From a58a50121da6199bde58b6341832029b355f75ad Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 8 May 2024 09:55:24 +0000 Subject: [PATCH] build based on 812b8ef --- dev/.documenter-siteinfo.json | 1 + dev/assets/documenter.js | 1050 ++++++++++++++++++++++++ dev/assets/logo.png | Bin 0 -> 52263 bytes dev/assets/themes/documenter-dark.css | 7 + dev/assets/themes/documenter-light.css | 9 + dev/assets/themeswap.js | 84 ++ dev/assets/warner.js | 52 ++ dev/index.html | 2 + dev/list_of_functions/index.html | 18 + dev/objects.inv | Bin 0 -> 554 bytes dev/reference/index.html | 7 + dev/search_index.js | 3 + dev/siteinfo.js | 1 + index.html | 2 + versions.js | 5 + 15 files changed, 1241 insertions(+) create mode 100644 dev/.documenter-siteinfo.json create mode 100644 dev/assets/documenter.js create mode 100644 dev/assets/logo.png create mode 100644 dev/assets/themes/documenter-dark.css create mode 100644 dev/assets/themes/documenter-light.css create mode 100644 dev/assets/themeswap.js create mode 100644 dev/assets/warner.js create mode 100644 dev/index.html create mode 100644 dev/list_of_functions/index.html create mode 100644 dev/objects.inv create mode 100644 dev/reference/index.html create mode 100644 dev/search_index.js create mode 100644 dev/siteinfo.js create mode 100644 index.html create mode 100644 versions.js diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json new file mode 100644 index 0000000..126e5ff --- /dev/null +++ b/dev/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-08T09:55:21","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js new file mode 100644 index 0000000..c6562b5 --- /dev/null +++ b/dev/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 = ` + + `; + + $(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/dev/assets/logo.png b/dev/assets/logo.png new file mode 100644 index 0000000000000000000000000000000000000000..b9e4de01f8b0c28c9af5e7ee50fed80bd3d1ef6c GIT binary patch literal 52263 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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 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 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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 .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 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GitHub

Introduction

PGopt is a software for determining optimal input trajectories with probabilistic performance and constraint satisfaction guarantees for unknown systems with latent states based on input-output measurements. In order to quantify uncertainties, which is crucial for deriving formal guarantees, a Bayesian approach is employed and a prior over the unknown dynamics and the system trajectory is formulated in state-space representation. Since for practical applicability, the prior must be updated based on input-output measurements, but the corresponding posterior distribution is analytically intractable, particle Gibbs (PG) sampling is utilized to draw samples from this distribution. Based on these samples, a scenario optimal control problem (OCP) is formulated and probabilistic performance and constraint satisfaction guarantees are inferred via a greedy constraint removal.

The approach is explained in the paper "Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States", available as a preprint on arXiv.

Installation

PGopt can be installed using the Julia package manager. Inside the Julia REPL, type ] to enter the Pkg REPL mode then run

pkg> add https://github.com/TUM-ITR/PGopt:Julia

Examples

diff --git a/dev/list_of_functions/index.html b/dev/list_of_functions/index.html new file mode 100644 index 0000000..4561508 --- /dev/null +++ b/dev/list_of_functions/index.html @@ -0,0 +1,18 @@ + +List of fuctions ·
GitHub

List of fuctions

PGopt.particle_Gibbs — Method
particle_Gibbs(u_training, y_training, K, K_b, k_d, N, phi::Function, Lambda_Q, ell_Q, Q_init, V, A_init, x_init_dist, g, R; x_prim=nothing)

Run particle Gibbs sampler with ancestor sampling to obtain samples $\{A, Q, x_{T:-1}\}^{[1:K]}$ from the joint parameter and state posterior distribution $p(A, Q, x_{T:-1} \mid \mathbb{D}=\{u_{T:-1}, y_{T:-1}\})$.

Arguments

  • u_training: training input trajectory
  • y_training: training output trajectory
  • K: number of models/scenarios to be sampled
  • K_b: length of the burn in period
  • k_d: number of models/scenarios to be skipped to decrease correlation (thinning)
  • N: number of particles
  • phi: basis functions
  • Lambda_Q: scale matrix of IW prior on $Q$
  • ell_Q: degrees of freedom of IW prior on $Q$
  • Q_init: initial value of $Q$
  • V: left covariance matrix of MN prior on $A$
  • A_init: initial value of $A$
  • x_init_dist: distribution of the initial state
  • g: observation function
  • R: variance of zero-mean Gaussian measurement noise
  • x_prim: prespecified trajectory for the first iteration

This function is based on the papers

A. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.
+
+F. Lindsten, T. B. Schön, and M. Jordan, “Ancestor sampling for particle Gibbs,” Advances in Neural Information Processing Systems, vol. 25, 2012.

and the code provided in the supplementary material.

source
PGopt.solve_PG_OCP — Method
solve_PG_OCP(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, active_constraints=nothing, opts=nothing, print_progress=true)

Solve the optimal control problem of the following form:

$\min \sum_{t=0}^{H} \frac{1}{2} u_t \operatorname{diag}(R_{\mathrm{cost}}) u_t$

subject to:

\[\begin{aligned} +\forall k, \forall t \\ +x_{t+1}^{[k]} &= f_{\theta^{[k]}}(x_t^{[k]}, u_t) + v_t^{[k]} \\ +x_{t, 1:n_y}^{[k]} &\geq y_{\mathrm{min},\ t} - e_t^{[k]} \\ +x_{t, 1:n_y}^{[k]} &\leq y_{\mathrm{max},\ t} - e_t^{[k]} \\ +u_t &\geq u_{\mathrm{min},\ t} \\ +u_t &\leq u_{\mathrm{max},\ t}. +\end{aligned}\]

Note that the output constraints imply the measurement function $y_t^{[k]} = x_{t, 1:n_y}^{[k]}$. Further note that the states of the individual models ($x^{[1:k]}$) are combined in the vector x_vec of dimension K * n_x.

Arguments

  • PG_samples: PG samples
  • phi: basis functions
  • R: variance of zero-mean Gaussian measurement noise - only used if e_vec is not passed
  • H: horizon of the OCP
  • u_min: array of dimension 1 x 1 or 1 x H containing the minimum control input for all timesteps
  • u_max: array of dimension 1 x 1 or 1 x H containing the maximum control input for all timesteps
  • y_min: array of dimension 1 x 1 or 1 x H containing the minimum system output for all timesteps
  • y_max: array of dimension 1 x 1 or 1 x H containing the maximum system output for all timesteps
  • R_cost_diag: parameter of the diagonal quadratic cost function
  • x_vec_0: vector with $K n_x$ elements containing the initial state of all models - if not provided, the initial states are sampled based on the PGS samples
  • v_vec: array of dimension n_x x H x K that contains the process noise for all models and all timesteps - if not provided, the noise is sampled based on the PGS samples
  • e_vec: array of dimension n_y x H x K that contains the measurement noise for all models and all timesteps - if not provided, the noise is sampled based on the provided R
  • u_init: initial guess for the optimal trajectory
  • K_pre_solve: if K_pre_solve > 0, an initial guess for the optimal trajectory is obtained by solving the OCP with only K_pre_solve < K models
  • active_constraints: vector containing the indices of the models, for which the output constraints are active - if not provided, the output constraints are considered for all models
  • opts: SolverOptions struct containing options of the solver
  • print_progress: if set to true, the progress is printed
source
PGopt.solve_PG_OCP_greedy_guarantees — Method
solve_PG_OCP_greedy_guarantees(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag, β; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, opts=nothing, print_progress=true)

Solve the following optimal control problem and determine a support sub-sample with cardinality $s$ via a greedy constraint removal. Based on the cardinality $s$, a bound on the probability that the incurred cost exceeds the worst-case cost or that the constraints are violated when the input trajectory $u_{0:H}$ is applied to the unknown system is calculated (i.e., $1-\epsilon$ is determined).

$\min \sum_{t=0}^{H} \frac{1}{2} u_t \operatorname{diag}(R_{\mathrm{cost}}) u_t$

subject to:

\[\begin{aligned} +\forall k, \forall t \\ +x_{t+1}^{[k]} &= f_{\theta^{[k]}}(x_t^{[k]}, u_t) + v_t^{[k]} \\ +x_{t, 1:n_y}^{[k]} &\geq y_{\mathrm{min},\ t} - e_t^{[k]} \\ +x_{t, 1:n_y}^{[k]} &\leq y_{\mathrm{max},\ t} - e_t^{[k]} \\ +u_t &\geq u_{\mathrm{min},\ t} \\ +u_t &\leq u_{\mathrm{max},\ t}. +\end{aligned}\]

Note that the output constraints imply the measurement function $y_t^{[k]} = x_{t, 1:n_y}^{[k]}$. Further note that the states of the individual models ($x^{[1:k]}$) are combined in the vector x_vec of dimension K * n_x.

Arguments

  • PG_samples: PG samples
  • phi: basis functions
  • R: variance of zero-mean Gaussian measurement noise - only used if e_vec is not passed
  • H: horizon of the OCP
  • u_min: array of dimension 1 x 1 or 1 x H containing the minimum control input for all timesteps
  • u_max: array of dimension 1 x 1 or 1 x H containing the maximum control input for all timesteps
  • y_min: array of dimension 1 x 1 or 1 x H containing the minimum system output for all timesteps
  • y_max: array of dimension 1 x 1 or 1 x H containing the maximum system output for all timesteps
  • R_cost_diag: parameter of the diagonal quadratic cost function
  • β: confidence parameter
  • x_vec_0: vector with K*n_x elements containing the initial state of all models - if not provided, the initial states are sampled based on the PGS samples
  • v_vec: array of dimension n_x x H x K that contains the process noise for all models and all timesteps - if not provided, the noise is sampled based on the PGS samples
  • e_vec: array of dimension n_y x H x K that contains the measurement noise for all models and all timesteps - if not provided, the noise is sampled based on the provided R
  • u_init: initial guess for the optimal trajectory
  • K_pre_solve: if K_pre_solve > 0, an initial guess for the optimal trajectory is obtained by solving the OCP with only K_pre_solve < K models
  • opts: SolverOptions struct containing options of the solver
  • print_progress: if set to true, the progress is printed
source
PGopt.test_prediction — Method
test_prediction(PG_samples::Vector{PG_sample}, phi::Function, g, R, k_n, u_test, y_test)

Simulate the PGS samples forward in time and compare the predictions to the test data.

Arguments

  • PG_samples: PG samples
  • phi: basis functions
  • g: observation function
  • R: variance of zero-mean Gaussian measurement noise
  • k_n: each model is simulated $k_n$ times
  • u_test: test input
  • y_test: test output
source
PGopt.plot_predictions — Method
plot_predictions(y_pred, y_test; plot_percentiles=false, y_min=nothing, y_max=nothing)

Plot the predictions and the test data.

Arguments

  • y_pred: matrix containing the output predictions
  • y_test: test output trajectory
  • plot_percentiles: if set to true, percentiles are plotted
  • y_min: min output to be plotted as constraint
  • y_max: max output to be plotted as constraint
source
PGopt.plot_autocorrelation — Method
plot_autocorrelation(PG_samples::Vector{PG_sample}; max_lag=0)

Plot the autocorrelation function (ACF) of the PG samples. This might be helpful when adjusting the thinning parameter $k_d$.

Arguments

  • PG_samples: PG samples
  • max_lag: maximum lag at which to calculate the ACF
source
PGopt.epsilon — Method
epsilon(s::Int64, K::Int64, β::Float64)

Determine the parameter $\epsilon$. $1-\epsilon$ corresponds to a bound on the probability that the incurred cost exceeds the worst-case cost or that the constraints are violated when the input trajectory $u_{0:H}$ is applied to the unknown system. $\epsilon$ is the unique solution over the interval $(0,1)$ of the polynomial equation in the $v$ variable:

$\binom{K}{s}(1-v)^{K-s}-\frac{\beta}{K}\sum_{m=s}^{K-1}\binom{m}{s}(1-v)^{m-s}=0$.

Arguments

  • s: cardinality of the support sub-sample
  • K: number of scenarios
  • β: confidence parameter

This function is based on the paper

S. Garatti and M. C. Campi, “Risk and complexity in scenario optimization,” Mathematical Programming, vol. 191, no. 1, pp. 243–279, 2022.

and the code provided in the appendix.

source
PGopt.MNIW_sample — Method
MNIW_sample(Phi, Psi, Sigma, V, Lambda_Q, ell_Q, T)

Sample new model parameters $\{A, Q\}$ from the conditional distribution $p(A, Q | x_{T:-1})$, which is a matrix normal inverse Wishart (MNIW) distribution.

Arguments

  • Phi: statistic; see paper below for definition
  • Psi: statistic; see paper below for definition
  • Sigma: statistic; see paper below for definition
  • V: left covariance matrix of MN prior on $A$
  • Lambda_Q: scale matrix of IW prior on $Q$
  • ell_Q: degrees of freedom of IW prior on $Q$
  • T: length of the training trajectory

This function is based on the paper

A. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.

and the code provided in the supplementary material.

source
PGopt.systematic_resampling — Method
systematic_resampling(W, N)

Sample N indices according to the weights W.

Arguments

  • W: vector containing the weights of the particles
  • N: number of indices to be sampled

This function is based on the paper

A. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.

and the code provided in the supplementary material.

source
diff --git a/dev/objects.inv b/dev/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..10177d4d6605d174e0a57629590f56da0f5ca91c GIT binary patch literal 554 zcmV+_0@eK^AX9K?X>NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGj)3L_v^ zWpZMd?av*PJAarPHb0B7EY-J#6b0A}HZE$jB zb8}^6Aa!$TZf78RY-wUH3V58YR9|m`Fc5#|Q#9Fllew8WjBlGxW3oA87WYUh9E_#5 zq%Dia_}y12FhDfu_5w$H_xp3XBcvXzk&s^BV=l7p5SmcQnHReln zD5f4yf7iN-eYBJy8u@*zMYL7 zk@(!T&?pt$LJQ0>54MkV(?Z?d4tGB!N@l_3g>Mwa{>16Z(TK2OFEeY2 zZ1rfUyB?*;yAO`^_uOvUmvr+#dS_RMWFsW3)K0h#hXgC6!DS6R0d=B_5Q&iFi>4O+ z;l72^*N8Bzf`h#n<{zL0A8YW3xj3 +Reference ·
GitHub

Reference

If you found this software useful for your research, consider citing us.

@article{PMCMC_OCP_arXiv_2023,
+      title={Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States},
+      author={Lefringhausen, Robert and Srithasan, Supitsana and Lederer, Armin and Hirche, Sandra},
+      journal={arXiv preprint arXiv:2303.17963},
+      year={2023}
+}
diff --git a/dev/search_index.js b/dev/search_index.js new file mode 100644 index 0000000..244efcd --- /dev/null +++ b/dev/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"list_of_functions/#List-of-fuctions","page":"List of fuctions","title":"List of fuctions","text":"","category":"section"},{"location":"list_of_functions/","page":"List of fuctions","title":"List of fuctions","text":"particle_Gibbs(u_training, y_training, K, K_b, k_d, N, phi::Function, Lambda_Q, ell_Q, Q_init, V, A_init, x_init_dist, g, R; x_prim=nothing)\nsolve_PG_OCP(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, active_constraints=nothing, opts=nothing, print_progress=true)\nsolve_PG_OCP_greedy_guarantees(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag, β; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, opts=nothing, print_progress=true)\ntest_prediction(PG_samples::Vector{PG_sample}, phi::Function, g, R, k_n, u_test, y_test)\nplot_predictions(y_pred, y_test; plot_percentiles=false, y_min=nothing, y_max=nothing)\nplot_autocorrelation(PG_samples::Vector{PG_sample}; max_lag=0)\nepsilon(s::Int64, K::Int64, β::Float64)\nMNIW_sample(Phi, Psi, Sigma, V, Lambda_Q, ell_Q, T)\nsystematic_resampling(W, N)","category":"page"},{"location":"list_of_functions/#PGopt.particle_Gibbs-Tuple{Any, Any, Any, Any, Any, Any, Function, Vararg{Any, 8}}","page":"List of fuctions","title":"PGopt.particle_Gibbs","text":"particle_Gibbs(u_training, y_training, K, K_b, k_d, N, phi::Function, Lambda_Q, ell_Q, Q_init, V, A_init, x_init_dist, g, R; x_prim=nothing)\n\nRun particle Gibbs sampler with ancestor sampling to obtain samples A Q x_T-1^1K from the joint parameter and state posterior distribution p(A Q x_T-1 mid mathbbD=u_T-1 y_T-1).\n\nArguments\n\nu_training: training input trajectory\ny_training: training output trajectory\nK: number of models/scenarios to be sampled\nK_b: length of the burn in period\nk_d: number of models/scenarios to be skipped to decrease correlation (thinning)\nN: number of particles\nphi: basis functions\nLambda_Q: scale matrix of IW prior on Q\nell_Q: degrees of freedom of IW prior on Q\nQ_init: initial value of Q\nV: left covariance matrix of MN prior on A\nA_init: initial value of A\nx_init_dist: distribution of the initial state\ng: observation function\nR: variance of zero-mean Gaussian measurement noise\nx_prim: prespecified trajectory for the first iteration\n\nThis function is based on the papers\n\nA. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.\n\nF. Lindsten, T. B. Schön, and M. Jordan, “Ancestor sampling for particle Gibbs,” Advances in Neural Information Processing Systems, vol. 25, 2012.\n\nand the code provided in the supplementary material.\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.solve_PG_OCP-Tuple{Vector{PG_sample}, Function, Vararg{Any, 7}}","page":"List of fuctions","title":"PGopt.solve_PG_OCP","text":"solve_PG_OCP(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, active_constraints=nothing, opts=nothing, print_progress=true)\n\nSolve the optimal control problem of the following form:\n\nmin sum_t=0^H frac12 u_t operatornamediag(R_mathrmcost) u_t\n\nsubject to:\n\nbeginaligned\nforall k forall t \nx_t+1^k = f_theta^k(x_t^k u_t) + v_t^k \nx_t 1n_y^k geq y_mathrmmin t - e_t^k \nx_t 1n_y^k leq y_mathrmmax t - e_t^k \nu_t geq u_mathrmmin t \nu_t leq u_mathrmmax t\nendaligned\n\nNote that the output constraints imply the measurement function y_t^k = x_t 1n_y^k. Further note that the states of the individual models (x^1k) are combined in the vector x_vec of dimension K * n_x.\n\nArguments\n\nPG_samples: PG samples\nphi: basis functions\nR: variance of zero-mean Gaussian measurement noise - only used if e_vec is not passed\nH: horizon of the OCP\nu_min: array of dimension 1 x 1 or 1 x H containing the minimum control input for all timesteps\nu_max: array of dimension 1 x 1 or 1 x H containing the maximum control input for all timesteps\ny_min: array of dimension 1 x 1 or 1 x H containing the minimum system output for all timesteps\ny_max: array of dimension 1 x 1 or 1 x H containing the maximum system output for all timesteps\nR_cost_diag: parameter of the diagonal quadratic cost function\nx_vec_0: vector with K n_x elements containing the initial state of all models - if not provided, the initial states are sampled based on the PGS samples\nv_vec: array of dimension n_x x H x K that contains the process noise for all models and all timesteps - if not provided, the noise is sampled based on the PGS samples\ne_vec: array of dimension n_y x H x K that contains the measurement noise for all models and all timesteps - if not provided, the noise is sampled based on the provided R\nu_init: initial guess for the optimal trajectory\nK_pre_solve: if K_pre_solve > 0, an initial guess for the optimal trajectory is obtained by solving the OCP with only K_pre_solve < K models\nactive_constraints: vector containing the indices of the models, for which the output constraints are active - if not provided, the output constraints are considered for all models\nopts: SolverOptions struct containing options of the solver\nprint_progress: if set to true, the progress is printed\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.solve_PG_OCP_greedy_guarantees-Tuple{Vector{PG_sample}, Function, Vararg{Any, 8}}","page":"List of fuctions","title":"PGopt.solve_PG_OCP_greedy_guarantees","text":"solve_PG_OCP_greedy_guarantees(PG_samples::Vector{PG_sample}, phi::Function, R, H, u_min, u_max, y_min, y_max, R_cost_diag, β; x_vec_0=nothing, v_vec=nothing, e_vec=nothing, u_init=nothing, K_pre_solve=0, opts=nothing, print_progress=true)\n\nSolve the following optimal control problem and determine a support sub-sample with cardinality s via a greedy constraint removal. Based on the cardinality s, a bound on the probability that the incurred cost exceeds the worst-case cost or that the constraints are violated when the input trajectory u_0H is applied to the unknown system is calculated (i.e., 1-epsilon is determined).\n\nmin sum_t=0^H frac12 u_t operatornamediag(R_mathrmcost) u_t\n\nsubject to:\n\nbeginaligned\nforall k forall t \nx_t+1^k = f_theta^k(x_t^k u_t) + v_t^k \nx_t 1n_y^k geq y_mathrmmin t - e_t^k \nx_t 1n_y^k leq y_mathrmmax t - e_t^k \nu_t geq u_mathrmmin t \nu_t leq u_mathrmmax t\nendaligned\n\nNote that the output constraints imply the measurement function y_t^k = x_t 1n_y^k. Further note that the states of the individual models (x^1k) are combined in the vector x_vec of dimension K * n_x.\n\nArguments\n\nPG_samples: PG samples\nphi: basis functions\nR: variance of zero-mean Gaussian measurement noise - only used if e_vec is not passed\nH: horizon of the OCP\nu_min: array of dimension 1 x 1 or 1 x H containing the minimum control input for all timesteps\nu_max: array of dimension 1 x 1 or 1 x H containing the maximum control input for all timesteps\ny_min: array of dimension 1 x 1 or 1 x H containing the minimum system output for all timesteps\ny_max: array of dimension 1 x 1 or 1 x H containing the maximum system output for all timesteps\nR_cost_diag: parameter of the diagonal quadratic cost function\nβ: confidence parameter\nx_vec_0: vector with K*n_x elements containing the initial state of all models - if not provided, the initial states are sampled based on the PGS samples\nv_vec: array of dimension n_x x H x K that contains the process noise for all models and all timesteps - if not provided, the noise is sampled based on the PGS samples\ne_vec: array of dimension n_y x H x K that contains the measurement noise for all models and all timesteps - if not provided, the noise is sampled based on the provided R\nu_init: initial guess for the optimal trajectory\nK_pre_solve: if K_pre_solve > 0, an initial guess for the optimal trajectory is obtained by solving the OCP with only K_pre_solve < K models\nopts: SolverOptions struct containing options of the solver\nprint_progress: if set to true, the progress is printed\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.test_prediction-Tuple{Vector{PG_sample}, Function, Vararg{Any, 5}}","page":"List of fuctions","title":"PGopt.test_prediction","text":"test_prediction(PG_samples::Vector{PG_sample}, phi::Function, g, R, k_n, u_test, y_test)\n\nSimulate the PGS samples forward in time and compare the predictions to the test data.\n\nArguments\n\nPG_samples: PG samples\nphi: basis functions\ng: observation function\nR: variance of zero-mean Gaussian measurement noise\nk_n: each model is simulated k_n times\nu_test: test input\ny_test: test output\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.plot_predictions-Tuple{Any, Any}","page":"List of fuctions","title":"PGopt.plot_predictions","text":"plot_predictions(y_pred, y_test; plot_percentiles=false, y_min=nothing, y_max=nothing)\n\nPlot the predictions and the test data.\n\nArguments\n\ny_pred: matrix containing the output predictions\ny_test: test output trajectory\nplot_percentiles: if set to true, percentiles are plotted\ny_min: min output to be plotted as constraint\ny_max: max output to be plotted as constraint\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.plot_autocorrelation-Tuple{Vector{PG_sample}}","page":"List of fuctions","title":"PGopt.plot_autocorrelation","text":"plot_autocorrelation(PG_samples::Vector{PG_sample}; max_lag=0)\n\nPlot the autocorrelation function (ACF) of the PG samples. This might be helpful when adjusting the thinning parameter k_d.\n\nArguments\n\nPG_samples: PG samples\nmax_lag: maximum lag at which to calculate the ACF\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.epsilon-Tuple{Int64, Int64, Float64}","page":"List of fuctions","title":"PGopt.epsilon","text":"epsilon(s::Int64, K::Int64, β::Float64)\n\nDetermine the parameter epsilon. 1-epsilon corresponds to a bound on the probability that the incurred cost exceeds the worst-case cost or that the constraints are violated when the input trajectory u_0H is applied to the unknown system. epsilon is the unique solution over the interval (01) of the polynomial equation in the v variable:\n\nbinomKs(1-v)^K-s-fracbetaKsum_m=s^K-1binomms(1-v)^m-s=0.\n\nArguments\n\ns: cardinality of the support sub-sample \nK: number of scenarios\nβ: confidence parameter\n\nThis function is based on the paper\n\nS. Garatti and M. C. Campi, “Risk and complexity in scenario optimization,” Mathematical Programming, vol. 191, no. 1, pp. 243–279, 2022.\n\nand the code provided in the appendix.\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.MNIW_sample-NTuple{7, Any}","page":"List of fuctions","title":"PGopt.MNIW_sample","text":"MNIW_sample(Phi, Psi, Sigma, V, Lambda_Q, ell_Q, T)\n\nSample new model parameters A Q from the conditional distribution p(A Q x_T-1), which is a matrix normal inverse Wishart (MNIW) distribution.\n\nArguments\n\nPhi: statistic; see paper below for definition\nPsi: statistic; see paper below for definition\nSigma: statistic; see paper below for definition\nV: left covariance matrix of MN prior on A\nLambda_Q: scale matrix of IW prior on Q\nell_Q: degrees of freedom of IW prior on Q\nT: length of the training trajectory\n\nThis function is based on the paper\n\nA. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.\n\nand the code provided in the supplementary material.\n\n\n\n\n\n","category":"method"},{"location":"list_of_functions/#PGopt.systematic_resampling-Tuple{Any, Any}","page":"List of fuctions","title":"PGopt.systematic_resampling","text":"systematic_resampling(W, N)\n\nSample N indices according to the weights W.\n\nArguments\n\nW: vector containing the weights of the particles\nN: number of indices to be sampled\n\nThis function is based on the paper\n\nA. Svensson and T. B. Schön, “A flexible state–space model for learning nonlinear dynamical systems,” Automatica, vol. 80, pp. 189–199, 2017.\n\nand the code provided in the supplementary material.\n\n\n\n\n\n","category":"method"},{"location":"reference/#Reference","page":"Reference","title":"Reference","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"If you found this software useful for your research, consider citing us.","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"@article{PMCMC_OCP_arXiv_2023,\n title={Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States},\n author={Lefringhausen, Robert and Srithasan, Supitsana and Lederer, Armin and Hirche, Sandra},\n journal={arXiv preprint arXiv:2303.17963},\n year={2023}\n}","category":"page"},{"location":"#Introduction","page":"Introduction","title":"Introduction","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"PGopt is a software for determining optimal input trajectories with probabilistic performance and constraint satisfaction guarantees for unknown systems with latent states based on input-output measurements. In order to quantify uncertainties, which is crucial for deriving formal guarantees, a Bayesian approach is employed and a prior over the unknown dynamics and the system trajectory is formulated in state-space representation. Since for practical applicability, the prior must be updated based on input-output measurements, but the corresponding posterior distribution is analytically intractable, particle Gibbs (PG) sampling is utilized to draw samples from this distribution. Based on these samples, a scenario optimal control problem (OCP) is formulated and probabilistic performance and constraint satisfaction guarantees are inferred via a greedy constraint removal.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"The approach is explained in the paper \"Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States\", available as a preprint on arXiv.","category":"page"},{"location":"#Installation","page":"Introduction","title":"Installation","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"PGopt can be installed using the Julia package manager. Inside the Julia REPL, type ] to enter the Pkg REPL mode then run","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"pkg> add https://github.com/TUM-ITR/PGopt:Julia","category":"page"},{"location":"#Examples","page":"Introduction","title":"Examples","text":"","category":"section"}] +} diff --git a/dev/siteinfo.js b/dev/siteinfo.js new file mode 100644 index 0000000..3343491 --- /dev/null +++ b/dev/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "dev"; diff --git a/index.html b/index.html new file mode 100644 index 0000000..1a6cc11 --- /dev/null +++ b/index.html @@ -0,0 +1,2 @@ + + diff --git a/versions.js b/versions.js new file mode 100644 index 0000000..4ec0f8f --- /dev/null +++ b/versions.js @@ -0,0 +1,5 @@ +var DOC_VERSIONS = [ + "dev", +]; +var DOCUMENTER_NEWEST = "dev"; +var DOCUMENTER_STABLE = "dev";