistribution, x)\ncdf(ef::ExponentialFamilyDistribution{D}, x) where {D <: Distribution}\ngetnaturalparameters\ngetattributes\ngetconditioner\nisproper\ngetbasemeasure\ngetlogbasemeasure\ngetsufficientstatistics\ngetlogpartition\ngetgradlogpartition\ngetfisherinformation\ngetsupport\nbasemeasure\nlogbasemeasure\nsufficientstatistics\nlogpartition\ngradlogpartition\nfisherinformation\nisbasemeasureconstant\nConstantBaseMeasure\nNonConstantBaseMeasure\nExponentialFamily._logpdf\nExponentialFamily.check_logpdf\nExponentialFamily.PointBasedLogpdfCall\nExponentialFamily.MapBasedLogpdfCall","category":"page"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistribution","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistribution","text":"ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)\n\nExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.\n\nnote: Note\nThe attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nOptionally\n\nlogbasemeasure::LB: The log of the basemeasure of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogbasemeasure","page":"Interface","title":"ExponentialFamily.getlogbasemeasure","text":"getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getlogbasemeasure defined particularly for distribution types from Distributions.jl package. Just computes log of basemeasure.\n\n\n\n\n\ngetlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. For conditional exponential family distributions requires an extra conditioner argument. Just computes log of basemeasure.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logbasemeasure","page":"Interface","title":"ExponentialFamily.logbasemeasure","text":"logbasemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of log(basemeasure) of the exponential family distribution at the point x.\n\nSee also basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] } diff --git a/stable b/stable index 8b3a0227..c9b3c015 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v1.3.0 \ No newline at end of file +v1.5.1 \ No newline at end of file diff --git a/v1 b/v1 index 8b3a0227..c9b3c015 120000 --- a/v1 +++ b/v1 @@ -1 +1 @@ -v1.3.0 \ No newline at end of file +v1.5.1 \ No newline at end of file diff --git a/v1.3.0/.documenter-siteinfo.json b/v1.3.0/.documenter-siteinfo.json index d9b83191..24d1729a 100644 --- a/v1.3.0/.documenter-siteinfo.json +++ b/v1.3.0/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-09T12:54:39","documenter_version":"1.2.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-12T15:02:21","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/v1.3.0/examples/index.html b/v1.3.0/examples/index.html index cc2ee026..80477036 100644 --- a/v1.3.0/examples/index.html +++ b/v1.3.0/examples/index.html @@ -1,5 +1,5 @@ -Examples · ExponentialFamily.jl
GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+Examples · ExponentialFamily.jl
GitHub
Examples
Product of two probability distributions over the same variable
In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X".  This operation results in another probability distribution, also centered around the variable "X".  It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y",  which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.
\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]
To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:
using ExponentialFamily, Distributions, BayesBase
 
 prior = Bernoulli(0.5)
 likelihood = Bernoulli(0.6)
@@ -10,7 +10,7 @@
 ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)
Or even more concisely:
prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)
In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:
prior = Laplace(2.0, 3.0)
 likelihood = Laplace(1.0, 4.0)
 
-prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)
Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.
Computing various useful attributes of an exponential family member
The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others.  In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:
using ExponentialFamily, Distributions
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)
Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.
Computing various useful attributes of an exponential family member
The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others.  In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:
using ExponentialFamily, Distributions
 
 # Returns a function
 basemeasure_of_normal = getbasemeasure(Normal)
@@ -45,4 +45,4 @@
 
 fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
  1.64493  2.0
- 2.0      4.0
Approximating attributes
Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.3.0/index.html b/v1.3.0/index.html index 2d9ef517..3a1c63a7 100644 --- a/v1.3.0/index.html +++ b/v1.3.0/index.html @@ -1,2 +1,2 @@ -Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

+Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.3.0/interface/index.html b/v1.3.0/interface/index.html index 59f7baaf..4814aa85 100644 --- a/v1.3.0/interface/index.html +++ b/v1.3.0/interface/index.html @@ -1,5 +1,5 @@ -Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+Interface · ExponentialFamily.jl
GitHub
The ExponentialFamilyDistribution Interface
This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.
Notation
In the context of the package, exponential family distributions are represented in the form:
\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]
Here:
  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.
In the following discussion we also use the following convention
  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.
ExponentialFamilyDistribution structure
ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)
ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:
\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]
Here:
  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.
For a given member of exponential family: 
  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function. 
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters. 
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. 
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note
The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.
julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
 ExponentialFamily(Bernoulli)
 
 julia> getsufficientstatistics(ef)
@@ -7,11 +7,11 @@
 ExponentialFamily(Laplace, conditioned on 1.0)
 
 julia> logpdf(ef, 4.0)
--6.0
See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport
source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)
A structure to represent the attributes of an exponential family member.
Fields
  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.
See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport
source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the log-density of the exponential family distribution for the input x.
source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the probability density function of the exponential family distribution for the input x.
source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }
Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.
source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)
Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.
source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)
Checks if the object of type ExponentialFamilyDistribution is a proper distribution.
source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }
A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.
See also: NaturalParametersSpace, MeanParametersSpace
source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
-getbasemeasure(::Type{ <: Distribution }, [ conditioner ])
Returns the base measure function of the exponential family distribution.
source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
-getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])
Returns the list of sufficient statistics of the exponential family distribution.
source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
-getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])
Returns the log partition function of the exponential family distribution.
source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
-getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])
Returns the function that computes the fisher information matrix of the exponential family distribution.
source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)
Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).
See also: getlogpartition
source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)
Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.
See also: getbasemeasure, basemeasure
source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the log-density of the exponential family distribution for the input x.
This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.
For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.
Examples
Evaluate the log-density of a Gamma distribution at a single point:
using ExponentialFamily, Distributions;
+-6.0
See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport
source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)
A structure to represent the attributes of an exponential family member.
Fields
  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.
See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport
source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the log-density of the exponential family distribution for the input x.
source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the probability density function of the exponential family distribution for the input x.
source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }
Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.
source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)
Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.
source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)
Checks if the object of type ExponentialFamilyDistribution is a proper distribution.
source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }
A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.
See also: NaturalParametersSpace, MeanParametersSpace
source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])
Returns the base measure function of the exponential family distribution.
source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])
Returns the list of sufficient statistics of the exponential family distribution.
source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])
Returns the log partition function of the exponential family distribution.
source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])
Returns the function that computes the fisher information matrix of the exponential family distribution.
source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)
Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).
See also: getlogpartition
source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)
Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.
See also: getbasemeasure, basemeasure
source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)
Evaluates and returns the log-density of the exponential family distribution for the input x.
This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.
For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.
Examples
Evaluate the log-density of a Gamma distribution at a single point:
using ExponentialFamily, Distributions;
 gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
 ExponentialFamily._logpdf(gamma, 1.0)
 # output
@@ -22,31 +22,31 @@
 3-element Vector{Float64}:
  -1.0
  -2.0
- -3.0
For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.
See also: check_logpdf
source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)
Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.
Strategies
  • For a Univariate distribution:
    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().
  • For a Multivariate distribution:
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).
  • For a Matrixvariate distribution:
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().
Examples
using ExponentialFamily
+ -3.0
For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.
See also: check_logpdf
source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)
Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.
Strategies
  • For a Univariate distribution:
    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().
  • For a Multivariate distribution:
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).
  • For a Matrixvariate distribution:
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().
Examples
using ExponentialFamily
 ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
 # output
 (ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
 ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
 # output
-(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])
See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall
source
Interfacing with Distributions Defined in the Distributions.jl Package
The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.
Conversion between Mean Parameters Space and Natural Parameters Space
The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:
using Distributions, ExponentialFamily
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])
See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall
source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
 
 distribution = Bernoulli(0.25)
 
-tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
 ((1.0,), 0.0)
 
 julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
 (0.0, 1.0)
 
 julia> Laplace(params...) == Laplace(0.0, 1.0)
-true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
 ((1.0,), 0.0)
 
 julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
 (0.0, 1.0)
 
 julia> Laplace(params...) == Laplace(0.0, 1.0)
-true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
 # The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
 # Hence, we return a tuple of tuple of actual parameter and the conditioner
 function separate_conditioner(::Type{Laplace}, params)
@@ -60,7 +60,7 @@
     (scale, ) = cparams
     location = conditioner
     return (location, scale)
-end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#342#343"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#348#349"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
 9-element Vector{Float64}:
  1.0
  2.0
@@ -70,6 +70,6 @@
  5.0
  8.0
  6.0
- 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
 
-basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.3.0/library/index.html b/v1.3.0/library/index.html index 0d7b7192..7664a9bf 100644 --- a/v1.3.0/library/index.html +++ b/v1.3.0/library/index.html @@ -1,2 +1,2 @@ -Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
+Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
diff --git a/v1.4 b/v1.4 new file mode 120000 index 00000000..44c34055 --- /dev/null +++ b/v1.4 @@ -0,0 +1 @@ +v1.4.4 \ No newline at end of file diff --git a/v1.4.0/.documenter-siteinfo.json b/v1.4.0/.documenter-siteinfo.json new file mode 100644 index 00000000..21e18724 --- /dev/null +++ b/v1.4.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-01-31T12:03:34","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/v1.4.0/assets/documenter.js b/v1.4.0/assets/documenter.js new file mode 100644 index 00000000..f5311607 --- /dev/null +++ b/v1.4.0/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.4.0/assets/themes/documenter-dark.css b/v1.4.0/assets/themes/documenter-dark.css new file mode 100644 index 00000000..9f5449f4 --- /dev/null +++ b/v1.4.0/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark .is-active.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--documenter-dark .is-active.button{outline:none}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark .pagination-next[disabled],html.theme--documenter-dark .pagination-link[disabled],html.theme--documenter-dark .pagination-ellipsis[disabled],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v1.4.0/assets/themeswap.js b/v1.4.0/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/v1.4.0/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v1.4.0/assets/warner.js b/v1.4.0/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/v1.4.0/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. 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Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v1.4.0/examples/index.html b/v1.4.0/examples/index.html new file mode 100644 index 00000000..5d329653 --- /dev/null +++ b/v1.4.0/examples/index.html @@ -0,0 +1,48 @@ + +Examples · ExponentialFamily.jl
GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.4.0/index.html b/v1.4.0/index.html new file mode 100644 index 00000000..68662910 --- /dev/null +++ b/v1.4.0/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.4.0/interface/index.html b/v1.4.0/interface/index.html new file mode 100644 index 00000000..a563f463 --- /dev/null +++ b/v1.4.0/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#422#423"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

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The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.4.0/library/index.html b/v1.4.0/library/index.html new file mode 100644 index 00000000..416f827e --- /dev/null +++ b/v1.4.0/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
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ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
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ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
diff --git a/v1.4.0/search_index.js b/v1.4.0/search_index.js new file mode 100644 index 00000000..9b40f9f0 --- /dev/null +++ b/v1.4.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"interface/#interface","page":"Interface","title":"The ExponentialFamilyDistribution Interface","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.","category":"page"},{"location":"interface/#Notation","page":"Interface","title":"Notation","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the context of the package, exponential family distributions are represented in the form:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"f_X(xmideta) = h(x) cdot expleft eta cdot T(x) - A(eta) right","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Here:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"h(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the following discussion we also use the following convention","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"η corresponds to the distribution's natural parameters in the natural parameter space.\nθ corresponds to the distribution's mean parameters in the mean parameter space.","category":"page"},{"location":"interface/#ExponentialFamilyDistribution-structure","page":"Interface","title":"ExponentialFamilyDistribution structure","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamilyDistribution\nExponentialFamilyDistributionAttributes\nlogpdf(ef::ExponentialFamilyDistribution, x)\npdf(ef::ExponentialFamilyDistribution, x)\ncdf(ef::ExponentialFamilyDistribution{D}, x) where {D <: Distribution}\ngetnaturalparameters\ngetattributes\ngetconditioner\nisproper\ngetbasemeasure\ngetsufficientstatistics\ngetlogpartition\ngetgradlogpartition\ngetfisherinformation\ngetsupport\nbasemeasure\nsufficientstatistics\nlogpartition\ngradlogpartition\nfisherinformation\nisbasemeasureconstant\nConstantBaseMeasure\nNonConstantBaseMeasure\nExponentialFamily._logpdf\nExponentialFamily.check_logpdf\nExponentialFamily.PointBasedLogpdfCall\nExponentialFamily.MapBasedLogpdfCall","category":"page"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistribution","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistribution","text":"ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)\n\nExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.\n\nnote: Note\nThe attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.4.0/siteinfo.js b/v1.4.0/siteinfo.js new file mode 100644 index 00000000..3d135fd6 --- /dev/null +++ b/v1.4.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.4.0"; diff --git a/v1.4.1/.documenter-siteinfo.json b/v1.4.1/.documenter-siteinfo.json new file mode 100644 index 00000000..53bf171b --- /dev/null +++ b/v1.4.1/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.1","generation_timestamp":"2024-02-22T12:30:03","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/v1.4.1/assets/documenter.js b/v1.4.1/assets/documenter.js new file mode 100644 index 00000000..f5311607 --- /dev/null +++ b/v1.4.1/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.4.1/assets/themes/documenter-dark.css b/v1.4.1/assets/themes/documenter-dark.css new file mode 100644 index 00000000..9f5449f4 --- /dev/null +++ b/v1.4.1/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.4.1/index.html b/v1.4.1/index.html new file mode 100644 index 00000000..49eff5ba --- /dev/null +++ b/v1.4.1/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.4.1/interface/index.html b/v1.4.1/interface/index.html new file mode 100644 index 00000000..4b1abb13 --- /dev/null +++ b/v1.4.1/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#422#423"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.4.1/library/index.html b/v1.4.1/library/index.html new file mode 100644 index 00000000..5d487035 --- /dev/null +++ b/v1.4.1/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
diff --git a/v1.4.1/search_index.js b/v1.4.1/search_index.js new file mode 100644 index 00000000..9b40f9f0 --- /dev/null +++ b/v1.4.1/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"interface/#interface","page":"Interface","title":"The ExponentialFamilyDistribution Interface","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. 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Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. 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In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.4.1/siteinfo.js b/v1.4.1/siteinfo.js new file mode 100644 index 00000000..05cb9ade --- /dev/null +++ b/v1.4.1/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.4.1"; diff --git a/v1.4.2/.documenter-siteinfo.json b/v1.4.2/.documenter-siteinfo.json new file mode 100644 index 00000000..ddc9869b --- /dev/null +++ b/v1.4.2/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-12T13:28:59","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/v1.4.2/assets/documenter.js b/v1.4.2/assets/documenter.js new file mode 100644 index 00000000..c6562b55 --- /dev/null +++ b/v1.4.2/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 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+$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.4.2/assets/themes/documenter-dark.css b/v1.4.2/assets/themes/documenter-dark.css new file mode 100644 index 00000000..1d717015 --- /dev/null +++ b/v1.4.2/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark .is-active.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--documenter-dark .is-active.button{outline:none}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark .pagination-next[disabled],html.theme--documenter-dark .pagination-link[disabled],html.theme--documenter-dark .pagination-ellipsis[disabled],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar 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.button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v1.4.2/assets/themeswap.js b/v1.4.2/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/v1.4.2/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v1.4.2/assets/warner.js b/v1.4.2/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/v1.4.2/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. 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Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v1.4.2/examples/index.html b/v1.4.2/examples/index.html new file mode 100644 index 00000000..8feffd79 --- /dev/null +++ b/v1.4.2/examples/index.html @@ -0,0 +1,48 @@ + +Examples · ExponentialFamily.jl
GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.4.2/index.html b/v1.4.2/index.html new file mode 100644 index 00000000..fbd0ab80 --- /dev/null +++ b/v1.4.2/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.4.2/interface/index.html b/v1.4.2/interface/index.html new file mode 100644 index 00000000..fec8703e --- /dev/null +++ b/v1.4.2/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#422#423"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

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ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

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The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.4.2/library/index.html b/v1.4.2/library/index.html new file mode 100644 index 00000000..3d8c3012 --- /dev/null +++ b/v1.4.2/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
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ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
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ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
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In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.","category":"page"},{"location":"interface/#Notation","page":"Interface","title":"Notation","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the context of the package, exponential family distributions are represented in the form:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"f_X(xmideta) = h(x) cdot expleft eta cdot T(x) - A(eta) right","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Here:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"h(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the following discussion we also use the following convention","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"η corresponds to the distribution's natural parameters in the natural parameter space.\nθ corresponds to the distribution's mean parameters in the mean parameter space.","category":"page"},{"location":"interface/#ExponentialFamilyDistribution-structure","page":"Interface","title":"ExponentialFamilyDistribution structure","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamilyDistribution\nExponentialFamilyDistributionAttributes\nlogpdf(ef::ExponentialFamilyDistribution, x)\npdf(ef::ExponentialFamilyDistribution, x)\ncdf(ef::ExponentialFamilyDistribution{D}, x) where {D <: Distribution}\ngetnaturalparameters\ngetattributes\ngetconditioner\nisproper\ngetbasemeasure\ngetsufficientstatistics\ngetlogpartition\ngetgradlogpartition\ngetfisherinformation\ngetsupport\nbasemeasure\nsufficientstatistics\nlogpartition\ngradlogpartition\nfisherinformation\nisbasemeasureconstant\nConstantBaseMeasure\nNonConstantBaseMeasure\nExponentialFamily._logpdf\nExponentialFamily.check_logpdf\nExponentialFamily.PointBasedLogpdfCall\nExponentialFamily.MapBasedLogpdfCall","category":"page"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistribution","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistribution","text":"ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)\n\nExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.\n\nnote: Note\nThe attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.4.2/siteinfo.js b/v1.4.2/siteinfo.js new file mode 100644 index 00000000..c224bb01 --- /dev/null +++ b/v1.4.2/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.4.2"; diff --git a/v1.4.3/.documenter-siteinfo.json b/v1.4.3/.documenter-siteinfo.json new file mode 100644 index 00000000..f3cfc961 --- /dev/null +++ b/v1.4.3/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-16T09:00:53","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/v1.4.3/assets/documenter.js b/v1.4.3/assets/documenter.js new file mode 100644 index 00000000..c6562b55 --- /dev/null +++ b/v1.4.3/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.4.3/assets/themes/documenter-dark.css b/v1.4.3/assets/themes/documenter-dark.css new file mode 100644 index 00000000..1d717015 --- /dev/null +++ b/v1.4.3/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark 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.button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--documenter-dark .image.is-16x16,html.theme--documenter-dark #documenter .docs-sidebar 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GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.4.3/index.html b/v1.4.3/index.html new file mode 100644 index 00000000..fd3b2393 --- /dev/null +++ b/v1.4.3/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.4.3/interface/index.html b/v1.4.3/interface/index.html new file mode 100644 index 00000000..dfcdb95c --- /dev/null +++ b/v1.4.3/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

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ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#422#423"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.4.3/library/index.html b/v1.4.3/library/index.html new file mode 100644 index 00000000..58b8a924 --- /dev/null +++ b/v1.4.3/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
diff --git a/v1.4.3/objects.inv b/v1.4.3/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..d4d0487386ce62553c21585e87a78ef37b432e48 GIT binary patch literal 1420 zcmV;71#|i%AX9K?X>NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGkKcyMoS zWo~q7VQfZWZE0+IE^2HFBOq2~a&u{KZaN?_E;KGP3L_v?Xk{RBWo=<;Ze(S0Aa78b#rNMXCQiPX<{x4c%02xO>^5e5WVYH>`bd$ zP^ZZuGoD@)$w}RbJepc5wm~m@j45TPai;;Mx?TN$K8&DI0V}C%6 zrOX-GCLHN&Q}X~lhu5@pzkLUL0n|8TJ<>J}d= zd@%UXLO=d@KTV&=+pM@EZib$)99w)99~^#z|Oda%i=! z6;xISHFl@aslHK7B3Nv$n?MQbC&b{p1Kv~{49OoQ;Qk%m@q}xi-KYXAsAZwTBH00B z`s|4st!eh&Na2&b%fe_$lLYRQOZ}8FIBJr|)*FdiCfG*_wh1P_IFkgeqe29>mIDyh z4>veyXkrMvl=edfGPRAt$@wY!JEl!5NEuazbtAo(zCSa57i$)p7&bWzxRui25K54b zG)?JnBQugGq^(Wb-{+)E74_Lbnc=E54;1-Jp!2WW0?GPy`}_*3C&aY>VsDIbFg!oQ zW6Uts+utrd;i7;1mRN><{3HF(-@Uhf&ENUE)%?wJ{^oV_24nFSs+i3G=GAK(nK78Z zUC!Swy!cL~B8VB5A+g*aTLPbXFPXg~w=bKtHO2M)isw9t6Q+j~uMiViZw1;|mosfd zw=(8iSr5PwhG#OQf6$Ey+-Z_$G$<22%{8yxj`;?z9Jb++2=yxTSdeRbK4G7^iZPB4 zRCSWZKjxNcC#95nv-t`Z;_10dMct?Ij_Bh%QG}^wc;Ym- zHhNB-JDT!XmgX zZ`fNZbC@av6puUYR?W2Qm6F|OR9cU~)vyuR;oO;dtD~9MuW8q!l(s(zR|5wjS9pNW z#+PeSGe3~Yf1Nwrgikqh9Qz!1=s1<l zP9JHZ6du2amv4Hb&S^NMPYxKu-Ao_Aw(mqa-{W|$O(tE{)3?(8lrn-C_ehK{6Po!% zUZPf~QbaK`LN%N672o49fuEAnEHl4Go^zVXGMSG)s*Yg#|C#K!%V{=hfE_i# amzrW7j(^lB^N%h+;3{+OJ?0zeX5wPqA(>JD literal 0 HcmV?d00001 diff --git a/v1.4.3/search_index.js b/v1.4.3/search_index.js new file mode 100644 index 00000000..9b40f9f0 --- /dev/null +++ b/v1.4.3/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"interface/#interface","page":"Interface","title":"The ExponentialFamilyDistribution Interface","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.","category":"page"},{"location":"interface/#Notation","page":"Interface","title":"Notation","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the context of the package, exponential family distributions are represented in the form:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"f_X(xmideta) = h(x) cdot expleft eta cdot T(x) - A(eta) right","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Here:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"h(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the following discussion we also use the following convention","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"η corresponds to the distribution's natural parameters in the natural parameter space.\nθ corresponds to the distribution's mean parameters in the mean parameter space.","category":"page"},{"location":"interface/#ExponentialFamilyDistribution-structure","page":"Interface","title":"ExponentialFamilyDistribution structure","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamilyDistribution\nExponentialFamilyDistributionAttributes\nlogpdf(ef::ExponentialFamilyDistribution, x)\npdf(ef::ExponentialFamilyDistribution, x)\ncdf(ef::ExponentialFamilyDistribution{D}, x) where {D <: Distribution}\ngetnaturalparameters\ngetattributes\ngetconditioner\nisproper\ngetbasemeasure\ngetsufficientstatistics\ngetlogpartition\ngetgradlogpartition\ngetfisherinformation\ngetsupport\nbasemeasure\nsufficientstatistics\nlogpartition\ngradlogpartition\nfisherinformation\nisbasemeasureconstant\nConstantBaseMeasure\nNonConstantBaseMeasure\nExponentialFamily._logpdf\nExponentialFamily.check_logpdf\nExponentialFamily.PointBasedLogpdfCall\nExponentialFamily.MapBasedLogpdfCall","category":"page"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistribution","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistribution","text":"ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)\n\nExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.\n\nnote: Note\nThe attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.4.3/siteinfo.js b/v1.4.3/siteinfo.js new file mode 100644 index 00000000..2f6db034 --- /dev/null +++ b/v1.4.3/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.4.3"; diff --git a/v1.4.4/.documenter-siteinfo.json b/v1.4.4/.documenter-siteinfo.json new file mode 100644 index 00000000..8e78b42f --- /dev/null +++ b/v1.4.4/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-24T10:50:11","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/v1.4.4/assets/documenter.js b/v1.4.4/assets/documenter.js new file mode 100644 index 00000000..c6562b55 --- /dev/null +++ b/v1.4.4/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.4.4/assets/themes/documenter-dark.css b/v1.4.4/assets/themes/documenter-dark.css new file mode 100644 index 00000000..1d717015 --- /dev/null +++ b/v1.4.4/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons 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GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.4.4/index.html b/v1.4.4/index.html new file mode 100644 index 00000000..2e1342e9 --- /dev/null +++ b/v1.4.4/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.4.4/interface/index.html b/v1.4.4/interface/index.html new file mode 100644 index 00000000..175c7cc4 --- /dev/null +++ b/v1.4.4/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#422#423"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.4.4/library/index.html b/v1.4.4/library/index.html new file mode 100644 index 00000000..51f5dc78 --- /dev/null +++ b/v1.4.4/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
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In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.","category":"page"},{"location":"interface/#Notation","page":"Interface","title":"Notation","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the context of the package, exponential family distributions are represented in the form:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"f_X(xmideta) = h(x) cdot expleft eta cdot T(x) - A(eta) right","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Here:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"h(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In the following discussion we also use the following convention","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"η corresponds to the distribution's natural parameters in the natural parameter space.\nθ corresponds to the distribution's mean parameters in the mean parameter space.","category":"page"},{"location":"interface/#ExponentialFamilyDistribution-structure","page":"Interface","title":"ExponentialFamilyDistribution structure","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamilyDistribution\nExponentialFamilyDistributionAttributes\nlogpdf(ef::ExponentialFamilyDistribution, x)\npdf(ef::ExponentialFamilyDistribution, x)\ncdf(ef::ExponentialFamilyDistribution{D}, x) where {D <: Distribution}\ngetnaturalparameters\ngetattributes\ngetconditioner\nisproper\ngetbasemeasure\ngetsufficientstatistics\ngetlogpartition\ngetgradlogpartition\ngetfisherinformation\ngetsupport\nbasemeasure\nsufficientstatistics\nlogpartition\ngradlogpartition\nfisherinformation\nisbasemeasureconstant\nConstantBaseMeasure\nNonConstantBaseMeasure\nExponentialFamily._logpdf\nExponentialFamily.check_logpdf\nExponentialFamily.PointBasedLogpdfCall\nExponentialFamily.MapBasedLogpdfCall","category":"page"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistribution","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistribution","text":"ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)\n\nExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:\n\npₓ(x η) = h(x) exp η T(x) - A(η) \n\nHere:\n\nh(x) is the base measure.\nT(x) represents sufficient statistics.\nA(η) stands for the log partition.\nη denotes the natural parameters.\n\nFor a given member of exponential family: \n\ngetattributes returns either nothing or ExponentialFamilyDistributionAttributes.\ngetbasemeasure returns a positive a valued function. \ngetsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].\ngetnaturalparameters returns an iterable holding the values of the natural parameters. \ngetlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1. \ngetsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.\n\nnote: Note\nThe attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.\n\njulia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.4.4/siteinfo.js b/v1.4.4/siteinfo.js new file mode 100644 index 00000000..2cec5789 --- /dev/null +++ b/v1.4.4/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.4.4"; diff --git a/v1.5 b/v1.5 new file mode 120000 index 00000000..c9b3c015 --- /dev/null +++ b/v1.5 @@ -0,0 +1 @@ +v1.5.1 \ No newline at end of file diff --git a/v1.5.0/.documenter-siteinfo.json b/v1.5.0/.documenter-siteinfo.json new file mode 100644 index 00000000..55aa6671 --- /dev/null +++ b/v1.5.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-04T11:10:25","documenter_version":"1.5.0"}} \ No newline at end of file diff --git a/v1.5.0/assets/documenter.js b/v1.5.0/assets/documenter.js new file mode 100644 index 00000000..b2bdd43e --- /dev/null +++ b/v1.5.0/assets/documenter.js @@ -0,0 +1,1059 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 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+$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.5.0/assets/themes/catppuccin-frappe.css b/v1.5.0/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..54a5b77e --- /dev/null +++ b/v1.5.0/assets/themes/catppuccin-frappe.css @@ -0,0 +1 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.is-active.pagination-ellipsis,html.theme--catppuccin-frappe .is-active.file-cta,html.theme--catppuccin-frappe .is-active.file-name,html.theme--catppuccin-frappe .select select.is-active,html.theme--catppuccin-frappe .is-active.textarea,html.theme--catppuccin-frappe .is-active.input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--catppuccin-frappe .is-active.button{outline:none}html.theme--catppuccin-frappe .pagination-previous[disabled],html.theme--catppuccin-frappe .pagination-next[disabled],html.theme--catppuccin-frappe .pagination-link[disabled],html.theme--catppuccin-frappe .pagination-ellipsis[disabled],html.theme--catppuccin-frappe .file-cta[disabled],html.theme--catppuccin-frappe .file-name[disabled],html.theme--catppuccin-frappe .select select[disabled],html.theme--catppuccin-frappe .textarea[disabled],html.theme--catppuccin-frappe .input[disabled],html.theme--catppuccin-frappe #documenter .docs-sidebar 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kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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.button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe .image.is-3by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-frappe .image.is-5by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-frappe .image.is-16by9,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-frappe .image.is-2by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-frappe .image.is-3by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-frappe .image.is-4by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-frappe .image.is-3by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-frappe .image.is-2by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-frappe .image.is-3by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-frappe .image.is-9by16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-frappe .image.is-1by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-frappe .image.is-1by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-frappe .image.is-16x16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-frappe .image.is-24x24,html.theme--catppuccin-frappe #documenter 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kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte 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kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-hovered.docs-sourcelink{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-primary.is-inverted[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-loading::after,html.theme--catppuccin-latte 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#1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons 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.content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table 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.has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte .image.is-3by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-latte .image.is-4by5 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#documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-latte .image.is-9by16 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-latte .image.is-9by16 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-latte .image.is-1by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-latte .image.is-1by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-latte .image.is-1by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-latte .image.is-1by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-latte .image.is-square,html.theme--catppuccin-latte #documenter 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.navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte 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a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte 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.pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte 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rgba(10,10,10,0.25)}html.theme--catppuccin-macchiato .button.is-black:active,html.theme--catppuccin-macchiato .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff 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transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato 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.content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato 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.button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content h6{color:#cad3f5;font-weight:600;line-height:1.125}html.theme--catppuccin-macchiato .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-macchiato .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-macchiato .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-macchiato .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-macchiato .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-macchiato .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-macchiato .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-macchiato .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-macchiato .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-macchiato .content blockquote{background-color:#1e2030;border-left:5px solid #5b6078;padding:1.25em 1.5em}html.theme--catppuccin-macchiato .content 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rgba(10,10,10,0.25)}html.theme--catppuccin-mocha .button.is-black:active,html.theme--catppuccin-mocha .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light:hover,html.theme--catppuccin-mocha .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light:focus,html.theme--catppuccin-mocha .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light:focus:not(:active),html.theme--catppuccin-mocha .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-mocha .button.is-light:active,html.theme--catppuccin-mocha .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-mocha .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-dark,html.theme--catppuccin-mocha .content kbd.button{background-color:#313244;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:hover,html.theme--catppuccin-mocha .content kbd.button:hover,html.theme--catppuccin-mocha .button.is-dark.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus:not(:active),html.theme--catppuccin-mocha .content kbd.button:focus:not(:active),html.theme--catppuccin-mocha .button.is-dark.is-focused:not(:active),html.theme--catppuccin-mocha .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(49,50,68,0.25)}html.theme--catppuccin-mocha .button.is-dark:active,html.theme--catppuccin-mocha .content kbd.button:active,html.theme--catppuccin-mocha .button.is-dark.is-active,html.theme--catppuccin-mocha .content kbd.button.is-active{background-color:#262735;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark[disabled],html.theme--catppuccin-mocha .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button{background-color:#313244;border-color:#313244;box-shadow:none}html.theme--catppuccin-mocha .button.is-dark.is-inverted,html.theme--catppuccin-mocha .content kbd.button.is-inverted{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-dark.is-inverted[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-focused{background-color:#313244;border-color:#313244;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-dark.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-outlined{background-color:transparent;border-color:#313244;box-shadow:none;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-primary,html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink{background-color:#89b4fa;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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rgba(137,180,250,0.25)}html.theme--catppuccin-mocha .button.is-primary:active,html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink:active,html.theme--catppuccin-mocha .button.is-primary.is-active,html.theme--catppuccin-mocha .docstring>section>a.button.is-active.docs-sourcelink{background-color:#71a4f9;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-primary[disabled],html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-primary,fieldset[disabled] html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink{background-color:#89b4fa;border-color:#89b4fa;box-shadow:none}html.theme--catppuccin-mocha .button.is-primary.is-inverted,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#89b4fa}html.theme--catppuccin-mocha .button.is-primary.is-inverted:hover,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-hovered.docs-sourcelink{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-primary.is-inverted[disabled],html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-primary.is-inverted,fieldset[disabled] html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#89b4fa}html.theme--catppuccin-mocha .button.is-primary.is-loading::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-primary.is-outlined,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#89b4fa;color:#89b4fa}html.theme--catppuccin-mocha .button.is-primary.is-outlined:hover,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-mocha .button.is-primary.is-outlined:focus,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#89b4fa;border-color:#89b4fa;color:#fff}html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-loading::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #89b4fa #89b4fa !important}html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-mocha .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff 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.docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.is-focused.docs-sourcelink{background-color:#fff;color:#89b4fa}html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #89b4fa #89b4fa !important}html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha 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.button.is-link.is-outlined.is-focused{background-color:#89b4fa;border-color:#89b4fa;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #89b4fa #89b4fa !important}html.theme--catppuccin-mocha .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-link.is-outlined{background-color:transparent;border-color:#89b4fa;box-shadow:none;color:#89b4fa}html.theme--catppuccin-mocha 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha 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.button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha 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.button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table 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html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content 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html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content 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.button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 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.button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v1.5.0/assets/themeswap.js b/v1.5.0/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/v1.5.0/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v1.5.0/assets/warner.js b/v1.5.0/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/v1.5.0/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v1.5.0/examples/index.html b/v1.5.0/examples/index.html new file mode 100644 index 00000000..7c547214 --- /dev/null +++ b/v1.5.0/examples/index.html @@ -0,0 +1,48 @@ + +Examples · ExponentialFamily.jl
GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.5.0/index.html b/v1.5.0/index.html new file mode 100644 index 00000000..200cefda --- /dev/null +++ b/v1.5.0/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.5.0/interface/index.html b/v1.5.0/interface/index.html new file mode 100644 index 00000000..2ab9c710 --- /dev/null +++ b/v1.5.0/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

Optionally

  • logbasemeasure::LB: The log of the basemeasure of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getlogbasemeasure — Function
getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])

A generic verion of getlogbasemeasure defined particularly for distribution types from Distributions.jl package. Just computes log of basemeasure.

source
getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])

A generic verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. For conditional exponential family distributions requires an extra conditioner argument. Just computes log of basemeasure.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#440#441"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.5.0/library/index.html b/v1.5.0/library/index.html new file mode 100644 index 00000000..199741a1 --- /dev/null +++ b/v1.5.0/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
source
ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

source
ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

source
ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
source
ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
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getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nOptionally\n\nlogbasemeasure::LB: The log of the basemeasure of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogbasemeasure","page":"Interface","title":"ExponentialFamily.getlogbasemeasure","text":"getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getlogbasemeasure defined particularly for distribution types from Distributions.jl package. Just computes log of basemeasure.\n\n\n\n\n\ngetlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. For conditional exponential family distributions requires an extra conditioner argument. Just computes log of basemeasure.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logbasemeasure","page":"Interface","title":"ExponentialFamily.logbasemeasure","text":"logbasemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of log(basemeasure) of the exponential family distribution at the point x.\n\nSee also basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.5.0/siteinfo.js b/v1.5.0/siteinfo.js new file mode 100644 index 00000000..4f155ae3 --- /dev/null +++ b/v1.5.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.5.0"; diff --git a/v1.5.1/.documenter-siteinfo.json b/v1.5.1/.documenter-siteinfo.json new file mode 100644 index 00000000..3e493771 --- /dev/null +++ b/v1.5.1/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-24T14:11:00","documenter_version":"1.5.0"}} \ No newline at end of file diff --git a/v1.5.1/assets/documenter.js b/v1.5.1/assets/documenter.js new file mode 100644 index 00000000..b2bdd43e --- /dev/null +++ b/v1.5.1/assets/documenter.js @@ -0,0 +1,1059 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.5.1/assets/themes/catppuccin-frappe.css b/v1.5.1/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..54a5b77e --- /dev/null +++ b/v1.5.1/assets/themes/catppuccin-frappe.css @@ -0,0 +1 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.button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:hover,html.theme--catppuccin-frappe .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus,html.theme--catppuccin-frappe .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus:not(:active),html.theme--catppuccin-frappe .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-frappe .button.is-light:active,html.theme--catppuccin-frappe .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe 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.button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe 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kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe 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!important}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:hover,html.theme--catppuccin-frappe .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-primary:focus,html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe 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.button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-white.is-outlined:hover,html.theme--catppuccin-latte .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-white.is-outlined:focus,html.theme--catppuccin-latte .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:hover,html.theme--catppuccin-latte .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus:not(:active),html.theme--catppuccin-latte .content kbd.button:focus:not(:active),html.theme--catppuccin-latte .button.is-dark.is-focused:not(:active),html.theme--catppuccin-latte .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(204,208,218,0.25)}html.theme--catppuccin-latte .button.is-dark:active,html.theme--catppuccin-latte .content kbd.button:active,html.theme--catppuccin-latte .button.is-dark.is-active,html.theme--catppuccin-latte .content kbd.button.is-active{background-color:#bdc2cf;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark[disabled],html.theme--catppuccin-latte .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:#ccd0da;box-shadow:none}html.theme--catppuccin-latte .button.is-dark.is-inverted,html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-latte 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.button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte 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.file.is-link.is-active .file-cta{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info .file-cta{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:hover .file-cta,html.theme--catppuccin-latte .file.is-info.is-hovered .file-cta{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:focus .file-cta,html.theme--catppuccin-latte .file.is-info.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(23,146,153,0.25);color:#fff}html.theme--catppuccin-latte .file.is-info:active .file-cta,html.theme--catppuccin-latte .file.is-info.is-active .file-cta{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success .file-cta{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:hover .file-cta,html.theme--catppuccin-latte .file.is-success.is-hovered .file-cta{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:focus .file-cta,html.theme--catppuccin-latte .file.is-success.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(64,160,43,0.25);color:#fff}html.theme--catppuccin-latte .file.is-success:active .file-cta,html.theme--catppuccin-latte .file.is-success.is-active .file-cta{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning .file-cta{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:hover .file-cta,html.theme--catppuccin-latte .file.is-warning.is-hovered .file-cta{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:focus .file-cta,html.theme--catppuccin-latte .file.is-warning.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(223,142,29,0.25);color:#fff}html.theme--catppuccin-latte .file.is-warning:active .file-cta,html.theme--catppuccin-latte .file.is-warning.is-active .file-cta{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger .file-cta{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:hover .file-cta,html.theme--catppuccin-latte .file.is-danger.is-hovered .file-cta{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:focus .file-cta,html.theme--catppuccin-latte .file.is-danger.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(210,15,57,0.25);color:#fff}html.theme--catppuccin-latte .file.is-danger:active .file-cta,html.theme--catppuccin-latte .file.is-danger.is-active .file-cta{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:not(:last-child){margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field.is-horizontal{display:flex}}html.theme--catppuccin-latte .field-label .label{font-size:inherit}@media screen and (max-width: 768px){html.theme--catppuccin-latte .field-label{margin-bottom:0.5rem}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-label{flex-basis:0;flex-grow:1;flex-shrink:0;margin-right:1.5rem;text-align:right}html.theme--catppuccin-latte .field-label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.field-label{font-size:.75rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-normal{padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-medium{font-size:1.25rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-large{font-size:1.5rem;padding-top:0.375em}}html.theme--catppuccin-latte .field-body .field 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.navbar{background-color:#1e66f5;min-height:4rem;position:relative;z-index:30}html.theme--catppuccin-latte .navbar.is-white{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-brand>.navbar-item,html.theme--catppuccin-latte .navbar.is-white .navbar-brand .navbar-link{color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-brand>a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-brand>a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-brand>a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-white .navbar-brand .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-brand .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-brand .navbar-link.is-active{background-color:#f2f2f2;color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-brand .navbar-link::after{border-color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-burger{color:#0a0a0a}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .navbar.is-white .navbar-start>.navbar-item,html.theme--catppuccin-latte .navbar.is-white .navbar-start .navbar-link,html.theme--catppuccin-latte .navbar.is-white .navbar-end>.navbar-item,html.theme--catppuccin-latte .navbar.is-white .navbar-end .navbar-link{color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-start>a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-start>a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-start>a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-white .navbar-start .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-start .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-start .navbar-link.is-active,html.theme--catppuccin-latte .navbar.is-white .navbar-end>a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-end>a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-end>a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-white .navbar-end .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-white .navbar-end .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-white .navbar-end .navbar-link.is-active{background-color:#f2f2f2;color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-start .navbar-link::after,html.theme--catppuccin-latte .navbar.is-white .navbar-end .navbar-link::after{border-color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link{background-color:#f2f2f2;color:#0a0a0a}html.theme--catppuccin-latte .navbar.is-white .navbar-dropdown a.navbar-item.is-active{background-color:#fff;color:#0a0a0a}}html.theme--catppuccin-latte .navbar.is-black{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .navbar.is-black .navbar-brand>.navbar-item,html.theme--catppuccin-latte .navbar.is-black .navbar-brand .navbar-link{color:#fff}html.theme--catppuccin-latte .navbar.is-black .navbar-brand>a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-black .navbar-brand>a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-black .navbar-brand>a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-black .navbar-brand .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-black .navbar-brand .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-black .navbar-brand .navbar-link.is-active{background-color:#000;color:#fff}html.theme--catppuccin-latte .navbar.is-black .navbar-brand .navbar-link::after{border-color:#fff}html.theme--catppuccin-latte .navbar.is-black .navbar-burger{color:#fff}@media 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.navbar.is-light{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .navbar.is-light .navbar-brand>.navbar-item,html.theme--catppuccin-latte .navbar.is-light .navbar-brand .navbar-link{color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .navbar.is-light .navbar-brand>a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-light .navbar-brand>a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-light .navbar-brand>a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-light .navbar-brand .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-light .navbar-brand .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-light .navbar-brand .navbar-link.is-active{background-color:#e8e8e8;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .navbar.is-light .navbar-brand .navbar-link::after{border-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .navbar.is-light .navbar-burger{color:rgba(0,0,0,0.7)}@media screen and (min-width: 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.navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte 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.navbar-dropdown.is-boxed,.navbar.is-spaced html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown,html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed{opacity:1;pointer-events:auto;transform:translateY(0)}html.theme--catppuccin-latte .navbar-menu{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .navbar-start{justify-content:flex-start;margin-right:auto}html.theme--catppuccin-latte .navbar-end{justify-content:flex-end;margin-left:auto}html.theme--catppuccin-latte .navbar-dropdown{background-color:#1e66f5;border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid rgba(0,0,0,0.2);box-shadow:0 8px 8px rgba(10,10,10,0.1);display:none;font-size:0.875rem;left:0;min-width:100%;position:absolute;top:100%;z-index:20}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding:0.375rem 1rem;white-space:nowrap}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar 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body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte .pagination.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-latte .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-latte .pagination.is-rounded .pagination-previous,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-latte .pagination.is-rounded .pagination-next,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-latte .pagination.is-rounded .pagination-link,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-latte .pagination,html.theme--catppuccin-latte .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte .pagination-previous:active,html.theme--catppuccin-latte .pagination-next:active,html.theme--catppuccin-latte .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--catppuccin-latte .pagination-previous[disabled],html.theme--catppuccin-latte .pagination-previous.is-disabled,html.theme--catppuccin-latte .pagination-next[disabled],html.theme--catppuccin-latte .pagination-next.is-disabled,html.theme--catppuccin-latte .pagination-link[disabled],html.theme--catppuccin-latte .pagination-link.is-disabled{background-color:#acb0be;border-color:#acb0be;box-shadow:none;color:#616587;opacity:0.5}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{padding-left:.75em;padding-right:.75em;white-space:nowrap}html.theme--catppuccin-latte .pagination-link.is-current{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .pagination-ellipsis{color:#9ca0b0;pointer-events:none}html.theme--catppuccin-latte .pagination-list{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-list li{list-style:none}@media screen and (max-width: 768px){html.theme--catppuccin-latte .pagination{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination-previous{order:2}html.theme--catppuccin-latte .pagination-next{order:3}html.theme--catppuccin-latte .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-latte 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.panel-heading{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-tabs a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-latte .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-latte .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-latte .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-latte .panel.is-dark .panel-heading,html.theme--catppuccin-latte .content kbd.panel .panel-heading{background-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-latte .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#ccd0da}html.theme--catppuccin-latte .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .content 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.panel-heading{background-color:#179299;color:#fff}html.theme--catppuccin-latte .panel.is-info .panel-tabs a.is-active{border-bottom-color:#179299}html.theme--catppuccin-latte .panel.is-info .panel-block.is-active .panel-icon{color:#179299}html.theme--catppuccin-latte .panel.is-success .panel-heading{background-color:#40a02b;color:#fff}html.theme--catppuccin-latte .panel.is-success .panel-tabs a.is-active{border-bottom-color:#40a02b}html.theme--catppuccin-latte .panel.is-success .panel-block.is-active .panel-icon{color:#40a02b}html.theme--catppuccin-latte .panel.is-warning .panel-heading{background-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .panel.is-warning .panel-tabs a.is-active{border-bottom-color:#df8e1d}html.theme--catppuccin-latte .panel.is-warning .panel-block.is-active .panel-icon{color:#df8e1d}html.theme--catppuccin-latte .panel.is-danger .panel-heading{background-color:#d20f39;color:#fff}html.theme--catppuccin-latte .panel.is-danger .panel-tabs 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kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small 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.container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content 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ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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.button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;box-shadow:none;color:#375a7f}html.theme--documenter-dark 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.button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark 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.button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#effded;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark 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rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 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.buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 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.docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar 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GitHub

Examples

Product of two probability distributions over the same variable

In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable "X". This operation results in another probability distribution, also centered around the variable "X". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as "X" and "Y", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.

\[p(X\vert D) \propto \underbrace{p(X)p(D|X)}_{\mathrm{product~of~two~distributions}}\]

To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:

using ExponentialFamily, Distributions, BayesBase
+
+prior = Bernoulli(0.5)
+likelihood = Bernoulli(0.6)
+
+posterior = prod(PreserveTypeProd(Distribution), prior, likelihood)
Bernoulli{Float64}(p=0.6)

You can achieve the same result in the general exponential family form, which operates within the natural parameter space:

ef_prior = convert(ExponentialFamilyDistribution, prior)
+ef_likelihood = convert(ExponentialFamilyDistribution, likelihood)
+
+ef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)
ExponentialFamily(Bernoulli)

Or even more concisely:

prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Bernoulli)

In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:

prior = Laplace(2.0, 3.0)
+likelihood = Laplace(1.0, 4.0)
+
+prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)
ExponentialFamily(Univariate)

Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.

Computing various useful attributes of an exponential family member

The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member "tag," such as Normal or Bernoulli. Here are some examples of how to use these attributes:

using ExponentialFamily, Distributions
+
+# Returns a function
+basemeasure_of_normal = getbasemeasure(Normal)
+
+basemeasure_of_normal(0.0)
0.3989422804014327
# Returns an iterable of functions
+sufficientstatistics_of_gamma = getsufficientstatistics(Gamma)
+
+map(f -> f(1.0), sufficientstatistics_of_gamma)
(0.0, 1.0)

Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:

laplace = Laplace(2.0, 1.0)
+
+canonical = convert(ExponentialFamilyDistribution, laplace)
+
+getconditioner(canonical)
2.0
# For conditioned distributions, the `conditioner` must be present as a second argument
+basemeasure_of_laplace = getbasemeasure(Laplace, 2.0)
+
+basemeasure_of_laplace(1.0)
1.0

The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:

logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)
+
+gamma_parameters_in_mean_space = [ 1.0, 2.0 ]
+
+logpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
0.6931471805599453
logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)
+
+gamma_parameters_in_natural_space = map(
+    MeanParametersSpace() => NaturalParametersSpace(),
+    Gamma,
+    gamma_parameters_in_mean_space
+)
+
+logparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
0.6931471805599453

The same principle applies to the Fisher information matrix:

fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  0.5
+ 0.5      0.25
fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)
+
+fisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)
2×2 StaticArraysCore.SMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
+ 1.64493  2.0
+ 2.0      4.0

Approximating attributes

Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.

diff --git a/v1.5.1/index.html b/v1.5.1/index.html new file mode 100644 index 00000000..e19286b0 --- /dev/null +++ b/v1.5.1/index.html @@ -0,0 +1,2 @@ + +Home · ExponentialFamily.jl
GitHub

ExponentialFamily.jl

Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.

Core Principles

The package is built around several core principles:

  • High performance with minimal allocations, striving for complete type stability.
  • Compatibility with distributions defined in Distributions.jl.
  • Ease of use and rich functionality.

Table of Contents

Index

diff --git a/v1.5.1/interface/index.html b/v1.5.1/interface/index.html new file mode 100644 index 00000000..3156a047 --- /dev/null +++ b/v1.5.1/interface/index.html @@ -0,0 +1,75 @@ + +Interface · ExponentialFamily.jl
GitHub

The ExponentialFamilyDistribution Interface

This page describes the philosophy and design concepts behind the ExponentialFamilyDistribution interface. In a nutshell, the primary purpose of the ExponentialFamily package is to provide a generic interface for an ExponentialFamilyDistribution. It is beneficial to become familiar with the Wikipedia article on the exponential family before delving into the implementation details of this package.

Notation

In the context of the package, exponential family distributions are represented in the form:

\[f_X(x\mid\eta) = h(x) \cdot \exp\left[ \eta \cdot T(x) - A(\eta) \right]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

In the following discussion we also use the following convention

  • η corresponds to the distribution's natural parameters in the natural parameter space.
  • θ corresponds to the distribution's mean parameters in the mean parameter space.

ExponentialFamilyDistribution structure

ExponentialFamily.ExponentialFamilyDistribution — Type
ExponentialFamilyDistribution(::Type{T}, naturalparameters, conditioner, attributes)

ExponentialFamilyDistribution structure represents a generic exponential family distribution in natural parameterization. Type T can be either a distribution type (e.g. from the Distributions.jl package) or a variate type (e.g. Univariate). In the context of the package, exponential family distributions are represented in the form:

\[pₓ(x ∣ η) = h(x) ⋅ exp[ η ⋅ T(x) - A(η) ]\]

Here:

  • h(x) is the base measure.
  • T(x) represents sufficient statistics.
  • A(η) stands for the log partition.
  • η denotes the natural parameters.

For a given member of exponential family:

  • getattributes returns either nothing or ExponentialFamilyDistributionAttributes.
  • getbasemeasure returns a positive a valued function.
  • getsufficientstatistics returns an iterable of functions such as [x, x^2] or [x, logx].
  • getnaturalparameters returns an iterable holding the values of the natural parameters.
  • getlogpartition return a function that depends on the naturalparameters and it ensures that the distribution is normalized to 1.
  • getsupport returns the set that the distribution is defined over. Could be real numbers, positive integers, 3d cube etc. Use ither the ∈ operator or the insupport() function to check if a value belongs to the support.
Note

The attributes can be nothing. In which case the package will try to derive the corresponding attributes from the type T.

julia> ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))
+ExponentialFamily(Bernoulli)
+
+julia> getsufficientstatistics(ef)
+(identity,)
julia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))
+ExponentialFamily(Laplace, conditioned on 1.0)
+
+julia> logpdf(ef, 4.0)
+-6.0

See also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport

source
ExponentialFamily.ExponentialFamilyDistributionAttributes — Type
ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)

A structure to represent the attributes of an exponential family member.

Fields

  • basemeasure::B: The basemeasure of the exponential family member.
  • sufficientstatistics::S: The sufficient statistics of the exponential family member.
  • logpartition::L: The log-partition (cumulant) of the exponential family member.
  • support::P: The support of the exponential family member.

Optionally

  • logbasemeasure::LB: The log of the basemeasure of the exponential family member.

See also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport

source
Distributions.logpdf — Method
logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

source
Distributions.pdf — Method
pdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the probability density function of the exponential family distribution for the input x.

source
Distributions.cdf — Method
cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }

Evaluates and returns the cumulative distribution function of the exponential family distribution for the input x.

source
ExponentialFamily.getconditioner — Function
getconditioner(::ExponentialFamilyDistribution)

Returns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.

source
ExponentialFamily.isproper — Function
isproper(::ExponentialFamilyDistribution)

Checks if the object of type ExponentialFamilyDistribution is a proper distribution.

source
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Function
getbasemeasure(::ExponentialFamilyDistribution)
+getbasemeasure(::Type{ <: Distribution }, [ conditioner ])

Returns the base measure function of the exponential family distribution.

source
ExponentialFamily.getlogbasemeasure — Function
getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])

A generic verion of getlogbasemeasure defined particularly for distribution types from Distributions.jl package. Just computes log of basemeasure.

source
getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])

A generic verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. For conditional exponential family distributions requires an extra conditioner argument. Just computes log of basemeasure.

source
ExponentialFamily.getsufficientstatistics — Function
getsufficientstatistics(::ExponentialFamilyDistribution)
+getsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])

Returns the list of sufficient statistics of the exponential family distribution.

source
ExponentialFamily.getlogpartition — Function
getlogpartition(::ExponentialFamilyDistribution)
+getlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the log partition function of the exponential family distribution.

source
ExponentialFamily.getgradlogpartition — Function
getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getfisherinformation — Function
getfisherinformation(::ExponentialFamilyDistribution)
+getfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])

Returns the function that computes the fisher information matrix of the exponential family distribution.

source
ExponentialFamily.logpartition — Function
logpartition(::ExponentialFamilyDistribution, η)

Return the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).

See also: getlogpartition

source
ExponentialFamily.isbasemeasureconstant — Function
isbasemeasureconstant(something)

Returns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.

See also: getbasemeasure, basemeasure

source
ExponentialFamily._logpdf — Function
_logpdf(ef::ExponentialFamilyDistribution, x)

Evaluates and returns the log-density of the exponential family distribution for the input x.

This inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.

For instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.

Examples

Evaluate the log-density of a Gamma distribution at a single point:

using ExponentialFamily, Distributions;
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, 1.0)
+# output
+-1.0

Evaluate the log-density of a Gamma distribution at multiple points:

using ExponentialFamily, Distributions
+gamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))
+ExponentialFamily._logpdf(gamma, [1, 2, 3])
+# output
+3-element Vector{Float64}:
+ -1.0
+ -2.0
+ -3.0

For details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.

See also: check_logpdf

source
ExponentialFamily.check_logpdf — Function
check_logpdf(variate_form, typeof(x), eltype(x), ef, x)

Determines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.

Strategies

  • For a Univariate distribution:

    • If x is a Number, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().

  • For a Multivariate distribution:

    • If x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().
    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).

  • For a Matrixvariate distribution:

    • If x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().
    • If x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().

Examples

using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)
+# output
+(ExponentialFamily.PointBasedLogpdfCall(), 1.0)
using ExponentialFamily
+ExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])
+# output
+(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])

See also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall

source

Interfacing with Distributions Defined in the Distributions.jl Package

The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.

Conversion between Mean Parameters Space and Natural Parameters Space

The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:

using Distributions, ExponentialFamily
+
+distribution = Bernoulli(0.25)
+
+tuple_of_θ = params(distribution)
(0.25,)

These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:

To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:

tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)
(-1.0986122886681098,)

And to convert back:

tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)
(0.25,)

Alternatuvely, the following API is supported 

map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)
(-1.0986122886681098,)
map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)
(0.25,)

While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.

ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Note on the conditioned distributions

For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.

ExponentialFamily.separate_conditioner — Function
separate_conditioner(::Type{T}, params) where {T <: Distribution}

Separates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.join_conditioner

source
ExponentialFamily.join_conditioner — Function
join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }

Joins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.

julia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))
+((1.0,), 0.0)
+
+julia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)
+(0.0, 1.0)
+
+julia> Laplace(params...) == Laplace(0.0, 1.0)
+true

See also: ExponentialFamily.separate_conditioner

source

For example, Laplace distribution defines the functions in the following way

# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)
+# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace
+# Hence, we return a tuple of tuple of actual parameter and the conditioner
+function separate_conditioner(::Type{Laplace}, params)
+    location, scale = params
+    return ((scale, ), location)
+end
+
+# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible 
+# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.
+function join_conditioner(::Type{Laplace}, cparams, conditioner) 
+    (scale, ) = cparams
+    location = conditioner
+    return (location, scale)
+end

In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the "conditioned" versions of such functions by explicitly requiring the conditioner parameter, e.g.

getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`
(ExponentialFamily.var"#440#441"{Float64}(1.0),)

Efficient packing of the natural parameters into a vectorized form

The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.

ExponentialFamily.flatten_parameters — Function
flatten_parameters(::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.

source
ExponentialFamily.pack_parameters — Function
pack_parameters([ space ], ::Type{T}, params::Tuple)

This function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

julia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))
+9-element Vector{Float64}:
+ 1.0
+ 2.0
+ 3.0
+ 4.0
+ 7.0
+ 5.0
+ 8.0
+ 6.0
+ 9.0
source
ExponentialFamily.unpack_parameters — Function
unpack_parameters([ space ], ::Type{T}, parameters)

This function "unpack" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.

See also: MeanParametersSpace, NaturalParametersSpace

source

These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.

Attributes of the exponential family distribution based on Distribution

The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:

basemeasure_of_bernoilli = getbasemeasure(Bernoulli)
+
+basemeasure_of_bernoilli(0)
1
ExponentialFamily.isproper — Method
isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }

A specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getbasemeasure — Method
getbasemeasure(::Type{<:Distribution}, [ conditioner ])

A specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getsufficientstatistics — Method
getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])

A specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.

source
ExponentialFamily.getlogpartition — Method
getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }

A specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source
ExponentialFamily.getfisherinformation — Method
getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }

A specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.

See also: NaturalParametersSpace, MeanParametersSpace

source

Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.

getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)
true
ExponentialFamily.NaturalParametersSpace — Type
NaturalParametersSpace

Specifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.

See also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural

source
ExponentialFamily.MeanParametersSpace — Type
MeanParametersSpace

Specifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.

See also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural

source

The isbasemeasureconstant function is defined for all supported distributions as well.

isbasemeasureconstant(Bernoulli)
ConstantBaseMeasure()

Extra defined distributions

The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.

diff --git a/v1.5.1/library/index.html b/v1.5.1/library/index.html new file mode 100644 index 00000000..a59ed822 --- /dev/null +++ b/v1.5.1/library/index.html @@ -0,0 +1,2 @@ + +Library · ExponentialFamily.jl
GitHub

Library API

Additional distributions

These are the distributions that are not included in the Distributions.jl package.

ExponentialFamily.MatrixDirichlet — Type
MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

A matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.

Fields

  • a::A: The matrix parameter of the MatrixDirichlet distribution.
source
ExponentialFamily.GammaShapeRate — Type
GammaShapeRate{T <: Real}

A univariate gamma distribution parametrized by its shape a and rate b.

Fields

  • a: The shape parameter of the gamma distribution. It should be a positive real number.
  • b: The rate parameter of the gamma distribution. It should be a positive real number.
source
ExponentialFamily.GammaShapeScale — Type
GammaShapeScale{T}

A continuous univariate gamma distribution parametrized by its shape α and scale β parameters.

Fields

  • α: The shape parameter of the gamma distribution. It should be a positive real number.
  • β: The scale parameter of the gamma distribution. It should be a positive real number.

Note

  • GammaShapeScale is an alias for Gamma from Distributions.jl.
source
ExponentialFamily.NormalMeanPrecision — Type
NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and precision w.

Fields

  • μ::T: The mean of the normal distribution.
  • w::T: The precision of the normal distribution.
source
ExponentialFamily.NormalMeanVariance — Type
NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution with a known mean μ and variance v.

Fields

  • μ::T: The mean of the normal distribution.
  • v::T: The variance of the normal distribution.
source
ExponentialFamily.NormalWeightedMeanPrecision — Type
NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution

A normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.

Fields

  • xi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.
  • w::T: The precision (inverse variance) of the normal distribution.
source
ExponentialFamily.MvNormalMeanPrecision — Type
MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
source
ExponentialFamily.MvNormalMeanCovariance — Type
MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Σ::P: The covariance matrix of the multivariate normal distribution
source
ExponentialFamily.MvNormalWeightedMeanPrecision — Type
MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal

A multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.

Fields

  • xi::M: The weighted mean vector of the multivariate normal distribution.
  • Λ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.
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ExponentialFamily.JointNormal — Type
JointNormal{D, S}

JointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.

Use ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.

Fields

  • dist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)
  • ds: a tuple with the original dimensionalities of individual Normal distributions
  • ds[k] = (n,) where n is an integer indicates Multivariate normal of size n
  • ds[k] = () indicates Univariate normal
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ExponentialFamily.WishartFast — Type
WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.

For model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the Wishart distribution.
  • invS::A: The inverse scale matrix parameter of the Wishart distribution.

Note

Internally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.

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ExponentialFamily.InverseWishartFast — Type
InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution

The InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages.

For model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.

Fields

  • ν::T: The degrees of freedom parameter of the inverse Wishart distribution.
  • S::A: The scale matrix parameter of the inverse Wishart distribution.

Note

The InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.

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ExponentialFamily.NormalGamma — Type
NormalGamma{T <: Real} <: ContinuousMultivariateDistribution

A normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.

Fields

  • μ::T: The mean of the normal distribution.
  • λ::T: The precision of the normal distribution.
  • α::T: The shape parameter of the gamma distribution.
  • β::T: The rate parameter of the gamma distribution.
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ExponentialFamily.MvNormalWishart — Type
MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution

A multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.

Fields

  • μ::M: The mean vector of the multivariate normal distribution.
  • Ψ::V: The scale matrix of the Wishart distribution.
  • κ::K: The scaling parameter of the Wishart distribution.
  • ν::N: The degrees of freedom of the Wishart distribution
source
diff --git a/v1.5.1/objects.inv b/v1.5.1/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..719995ff600d86c1f59c4067cf4ce3344537e9ee GIT binary patch literal 1429 zcmV;G1#0>uAX9K?X>NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGkKcyMoS zWo~q7VQfZWZE0+IE^2HFBOq2~a&u{KZaN?_E;TMO3L_v?Xk{RBWo=<;Ze(S0Aa78b#rNMXCQiPX<{x4c%02xO^@3)5WV|X5NLf1 zyJ>O=u;|6HH|ZAf!sxoqF`y;N;#MLBk=l<2``;MyX|*Ef&1mMm8PY8TP9-x% z4zXk`XDNr&XbQpg($AttbDLZSqWVxPAKW{;YJx|UvrE>8cJ(&<{Q_10@Fnp3fu?j@XTg)09cd5^5l%t(Uj>%Uwb@kaD)~ z%Yoy7pabGzkjeqr*qR+WAe94%v(}qi7CKvGS*{*M$}ImKPIeO7vv62ETX<^0&pja* zH+yu)G~@;zyqb3BV&O>!zxRY@To1&0An@RNK(26fi!laDmZgPAywdi>f%XWB5jge- z)L5#V(@id9AetuRCLh;HyAJ#1J&4REhMNb@C0%o9I-6G9w;)jtjVPoymGTc4d!laf zNrg`kpR^F9gaCX};U6u|j`WBuJLXldY$-ez0XXOjw_o@Tg5Ts%GPY^-SEz9sR+=1I zZEHm;tAiT5Q|MIRs3s9vY_6L?Dd;DJ;JX9fR2z`w4~oG49ovaS7@yss0w}0up@t&a z0fT+^M2*%gdyi81r1n`DEm@L~yX4Y5Wt-PB-sh$AS{tL}D zhRO2$Odetmsowr}=_w!l!?(mL^y44tfBx>h^^1S!?^g3S%lVtv%^QftTc~2f|MAsp z8yOnR-!A8G7hZg)QW3-)%8*#`j4grByqC=0k=vI|+M2=o<4WWrh!bvx6R(gHS#Jf} zSeHX_M7u-tt*R&J2*WcO(myH31nxA+Ga3{|&vGMbw`0CRXoqcZrUJc6GZy699&q?) zp<{^S1Jj+P@z2R++G#1J-fX@i3;FcirJ`a47G}aME)OGT6Ls1_2Ao&d>hrskJptUtEaQJNGh!ZB4QWDSgXr7q zPJVvew*gB=1m1AJ)b%h;2OvFnR<4>^*(*f54>ev7(ABU3+Tq-pn5(0S+20Xdi?T8J zV{|oej0z3+hirVgCXIpvk^R@H#ZCB>6U(vBaYvR@c^-OP>8<9%Yq~@AcB9~~QjS8r zeXZM`GZf(uyt#d3h1PI*A6~xcZ9Zq=lrB49gm*K20NcJ3<$RChxi*<}RZrh4`%BIU zV%z~SzD#K56L|?*ok|hSafBK^ ef = convert(ExponentialFamilyDistribution, Bernoulli(0.5))\nExponentialFamily(Bernoulli)\n\njulia> getsufficientstatistics(ef)\n(identity,)\n\njulia> ef = convert(ExponentialFamilyDistribution, Laplace(1.0, 0.5))\nExponentialFamily(Laplace, conditioned on 1.0)\n\njulia> logpdf(ef, 4.0)\n-6.0\n\nSee also: getbasemeasure, getsufficientstatistics, getnaturalparameters, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.ExponentialFamilyDistributionAttributes","page":"Interface","title":"ExponentialFamily.ExponentialFamilyDistributionAttributes","text":"ExponentialFamilyDistributionAttributes(basemeasure, sufficientstatistics, logpartition, support)\n\nA structure to represent the attributes of an exponential family member.\n\nFields\n\nbasemeasure::B: The basemeasure of the exponential family member.\nsufficientstatistics::S: The sufficient statistics of the exponential family member.\nlogpartition::L: The log-partition (cumulant) of the exponential family member.\nsupport::P: The support of the exponential family member.\n\nOptionally\n\nlogbasemeasure::LB: The log of the basemeasure of the exponential family member.\n\nSee also: ExponentialFamilyDistribution, getbasemeasure, getsufficientstatistics, getlogpartition, getsupport\n\n\n\n\n\n","category":"type"},{"location":"interface/#Distributions.logpdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.logpdf","text":"logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.pdf-Tuple{ExponentialFamilyDistribution, Any}","page":"Interface","title":"Distributions.pdf","text":"pdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the probability density function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#Distributions.cdf-Union{Tuple{D}, Tuple{ExponentialFamilyDistribution{D}, Any}} where D<:Distribution","page":"Interface","title":"Distributions.cdf","text":"cdf(ef::ExponentialFamilyDistribution{D}, x) where { D <: Distribution }\n\nEvaluates and returns the cumulative distribution function of the exponential family distribution for the input x.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getnaturalparameters","page":"Interface","title":"ExponentialFamily.getnaturalparameters","text":"getnaturalparameters(::ExponentialFamilyDistribution)\n\nGet the natural parameters of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getattributes","page":"Interface","title":"ExponentialFamily.getattributes","text":"getattributes(::ExponentialFamilyDistribution)\n\nReturns iether the attributes of the exponential family member or nothing. \n\nSee also: ExponentialFamilyDistributionAttributes\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getconditioner","page":"Interface","title":"ExponentialFamily.getconditioner","text":"getconditioner(::ExponentialFamilyDistribution)\n\nReturns either the conditioner of the exponential family distribution or nothing. conditioner is a fixed parameter that is used to ensure that the distribution belongs to the exponential family.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isproper","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper(::ExponentialFamilyDistribution)\n\nChecks if the object of type ExponentialFamilyDistribution is a proper distribution.\n\n\n\n\n\nisproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getbasemeasure","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::ExponentialFamilyDistribution)\ngetbasemeasure(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the base measure function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogbasemeasure","page":"Interface","title":"ExponentialFamily.getlogbasemeasure","text":"getlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getlogbasemeasure defined particularly for distribution types from Distributions.jl package. Just computes log of basemeasure.\n\n\n\n\n\ngetlogbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA generic verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. For conditional exponential family distributions requires an extra conditioner argument. Just computes log of basemeasure.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsufficientstatistics","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::ExponentialFamilyDistribution)\ngetsufficientstatistics(::Type{ <: Distribution }, [ conditioner ])\n\nReturns the list of sufficient statistics of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getlogpartition","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition(::ExponentialFamilyDistribution)\ngetlogpartition([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the log partition function of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getgradlogpartition","page":"Interface","title":"ExponentialFamily.getgradlogpartition","text":"getgradlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getgradlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getfisherinformation","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation(::ExponentialFamilyDistribution)\ngetfisherinformation([ space ], ::Type{ <: Distribution }, [ conditioner ])\n\nReturns the function that computes the fisher information matrix of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.getsupport","page":"Interface","title":"ExponentialFamily.getsupport","text":"getsupport(distribution_or_type)\n\nReturns the support of the exponential family distribution.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.basemeasure","page":"Interface","title":"ExponentialFamily.basemeasure","text":"basemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of basemeasure of the exponential family distribution at the point x.\n\nSee also: getbasemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logbasemeasure","page":"Interface","title":"ExponentialFamily.logbasemeasure","text":"logbasemeasure(::ExponentialFamilyDistribution, x)\n\nReturns the computed value of log(basemeasure) of the exponential family distribution at the point x.\n\nSee also basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.sufficientstatistics","page":"Interface","title":"ExponentialFamily.sufficientstatistics","text":"sufficientstatistics(::ExponentialFamilyDistribution)\n\nReturns the computed values of sufficientstatistics of the exponential family distribution at the point x.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.logpartition","page":"Interface","title":"ExponentialFamily.logpartition","text":"logpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of logpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.gradlogpartition","page":"Interface","title":"ExponentialFamily.gradlogpartition","text":"gradlogpartition(::ExponentialFamilyDistribution, η)\n\nReturn the computed value of gradlogpartition of the exponential family distribution at the point η. By default η = getnaturalparameters(ef).\n\nSee also: getgradlogpartition\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.fisherinformation","page":"Interface","title":"ExponentialFamily.fisherinformation","text":"fisherinformation(distribution, η)\n\nReturn the computed value of fisherinformation of the exponential family distribution at the point η By default η = getnaturalparameters(ef).\n\nSee also: getfisherinformation\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.isbasemeasureconstant","page":"Interface","title":"ExponentialFamily.isbasemeasureconstant","text":"isbasemeasureconstant(something)\n\nReturns either NonConstantBaseMeasure() or ConstantBaseMeasure() depending on if the base measure is a constant with respect to the natural parameters of something or not. By default the package assumes that any base measure in a form of the Function is not a constant. It, however, is not true for basemeasure that simply return a constant. In such cases the isbasemeasureconstant must have a specific method.\n\nSee also: getbasemeasure, basemeasure\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.ConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.ConstantBaseMeasure","text":"A trait object representing that the base measure is constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NonConstantBaseMeasure","page":"Interface","title":"ExponentialFamily.NonConstantBaseMeasure","text":"A trait object representing that the base measure is not constant.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily._logpdf","page":"Interface","title":"ExponentialFamily._logpdf","text":"_logpdf(ef::ExponentialFamilyDistribution, x)\n\nEvaluates and returns the log-density of the exponential family distribution for the input x.\n\nThis inner function dispatches to the appropriate version of _logpdf based on the types of x and ef, utilizing the check_logpdf function. The dispatch mechanism ensures that _logpdf correctly handles the input x, whether it is a single point or a container of points, according to the nature of the exponential family distribution and x.\n\nFor instance, with a Univariate distribution, _logpdf evaluates the log-density for a single point if x is a Number, and for a container of points if x is an AbstractVector.\n\nExamples\n\nEvaluate the log-density of a Gamma distribution at a single point:\n\nusing ExponentialFamily, Distributions;\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, 1.0)\n# output\n-1.0\n\nEvaluate the log-density of a Gamma distribution at multiple points:\n\nusing ExponentialFamily, Distributions\ngamma = convert(ExponentialFamilyDistribution, Gamma(1, 1))\nExponentialFamily._logpdf(gamma, [1, 2, 3])\n# output\n3-element Vector{Float64}:\n -1.0\n -2.0\n -3.0\n\nFor details on the dispatch mechanism of _logpdf, refer to the check_logpdf function.\n\nSee also: check_logpdf\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.check_logpdf","page":"Interface","title":"ExponentialFamily.check_logpdf","text":"check_logpdf(variate_form, typeof(x), eltype(x), ef, x)\n\nDetermines an appropriate strategy of evaluation of _logpdf (PointBasedLogpdfCall or MapBasedLogpdfCall) to use based on the types of x and ef. This function employs a dispatch mechanism that adapts to the input x, whether it is a single point or a container of points, in accordance with the characteristics of the exponential family distribution (ef) and the variate form of x.\n\nStrategies\n\nFor a Univariate distribution:\nIf x is a Number, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with MapBasedLogpdfCall().\nFor a Multivariate distribution:\nIf x is an AbstractVector containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractVectors, _logpdf is invoked with MapBasedLogpdfCall().\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with MapBasedLogpdfCall(), transforming x to eachcol(x).\nFor a Matrixvariate distribution:\nIf x is an AbstractMatrix containing Numbers, _logpdf is invoked with PointBasedLogpdfCall().\nIf x is an AbstractVector containing AbstractMatrixs, _logpdf is invoked with MapBasedLogpdfCall().\n\nExamples\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof(1.0), eltype(1.0), Gamma(1, 1), 1.0)\n# output\n(ExponentialFamily.PointBasedLogpdfCall(), 1.0)\n\nusing ExponentialFamily\nExponentialFamily.check_logpdf(Univariate, typeof([1.0, 2.0, 3.0]), eltype([1.0, 2.0, 3.0]), Gamma(1, 1), [1.0, 2.0, 3.0])\n# output\n(ExponentialFamily.MapBasedLogpdfCall(), [1.0, 2.0, 3.0])\n\nSee also: _logpdf PointBasedLogpdfCall MapBasedLogpdfCall\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.PointBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.PointBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as one point from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MapBasedLogpdfCall","page":"Interface","title":"ExponentialFamily.MapBasedLogpdfCall","text":"A trait object, signifying that the _logpdf method should treat it second argument as a container of points from the distrubution domain.\n\n\n\n\n\n","category":"type"},{"location":"interface/#Interfacing-with-Distributions-Defined-in-the-Distributions.jl-Package","page":"Interface","title":"Interfacing with Distributions Defined in the Distributions.jl Package","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions.jl package is a comprehensive library that defines a wide collection of standard distributions. The main objective of the Distributions package is to offer a unified interface for evaluating likelihoods of various distributions, along with convenient sampling routines from these distributions. The ExponentialFamily package provides a lightweight interface for a subset of the distributions defined in the Distributions package.","category":"page"},{"location":"interface/#Conversion-between-Mean-Parameters-Space-and-Natural-Parameters-Space","page":"Interface","title":"Conversion between Mean Parameters Space and Natural Parameters Space","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The Distributions package introduces the params function, which allows the retrieval of parameters for different distributions. For example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"using Distributions, ExponentialFamily\n\ndistribution = Bernoulli(0.25)\n\ntuple_of_θ = params(distribution)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"These parameters are typically defined in what's known as the mean parameters space. However, the ExponentialFamilyDistribution expects parameters to be in the natural parameters space. To facilitate conversion between these two representations, the ExponentialFamily package provides two structures:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"MeanToNatural\nNaturalToMean\nExponentialFamily.getmapping","category":"page"},{"location":"interface/#ExponentialFamily.MeanToNatural","page":"Interface","title":"ExponentialFamily.MeanToNatural","text":"MeanToNatural(::Type{T})\n\nReturn the transformation function that maps the parameters in the mean parameters space to the natural parameters space for a distribution of type T. The transformation function is of signature (params_in_mean_space, [ conditioner ]) -> params_in_natural_space.\n\nSee also: NaturalToMean, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.NaturalToMean","page":"Interface","title":"ExponentialFamily.NaturalToMean","text":"NaturalToMean(::Type{T})\n\nReturn the transformation function that maps the parameters in the natural parameters space to the mean parameters space for a distribution of type T. The transformation function is of signature (params_in_natural_space, [ conditioner ]) -> params_in_mean_space.\n\nSee also: MeanToNatural, NaturalParametersSpace, MeanParametersSpace, getmapping\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.getmapping","page":"Interface","title":"ExponentialFamily.getmapping","text":"getmapping(::Pair{L, R}, T)\n\nReturns a transformation L -> R between different parametrizations of a distribution of type T.\n\nSee also: NaturalParametersSpace, MeanParametersSpace, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"To convert from the mean parameters space to the corresponding natural parameters space, you can use the following code:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_η = MeanToNatural(Bernoulli)(tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"And to convert back:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"tuple_of_θ = NaturalToMean(Bernoulli)(tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Alternatuvely, the following API is supported ","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(MeanParametersSpace() => NaturalParametersSpace(), Bernoulli, tuple_of_θ)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"map(NaturalParametersSpace() => MeanParametersSpace(), Bernoulli, tuple_of_η)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"While the ExponentialFamily package employs the respective mappings where needed, it's also possible to call these functions manually. For instance, the generic implementation of the convert function between ExponentialFamilyDistribution and Distribution is built in terms of MeanToNatural and NaturalToMean. Moreover, the convert function performs checks to ensure that the provided parameters and conditioner are suitable for a specific distribution type.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#Note-on-the-conditioned-distributions","page":"Interface","title":"Note on the conditioned distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"For the conditioned distributions, two additional functions separate_conditioner and join_conditioner are used to separate the conditioner and actual parameters returned from the Distributions.params function.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.separate_conditioner\nExponentialFamily.join_conditioner","category":"page"},{"location":"interface/#ExponentialFamily.separate_conditioner","page":"Interface","title":"ExponentialFamily.separate_conditioner","text":"separate_conditioner(::Type{T}, params) where {T <: Distribution}\n\nSeparates the conditioner argument from params and returns a tuple of (conditioned_params, conditioner). By default returns (params, nothing) but can be overwritten for certain distributions.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.join_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.join_conditioner","page":"Interface","title":"ExponentialFamily.join_conditioner","text":"join_conditioner(::Type{T}, params, conditioner) where { T <: Distribution }\n\nJoins the conditioner argument with the params and returns a tuple of joined params, such that it can be used in a constructor of the T distribution.\n\njulia> (cparams, conditioner) = ExponentialFamily.separate_conditioner(Laplace, (0.0, 1.0))\n((1.0,), 0.0)\n\njulia> params = ExponentialFamily.join_conditioner(Laplace, cparams, conditioner)\n(0.0, 1.0)\n\njulia> Laplace(params...) == Laplace(0.0, 1.0)\ntrue\n\nSee also: ExponentialFamily.separate_conditioner\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"For example, Laplace distribution defines the functions in the following way","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# `params` are coming from the `Distribution.params(::Laplace)` and return (location, scale)\n# The `location`, however is a fixed parameter in the exponential distribution representation of Laplace\n# Hence, we return a tuple of tuple of actual parameter and the conditioner\nfunction separate_conditioner(::Type{Laplace}, params)\n location, scale = params\n return ((scale, ), location)\nend\n\n# The `join_conditioner` must join the actual parameters and the conditioner in such a way, that it is compatible \n# with the `Laplace` structure from the `Distributions.jl`. In Laplace, the location parameter goes first.\nfunction join_conditioner(::Type{Laplace}, cparams, conditioner) \n (scale, ) = cparams\n location = conditioner\n return (location, scale)\nend","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"In general, all functions defined for the ExponentialFamilyDistribution, such as getlogpartition or getbasemeasure accept an optional conditioner parameter, which is assumed to be nothing. Conditioned distribution implement the \"conditioned\" versions of such functions by explicitly requiring the conditioner parameter, e.g.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getsufficientstatistics(Laplace, 1.0) # explicit `conditioner = 1.0`","category":"page"},{"location":"interface/#Efficient-packing-of-the-natural-parameters-into-a-vectorized-form","page":"Interface","title":"Efficient packing of the natural parameters into a vectorized form","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution type stores its natural parameters in a vectorized, or packed, format. This is done for the sake of efficiency and to enhance compatibility with autodiff packages like ForwardDiff, which anticipate a single parameter vector. As a result, the tuple of natural parameters needs to be converted to its corresponding vectorized form and vice versa. To achieve this, the package provides the flatten_parameters, pack_parameters and unpack_parameters functions.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"ExponentialFamily.flatten_parameters\nExponentialFamily.pack_parameters\nExponentialFamily.unpack_parameters","category":"page"},{"location":"interface/#ExponentialFamily.flatten_parameters","page":"Interface","title":"ExponentialFamily.flatten_parameters","text":"flatten_parameters(::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a flattened form without actually allocating the container.\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.pack_parameters","page":"Interface","title":"ExponentialFamily.pack_parameters","text":"pack_parameters([ space ], ::Type{T}, params::Tuple)\n\nThis function returns the parameters of a distribution of type T in a vectorized (packed) form. For most of the distributions the packed versions are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\njulia> ExponentialFamily.pack_parameters((1, [2.0, 3.0], [4.0 5.0 6.0; 7.0 8.0 9.0]))\n9-element Vector{Float64}:\n 1.0\n 2.0\n 3.0\n 4.0\n 7.0\n 5.0\n 8.0\n 6.0\n 9.0\n\n\n\n\n\n","category":"function"},{"location":"interface/#ExponentialFamily.unpack_parameters","page":"Interface","title":"ExponentialFamily.unpack_parameters","text":"unpack_parameters([ space ], ::Type{T}, parameters)\n\nThis function \"unpack\" the vectorized form of the parameters in a tuple. For most of the distributions the packed parameters are of the same structure in any parameters space. For some distributions, however, it is necessary to indicate the space of the packaged parameters.\n\nSee also: MeanParametersSpace, NaturalParametersSpace\n\n\n\n\n\n","category":"function"},{"location":"interface/","page":"Interface","title":"Interface","text":"These functions are not exported by default, but it's important to note that the ExponentialFamilyDistributions type doesn't actually store the parameter tuple internally. Instead, the getnaturalparameters function returns the corresponding vectorized (packed) form of the natural parameters. In general, only the ExponentialFamily.unpack_parameters function must be implemented, as others could be implemented in a generic way.","category":"page"},{"location":"interface/#Attributes-of-the-exponential-family-distribution-based-on-Distribution","page":"Interface","title":"Attributes of the exponential family distribution based on Distribution","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The ExponentialFamilyDistribution{T} where { T <: Distribution } type encompasses all fundamental attributes of the exponential family, including basemeasure, logpartition, sufficientstatistics, and fisherinformation. Furthermore, it's possible to retrieve the actual functions that compute these attributes. For instance, consider the following example:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"basemeasure_of_bernoilli = getbasemeasure(Bernoulli)\n\nbasemeasure_of_bernoilli(0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isproper(::Type{T}, parameters, conditioner) where {T <: Distribution}\ngetbasemeasure(::Type{T}, ::Nothing) where {T <: Distribution}\ngetsufficientstatistics(::Type{T}, ::Nothing) where { T <: Distribution }\ngetlogpartition(::Type{T}, _) where { T <: Distribution }\ngetfisherinformation(::Type{T}, _) where { T <: Distribution }","category":"page"},{"location":"interface/#ExponentialFamily.isproper-Union{Tuple{T}, Tuple{Type{T}, Any, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.isproper","text":"isproper([ space = NaturalParametersSpace() ], ::Type{T}, parameters, conditioner = nothing) where { T <: Distribution }\n\nA specific verion of isproper defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getbasemeasure-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getbasemeasure","text":"getbasemeasure(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getbasemeasure defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getsufficientstatistics-Union{Tuple{T}, Tuple{Type{T}, Nothing}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getsufficientstatistics","text":"getsufficientstatistics(::Type{<:Distribution}, [ conditioner ])\n\nA specific verion of getsufficientstatistics defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. For conditional exponential family distributions requires an extra conditioner argument.\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getlogpartition-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getlogpartition","text":"getlogpartition([ space = NaturalParametersSpace() ], ::Type{T}, [ conditioner ]) where { T <: Distribution }\n\nA specific verion of getlogpartition defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/#ExponentialFamily.getfisherinformation-Union{Tuple{T}, Tuple{Type{T}, Any}} where T<:Distribution","page":"Interface","title":"ExponentialFamily.getfisherinformation","text":"getfisherinformation([ space = NaturalParametersSpace() ], ::Type{T}) where { T <: Distribution }\n\nA specific verion of getfisherinformation defined particularly for distribution types from Distributions.jl package. Does not require an instance of the ExponentialFamilyDistribution and can be called directly with a specific distribution type instead. Optionally, accepts the space parameter, which defines the parameters space. For conditional exponential family distributions requires an extra conditioner argument.\n\nSee also: NaturalParametersSpace, MeanParametersSpace\n\n\n\n\n\n","category":"method"},{"location":"interface/","page":"Interface","title":"Interface","text":"Certain functions require knowledge about which parameter space is being used. By default, the NaturalParametersSpace is assumed.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"getlogpartition(Bernoulli) === getlogpartition(NaturalParametersSpace(), Bernoulli)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"NaturalParametersSpace\nMeanParametersSpace","category":"page"},{"location":"interface/#ExponentialFamily.NaturalParametersSpace","page":"Interface","title":"ExponentialFamily.NaturalParametersSpace","text":"NaturalParametersSpace\n\nSpecifies the natural parameters space η as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(NaturalParametersSpace() => MeanParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the natural parametrization to the corresponding mean parametrization.\n\nSee also: MeanParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/#ExponentialFamily.MeanParametersSpace","page":"Interface","title":"ExponentialFamily.MeanParametersSpace","text":"MeanParametersSpace\n\nSpecifies the mean parameters space θ as the desired parameters space. Some functions (such as logpartition or fisherinformation) accept an additional space parameter to disambiguate the desired parameters space. Use map(MeanParametersSpace() => NaturalParametersSpace(), T, parameters, conditioner) to map the parameters and the conditioner of a distribution of type T from the mean parametrization to the corresponding natural parametrization.\n\nSee also: NaturalParametersSpace, getmapping, NaturalToMean, MeanToNatural\n\n\n\n\n\n","category":"type"},{"location":"interface/","page":"Interface","title":"Interface","text":"The isbasemeasureconstant function is defined for all supported distributions as well.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"isbasemeasureconstant(Bernoulli)","category":"page"},{"location":"interface/#Extra-defined-distributions","page":"Interface","title":"Extra defined distributions","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"The package defines a list of extra distributions for a purpose of more efficiency in different circumstances. The list is available here.","category":"page"},{"location":"library/#library","page":"Library","title":"Library API","text":"","category":"section"},{"location":"library/#library-list-distributions-extra","page":"Library","title":"Additional distributions","text":"","category":"section"},{"location":"library/","page":"Library","title":"Library","text":"These are the distributions that are not included in the Distributions.jl package.","category":"page"},{"location":"library/","page":"Library","title":"Library","text":"ExponentialFamily.MatrixDirichlet\nExponentialFamily.GammaShapeRate\nExponentialFamily.GammaShapeScale\nExponentialFamily.NormalMeanPrecision\nExponentialFamily.NormalMeanVariance\nExponentialFamily.NormalWeightedMeanPrecision\nExponentialFamily.MvNormalMeanPrecision\nExponentialFamily.MvNormalMeanCovariance\nExponentialFamily.MvNormalWeightedMeanPrecision\nExponentialFamily.JointNormal\nExponentialFamily.JointGaussian\nExponentialFamily.WishartFast\nExponentialFamily.InverseWishartFast\nExponentialFamily.NormalGamma\nExponentialFamily.MvNormalWishart","category":"page"},{"location":"library/#ExponentialFamily.MatrixDirichlet","page":"Library","title":"ExponentialFamily.MatrixDirichlet","text":"MatrixDirichlet{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nA matrix-valued MatrixDirichlet distribution, where T is the element type of the matrix A. The a field stores the matrix parameter of the distribution.\n\nFields\n\na::A: The matrix parameter of the MatrixDirichlet distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeRate","page":"Library","title":"ExponentialFamily.GammaShapeRate","text":"GammaShapeRate{T <: Real}\n\nA univariate gamma distribution parametrized by its shape a and rate b.\n\nFields\n\na: The shape parameter of the gamma distribution. It should be a positive real number.\nb: The rate parameter of the gamma distribution. It should be a positive real number.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.GammaShapeScale","page":"Library","title":"ExponentialFamily.GammaShapeScale","text":"GammaShapeScale{T}\n\nA continuous univariate gamma distribution parametrized by its shape α and scale β parameters.\n\nFields\n\nα: The shape parameter of the gamma distribution. It should be a positive real number.\nβ: The scale parameter of the gamma distribution. It should be a positive real number.\n\nNote\n\nGammaShapeScale is an alias for Gamma from Distributions.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanPrecision","page":"Library","title":"ExponentialFamily.NormalMeanPrecision","text":"NormalMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and precision w.\n\nFields\n\nμ::T: The mean of the normal distribution.\nw::T: The precision of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalMeanVariance","page":"Library","title":"ExponentialFamily.NormalMeanVariance","text":"NormalMeanVariance{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution with a known mean μ and variance v.\n\nFields\n\nμ::T: The mean of the normal distribution.\nv::T: The variance of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.NormalWeightedMeanPrecision","text":"NormalWeightedMeanPrecision{T <: Real} <: ContinuousUnivariateDistribution\n\nA normal distribution parametrized by its natural parameters: the weighted mean xi and precision w.\n\nFields\n\nxi::T: The weighted mean of the normal distribution. xi is computed as w * μ, where μ is the mean of the distribution.\nw::T: The precision (inverse variance) of the normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalMeanPrecision","text":"MvNormalMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and precision matrix Λ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalMeanCovariance","page":"Library","title":"ExponentialFamily.MvNormalMeanCovariance","text":"MvNormalMeanCovariance{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with mean μ and covariance matrix Σ, where T is the element type of the vectors M and matrices P.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΣ::P: The covariance matrix of the multivariate normal distribution\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWeightedMeanPrecision","page":"Library","title":"ExponentialFamily.MvNormalWeightedMeanPrecision","text":"MvNormalWeightedMeanPrecision{T <: Real, M <: AbstractVector{T}, P <: AbstractMatrix{T}} <: AbstractMvNormal\n\nA multivariate normal distribution with a weighted mean vector xi and precision matrix Λ, where T is the element type of the vectors M and matrices P. This struct represents a natural parametrization of a multivariate Gaussian distribution.\n\nFields\n\nxi::M: The weighted mean vector of the multivariate normal distribution.\nΛ::P: The precision matrix (inverse of the covariance matrix) of the multivariate normal distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointNormal","page":"Library","title":"ExponentialFamily.JointNormal","text":"JointNormal{D, S}\n\nJointNormal is an auxilary structure used for the joint marginal over Normally distributed variables. JointNormal stores a vector with the original dimensionalities (ds), so statistics can later be re-separated.\n\nUse ExponentialFamily.getcomponent(joint, index) to get a specific component of the joint distribution.\n\nFields\n\ndist: joint distribution (typically just a big MvNormal distribution, but maybe a tuple of individual means and covariance matrices)\nds: a tuple with the original dimensionalities of individual Normal distributions\nds[k] = (n,) where n is an integer indicates Multivariate normal of size n\nds[k] = () indicates Univariate normal\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.JointGaussian","page":"Library","title":"ExponentialFamily.JointGaussian","text":"An alias for the JointNormal.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.WishartFast","page":"Library","title":"ExponentialFamily.WishartFast","text":"WishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe WishartFast struct represents a fast version of the Wishart distribution. It is similar to the Wishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper Wishart messages.\n\nFor model creation and regular usage, it is recommended to use Wishart from Distributions.jl. The WishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the Wishart distribution.\ninvS::A: The inverse scale matrix parameter of the Wishart distribution.\n\nNote\n\nInternally, WishartFast stores and creates the inverse of its scale matrix. However, the params() function returns the scale matrix itself for backward compatibility. This is done to ensure better stability in the message passing update rules for ReactiveMP.jl.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.InverseWishartFast","page":"Library","title":"ExponentialFamily.InverseWishartFast","text":"InverseWishartFast{T <: Real, A <: AbstractMatrix{T}} <: ContinuousMatrixDistribution\n\nThe InverseWishartFast struct represents an improper Inverse Wishart distribution. It is similar to the InverseWishart distribution from Distributions.jl, but it does not check input arguments, allowing the creation of improper InverseWishart messages. \n\nFor model creation and regular usage, it is recommended to use InverseWishart from Distributions.jl. The InverseWishartFast distribution is intended for internal purposes and should not be directly used by regular users.\n\nFields\n\nν::T: The degrees of freedom parameter of the inverse Wishart distribution.\nS::A: The scale matrix parameter of the inverse Wishart distribution.\n\nNote\n\nThe InverseWishartFast distribution does not enforce input argument validation, making it suitable for specialized cases where improper message constructions are needed.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.NormalGamma","page":"Library","title":"ExponentialFamily.NormalGamma","text":"NormalGamma{T <: Real} <: ContinuousMultivariateDistribution\n\nA normal-gamma distribution, where T is a real number. This distribution is a joint distribution of a normal random variable with mean μ and precision λ, and a gamma-distributed random variable with shape α and rate β.\n\nFields\n\nμ::T: The mean of the normal distribution.\nλ::T: The precision of the normal distribution.\nα::T: The shape parameter of the gamma distribution.\nβ::T: The rate parameter of the gamma distribution.\n\n\n\n\n\n","category":"type"},{"location":"library/#ExponentialFamily.MvNormalWishart","page":"Library","title":"ExponentialFamily.MvNormalWishart","text":"MvNormalWishart{T, M <: AbstractArray{T}, V <: AbstractMatrix{T}, K <: Real, N <: Real} <: ContinuousMatrixDistribution\n\nA multivariate normal-Wishart distribution, where T is the element type of the arrays M and matrices V, and K and N are real numbers. This distribution is a joint distribution of a multivariate normal random variable with mean μ and a Wishart-distributed random matrix with scale matrix Ψ, degrees of freedom ν, and the scalar κ as a scaling parameter.\n\nFields\n\nμ::M: The mean vector of the multivariate normal distribution.\nΨ::V: The scale matrix of the Wishart distribution.\nκ::K: The scaling parameter of the Wishart distribution.\nν::N: The degrees of freedom of the Wishart distribution\n\n\n\n\n\n","category":"type"},{"location":"examples/#examples","page":"Examples","title":"Examples","text":"","category":"section"},{"location":"examples/#examples-product","page":"Examples","title":"Product of two probability distributions over the same variable","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, we'll show you how to use the ExponentialFamily package to calculate the product of probability distributions that both relate to the same variable \"X\". This operation results in another probability distribution, also centered around the variable \"X\". It's essential to note that this is distinct from multiplying probability distributions for two different variables, such as \"X\" and \"Y\", which yields a joint probability distribution. Calculating the product of two probability distributions over the same variable is a crucial step in applying Bayes' rule.","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"p(Xvert D) propto underbracep(X)p(DX)_mathrmproductoftwodistributions","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"To perform this operation, the ExponentialFamily library employs the prod function. This function takes a product strategy as its first argument. For instance:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions, BayesBase\n\nprior = Bernoulli(0.5)\nlikelihood = Bernoulli(0.6)\n\nposterior = prod(PreserveTypeProd(Distribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"You can achieve the same result in the general exponential family form, which operates within the natural parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nef_prior = convert(ExponentialFamilyDistribution, prior)\nef_likelihood = convert(ExponentialFamilyDistribution, likelihood)\n\nef_posterior = prod(PreserveTypeProd(ExponentialFamilyDistribution), ef_prior, ef_likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Or even more concisely:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"prod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"In this example, multiplying two Bernoulli distributions will always result in another Bernoulli distribution. However, this is not the case for all distributions. For instance, the product of two Laplace distributions may not yield another Laplace distribution, and representing the result in the same form might not be possible. In such cases, it's advisable to calculate the result within the exponential family domain. This is because the product of two exponential family distributions can always be represented as another exponential family distribution, as shown here:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\nprior = Laplace(2.0, 3.0)\nlikelihood = Laplace(1.0, 4.0)\n\nprod(PreserveTypeProd(ExponentialFamilyDistribution), prior, likelihood)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Note that the result does not correspond to the Laplace distribution and returns a generic univariate ExponentialFamilyDistribution. This approach ensures consistency and compatibility, especially when dealing with a wide range of probability distributions. Refer to the BayesBase for the documentation about available product strategies.","category":"page"},{"location":"examples/#Computing-various-useful-attributes-of-an-exponential-family-member","page":"Examples","title":"Computing various useful attributes of an exponential family member","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"The package implements attributes of many well known exponential family members, which are defined in this table. The attributes include getbasemeasure, getsufficientstatistics, getlogpartition, getfisherinformation, and others. In general, the interface for these functions assumes a family member \"tag,\" such as Normal or Bernoulli. Here are some examples of how to use these attributes:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"using ExponentialFamily, Distributions\n\n# Returns a function\nbasemeasure_of_normal = getbasemeasure(Normal)\n\nbasemeasure_of_normal(0.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"\n# Returns an iterable of functions\nsufficientstatistics_of_gamma = getsufficientstatistics(Gamma)\n\nmap(f -> f(1.0), sufficientstatistics_of_gamma)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"Some distributions, like the Laplace distribution, qualify as exponential family members only under certain conditions or when specific information is known in advance. In such cases, the ExponentialFamily package introduces the concept of a conditioner. For instance, the Laplace distribution becomes a member of the exponential family only when the location parameter is known and fixed. Consequently, we condition on the location parameter:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"laplace = Laplace(2.0, 1.0)\n\ncanonical = convert(ExponentialFamilyDistribution, laplace)\n\ngetconditioner(canonical)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"# For conditioned distributions, the `conditioner` must be present as a second argument\nbasemeasure_of_laplace = getbasemeasure(Laplace, 2.0)\n\nbasemeasure_of_laplace(1.0)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The getlogpartition and getfisherinformation functions optionally accept a space parameter as the first argument. This space parameter specifies the parameterization space, such as MeanParametersSpace or [NaturalParametersSpace]. The result obtained from these functions (in general) depends on the chosen parameter space:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logpartition_of_gamma_in_mean_space = getlogpartition(MeanParametersSpace(), Gamma)\n\ngamma_parameters_in_mean_space = [ 1.0, 2.0 ]\n\nlogpartition_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"logparition_of_gamma_in_natural_space = getlogpartition(NaturalParametersSpace(), Gamma)\n\ngamma_parameters_in_natural_space = map(\n MeanParametersSpace() => NaturalParametersSpace(), \n Gamma,\n gamma_parameters_in_mean_space\n)\n\nlogparition_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"The same principle applies to the Fisher information matrix:","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_mean_space = getfisherinformation(MeanParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_mean_space(gamma_parameters_in_mean_space)","category":"page"},{"location":"examples/","page":"Examples","title":"Examples","text":"fisherinformation_of_gamma_in_natural_space = getfisherinformation(NaturalParametersSpace(), Gamma)\n\nfisherinformation_of_gamma_in_natural_space(gamma_parameters_in_natural_space)","category":"page"},{"location":"examples/#Approximating-attributes","page":"Examples","title":"Approximating attributes","text":"","category":"section"},{"location":"examples/","page":"Examples","title":"Examples","text":"Refer to the ExpectationApproximations.jl package for approximating various attributes of the members of the exponential family.","category":"page"},{"location":"#ExponentialFamily.jl","page":"Home","title":"ExponentialFamily.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Julia package that extends the functionality of Distributions.jl by providing a collection of exponential family distributions and customized implementations. It is designed to facilitate working with exponential family distributions and offers specialized functionality tailored to this class of distributions.","category":"page"},{"location":"#Core-Principles","page":"Home","title":"Core Principles","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The package is built around several core principles:","category":"page"},{"location":"","page":"Home","title":"Home","text":"High performance with minimal allocations, striving for complete type stability.\nCompatibility with distributions defined in Distributions.jl.\nEase of use and rich functionality.","category":"page"},{"location":"#Table-of-Contents","page":"Home","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Interface\nExamples\nLibrary","category":"page"},{"location":"#Index","page":"Home","title":"Index","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"","category":"page"}] +} diff --git a/v1.5.1/siteinfo.js b/v1.5.1/siteinfo.js new file mode 100644 index 00000000..032d61ee --- /dev/null +++ b/v1.5.1/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.5.1"; diff --git a/versions.js b/versions.js index d7532ef6..0a296fc2 100644 --- a/versions.js +++ b/versions.js @@ -1,10 +1,12 @@ var DOC_VERSIONS = [ "stable", + "v1.5", + "v1.4", "v1.3", "v1.2", "v1.1", "v1.0", "dev", ]; -var DOCUMENTER_NEWEST = "v1.3.0"; +var DOCUMENTER_NEWEST = "v1.5.1"; var DOCUMENTER_STABLE = "stable";