From 2b0b1cf4d4ad85c46063af2520bdc627be8ed4ee Mon Sep 17 00:00:00 2001
From: Lorenzo Terenzi <lorenzo.terenzi@lumos-dev.com>
Date: Wed, 11 Oct 2017 18:56:40 +0200
Subject: [PATCH] first commit

---
 .idea/workspace.xml                           |   28 +-
 src/implementations/costs.py                  |   16 +
 src/implementations/ex02.ipynb                | 1733 +++++++++++++++++
 src/implementations/gradient descent.py       |   50 +
 src/implementations/grid_search.py            |   27 +
 src/implementations/helpers.py                |   74 +
 src/implementations/plots.py                  |   80 +
 .../stochastic_gradient_descent.py            |   33 +
 src/logistic_regression.py                    |   61 +
 src/neural_network_torch.py                   |   93 +
 src/utils.py                                  |   69 +
 test/__pycache__/test_utils.cpython-36.pyc    |  Bin 0 -> 1105 bytes
 test/test_utils.py                            |   18 +
 13 files changed, 2267 insertions(+), 15 deletions(-)
 create mode 100644 src/implementations/costs.py
 create mode 100644 src/implementations/ex02.ipynb
 create mode 100644 src/implementations/gradient descent.py
 create mode 100644 src/implementations/grid_search.py
 create mode 100644 src/implementations/helpers.py
 create mode 100644 src/implementations/plots.py
 create mode 100644 src/implementations/stochastic_gradient_descent.py
 create mode 100644 src/logistic_regression.py
 create mode 100644 src/neural_network_torch.py
 create mode 100644 src/utils.py
 create mode 100644 test/__pycache__/test_utils.cpython-36.pyc
 create mode 100644 test/test_utils.py

diff --git a/.idea/workspace.xml b/.idea/workspace.xml
index 8d70011..26a24d7 100644
--- a/.idea/workspace.xml
+++ b/.idea/workspace.xml
@@ -1,7 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
   <component name="ChangeListManager">
-    <list default="true" id="051e3967-26e7-4bb3-88a5-b601a6048d74" name="Default" comment="" />
+    <list default="true" id="051e3967-26e7-4bb3-88a5-b601a6048d74" name="Default" comment="">
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/cs_433_ML_project_1.iml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/inspectionProfiles/profiles_settings.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/markdown-navigator.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/markdown-navigator/profiles_settings.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/misc.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/modules.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/vcs.xml" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/workspace.xml" />
+    </list>
     <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
     <option name="TRACKING_ENABLED" value="true" />
     <option name="SHOW_DIALOG" value="false" />
@@ -17,18 +26,7 @@
     <fileColor scope="Non-Project Files (Material Palenight)" color="2f2e43" />
   </component>
   <component name="FileEditorManager">
-    <leaf>
-      <file leaf-file-name=".gitignore" pinned="false" current-in-tab="true">
-        <entry file="file://$PROJECT_DIR$/.gitignore">
-          <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="115">
-              <caret line="5" column="0" lean-forward="true" selection-start-line="5" selection-start-column="0" selection-end-line="5" selection-end-column="0" />
-              <folding />
-            </state>
-          </provider>
-        </entry>
-      </file>
-    </leaf>
+    <leaf />
   </component>
   <component name="Git.Settings">
     <option name="RECENT_GIT_ROOT_PATH" value="$PROJECT_DIR$" />
@@ -130,8 +128,8 @@
       <window_info id="Run" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="2" side_tool="false" content_ui="tabs" />
       <window_info id="Version Control" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
       <window_info id="Python Console" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
-      <window_info id="Terminal" active="true" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.32876712" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
-      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="Terminal" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.32876712" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
+      <window_info id="Project" active="true" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
       <window_info id="Database" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
       <window_info id="Structure" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
       <window_info id="Debug" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.4" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
diff --git a/src/implementations/costs.py b/src/implementations/costs.py
new file mode 100644
index 0000000..d7789c9
--- /dev/null
+++ b/src/implementations/costs.py
@@ -0,0 +1,16 @@
+# -*- coding: utf-8 -*-
+"""Function used to compute the loss."""
+import numpy as np
+def compute_loss(y, tx, w, type='mse'):
+    """Calculate the loss.
+
+    You can calculate the loss using mse or mae.
+    """
+    N = tx.shape[0]
+    if type == 'mse':
+        cost = 1 / N * (y - tx @ w).T @ (y - tx @ w)
+    elif type == 'mae':
+        cost = 1/N * np.sum(np.abs((y - tx @ w)))
+    else:
+        raise ValueError("type not recognised")
+    return cost
\ No newline at end of file
diff --git a/src/implementations/ex02.ipynb b/src/implementations/ex02.ipynb
new file mode 100644
index 0000000..20e5e80
--- /dev/null
+++ b/src/implementations/ex02.ipynb
@@ -0,0 +1,1733 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Useful starting lines\n",
+    "%matplotlib inline\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Load the data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import datetime\n",
+    "from helpers import *\n",
+    "\n",
+    "height, weight, gender = load_data(sub_sample=False, add_outlier=False)\n",
+    "x, mean_x, std_x = standardize(height)\n",
+    "y, tx = build_model_data(x, weight)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((10000,), (10000, 2))"
+      ]
+     },
+     "execution_count": 99,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y.shape, tx.shape"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1 Computing the Cost Function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Fill in the `compute_loss` function below:\n",
+    "<a id='compute_loss'></a>\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_loss(y, tx, w):\n",
+    "    \"\"\"Calculate the loss.\"\"\"\n",
+    "    N = tx.shape[0]\n",
+    "    cost = 1/N * (y - tx @ w).T @ (y - tx @ w)\n",
+    "    return cost\n",
+    "# print(compute_loss(y, tx, [1, 2]))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2 Grid Search\n",
+    "\n",
+    "Fill in the function `grid_search()` below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def grid_search(y, tx, w0, w1):\n",
+    "    \"\"\"Algorithm for grid search.\"\"\"\n",
+    "    losses = np.zeros((len(w0), len(w1)))\n",
+    "    # ***************************************************\n",
+    "    for idx_0, w0_elem in enumerate(w0):\n",
+    "        for idx_1, w1_elem in enumerate(w1):\n",
+    "            losses[idx_0, idx_1] = compute_loss(y, tx, np.asarray([w0_elem, w1_elem]))\n",
+    "    # ***************************************************\n",
+    "    return losses"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us play with the grid search demo now!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Grid Search: loss*=84.84896629356497, w0*=66.66666666666669, w1*=16.666666666666686, execution time=0.019 seconds\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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bdvEiw3EIw3mRPbRhz7bwcb+SFarvp4OwiPN97nzfuGgibOlUwWo+co0kI/bH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\nRHLq/wNgkp9rtzq/IAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x114dd2748>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from grid_search import generate_w, get_best_parameters\n",
+    "from plots import grid_visualization\n",
+    "\n",
+    "# Generate the grid of parameters to be swept\n",
+    "grid_w0, grid_w1 = generate_w(num_intervals=10)\n",
+    "\n",
+    "# Start the grid search\n",
+    "start_time = datetime.datetime.now()\n",
+    "grid_losses = grid_search(y, tx, grid_w0, grid_w1)\n",
+    "\n",
+    "# Select the best combinaison\n",
+    "loss_star, w0_star, w1_star = get_best_parameters(grid_w0, grid_w1, grid_losses)\n",
+    "end_time = datetime.datetime.now()\n",
+    "execution_time = (end_time - start_time).total_seconds()\n",
+    "\n",
+    "# Print the results\n",
+    "print(\"Grid Search: loss*={l}, w0*={w0}, w1*={w1}, execution time={t:.3f} seconds\".format(\n",
+    "      l=loss_star, w0=w0_star, w1=w1_star, t=execution_time))\n",
+    "\n",
+    "# Plot the results\n",
+    "fig = grid_visualization(grid_losses, grid_w0, grid_w1, mean_x, std_x, height, weight)\n",
+    "fig.set_size_inches(10.0,6.0)\n",
+    "fig.savefig(\"grid_plot\")  # Optional saving"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3 Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Again, please fill in the functions `compute_gradient` below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def compute_gradient(y, tx, w):\n",
+    "    \"\"\"Compute the gradient.\"\"\"\n",
+    "    # ***************************************************\n",
+    "    gradient = -2/np.shape(tx)[0] * tx.T @ (y - tx @ w)\n",
+    "    # ***************************************************\n",
+    "    assert np.shape(gradient) == np.shape(w)\n",
+    "    return gradient"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Please fill in the functions `gradient_descent` below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def gradient_descent(y, tx, initial_w, max_iters, gamma):\n",
+    "    \"\"\"Gradient descent algorithm.\"\"\"\n",
+    "    # Define parameters to store w and loss\n",
+    "    ws = [initial_w]\n",
+    "    losses = []\n",
+    "    w = initial_w\n",
+    "    for n_iter in range(max_iters):\n",
+    "        loss = compute_loss(y, tx, w)\n",
+    "        dw = compute_gradient(y, tx, w)\n",
+    "        w = w - gamma * dw\n",
+    "        # store w and loss\n",
+    "        ws.append(w)\n",
+    "        losses.append(loss)\n",
+    "        print(\"Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}\".format(\n",
+    "              bi=n_iter, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))\n",
+    "\n",
+    "    return losses, ws"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Test your gradient descent function through gradient descent demo shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Gradient Descent(0/49): loss=5584.473425518334, w0=14.658784400421027, w1=2.6959424869977586\n",
+      "Gradient Descent(1/49): loss=3585.140831597294, w0=26.385811920757874, w1=4.852696476595991\n",
+      "Gradient Descent(2/49): loss=2305.5679714878243, w0=35.76743393702738, w1=6.578099668274586\n",
+      "Gradient Descent(3/49): loss=1486.6413410177618, w0=43.27273155004294, w1=7.958422221617478\n",
+      "Gradient Descent(4/49): loss=962.5282975169247, w0=49.27696964045539, w1=9.062680264291775\n",
+      "Gradient Descent(5/49): loss=627.0959496763892, w0=54.080360112785364, w1=9.946086698431223\n",
+      "Gradient Descent(6/49): loss=412.4192470584457, w0=57.923072490649346, w1=10.652811845742791\n",
+      "Gradient Descent(7/49): loss=275.0261573829619, w0=60.997242392940514, w1=11.218191963592046\n",
+      "Gradient Descent(8/49): loss=187.09457999065276, w0=63.45657831477345, w1=11.670496057871445\n",
+      "Gradient Descent(9/49): loss=130.8183704595749, w0=65.4240470522398, w1=12.032339333294962\n",
+      "Gradient Descent(10/49): loss=94.8015963596851, w0=66.99802204221288, w1=12.321813953633773\n",
+      "Gradient Descent(11/49): loss=71.75086093575561, w0=68.25720203419135, w1=12.553393649904825\n",
+      "Gradient Descent(12/49): loss=56.99839026444069, w0=69.2645460277741, w1=12.738657406921666\n",
+      "Gradient Descent(13/49): loss=47.55680903479934, w0=70.07042122264032, w1=12.886868412535142\n",
+      "Gradient Descent(14/49): loss=41.51419704782875, w0=70.7151213785333, w1=13.005437217025921\n",
+      "Gradient Descent(15/49): loss=37.64692537616756, w0=71.23088150324767, w1=13.100292260618547\n",
+      "Gradient Descent(16/49): loss=35.17187150630441, w0=71.64348960301918, w1=13.176176295492647\n",
+      "Gradient Descent(17/49): loss=33.587837029591995, w0=71.97357608283637, w1=13.236883523391926\n",
+      "Gradient Descent(18/49): loss=32.57405496449607, w0=72.23764526669014, w1=13.28544930571135\n",
+      "Gradient Descent(19/49): loss=31.925234442834643, w0=72.44890061377315, w1=13.32430193156689\n",
+      "Gradient Descent(20/49): loss=31.509989308971342, w0=72.61790489143955, w1=13.35538403225132\n",
+      "Gradient Descent(21/49): loss=31.24423242329884, w0=72.75310831357268, w1=13.380249712798866\n",
+      "Gradient Descent(22/49): loss=31.074148016468417, w0=72.86127105127919, w1=13.400142257236903\n",
+      "Gradient Descent(23/49): loss=30.96529399609695, w0=72.9478012414444, w1=13.416056292787331\n",
+      "Gradient Descent(24/49): loss=30.895627423059217, w0=73.01702539357655, w1=13.428787521227674\n",
+      "Gradient Descent(25/49): loss=30.851040816315066, w0=73.07240471528227, w1=13.438972503979949\n",
+      "Gradient Descent(26/49): loss=30.822505387998817, w0=73.11670817264685, w1=13.447120490181769\n",
+      "Gradient Descent(27/49): loss=30.804242713876413, w0=73.15215093853853, w1=13.453638879143226\n",
+      "Gradient Descent(28/49): loss=30.79255460243806, w0=73.18050515125186, w1=13.45885359031239\n",
+      "Gradient Descent(29/49): loss=30.785074211117532, w0=73.20318852142253, w1=13.463025359247721\n",
+      "Gradient Descent(30/49): loss=30.78028676067239, w0=73.22133521755906, w1=13.466362774395988\n",
+      "Gradient Descent(31/49): loss=30.777222792387498, w0=73.23585257446828, w1=13.4690327065146\n",
+      "Gradient Descent(32/49): loss=30.77526185268517, w0=73.24746645999566, w1=13.47116865220949\n",
+      "Gradient Descent(33/49): loss=30.77400685127568, w0=73.25675756841757, w1=13.472877408765402\n",
+      "Gradient Descent(34/49): loss=30.773203650373603, w0=73.2641904551551, w1=13.474244414010132\n",
+      "Gradient Descent(35/49): loss=30.772689601796273, w0=73.27013676454511, w1=13.475338018205916\n",
+      "Gradient Descent(36/49): loss=30.772360610706784, w0=73.27489381205713, w1=13.476212901562542\n",
+      "Gradient Descent(37/49): loss=30.772150056409508, w0=73.27869945006674, w1=13.476912808247844\n",
+      "Gradient Descent(38/49): loss=30.772015301659255, w0=73.28174396047443, w1=13.477472733596086\n",
+      "Gradient Descent(39/49): loss=30.77192905861909, w0=73.28417956880058, w1=13.477920673874678\n",
+      "Gradient Descent(40/49): loss=30.771873863073385, w0=73.2861280554615, w1=13.478279026097551\n",
+      "Gradient Descent(41/49): loss=30.771838537924136, w0=73.28768684479024, w1=13.47856570787585\n",
+      "Gradient Descent(42/49): loss=30.771815929828612, w0=73.28893387625324, w1=13.478795053298489\n",
+      "Gradient Descent(43/49): loss=30.771801460647485, w0=73.28993150142362, w1=13.478978529636601\n",
+      "Gradient Descent(44/49): loss=30.771792200371557, w0=73.29072960155993, w1=13.47912531070709\n",
+      "Gradient Descent(45/49): loss=30.771786273794966, w0=73.29136808166898, w1=13.479242735563481\n",
+      "Gradient Descent(46/49): loss=30.771782480785944, w0=73.29187886575622, w1=13.479336675448595\n",
+      "Gradient Descent(47/49): loss=30.771780053260173, w0=73.29228749302601, w1=13.479411827356685\n",
+      "Gradient Descent(48/49): loss=30.771778499643673, w0=73.29261439484185, w1=13.479471948883157\n",
+      "Gradient Descent(49/49): loss=30.771777505329123, w0=73.29287591629452, w1=13.479520046104335\n",
+      "Gradient Descent: execution time=0.033 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "# from gradient_descent import *\n",
+    "from plots import gradient_descent_visualization\n",
+    "\n",
+    "# Define the parameters of the algorithm.\n",
+    "max_iters = 50\n",
+    "gamma = 0.1\n",
+    "\n",
+    "# Initialization\n",
+    "w_initial = np.array([0, 0])\n",
+    "\n",
+    "# Start gradient descent.\n",
+    "start_time = datetime.datetime.now()\n",
+    "gradient_losses, gradient_ws = gradient_descent(y, tx, w_initial, max_iters, gamma)\n",
+    "end_time = datetime.datetime.now()\n",
+    "\n",
+    "# Print result\n",
+    "exection_time = (end_time - start_time).total_seconds()\n",
+    "print(\"Gradient Descent: execution time={t:.3f} seconds\".format(t=exection_time))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "eb33eb71975a417581d03abb8c1003a8"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<function __main__.plot_figure>"
+      ]
+     },
+     "execution_count": 106,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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oIV3D5Mnq9i3EbNRMMSHXB/ptf1Wzxhnx4mPAzSLy+8AgYLiIfAf4AzRuDuD/\nAt/y9rvqZ7rT208dD9+zQ0RKUVft/uwvxTCiI1N3oS/4Vq/Wkh0AL7+s7bVqazXBwbd+lZWp1Qw6\nW9/8oIRDhzqP9UbEdcWHP3xmv1VQS11Dg4q12bO1DMkll2hB4MrKoDxKX6ySccSSHYzOmIjLPvZv\n2iecc3Occ+c75y5Akxj+0zn3OTQm7hrvsk8AW7z954G7vEzU8Xj9TJ1zrcBBEZnmZavOpnMP1Lu9\n/du9d1h8nNGv6KoQbip+QsCCBRrjBtpqC1QYTZummaOtrSrMfLHWXXHfbLJxoxb8BbXOgc6zri4o\nL7J+vY7/8ped111ISQyZYha5uJGIegJGvyJBf/6e+gLwpGdBOwrcCz32M60Dvg0MRpMcVnrjTwNL\nvcSI91DBaBhFSTg+7PLL1RJ34IAKuP/9v3X8+uvPLPSbS0pKNMbOx4/Lu+oqzWBdsEBLjPjJGLNn\na7uuBQs6P6eQkhgypSiFXKwTHaLELEe5wzJYs4Jzrhlo9vZfAa7o4rq0/Uydc+uAyWnGjwJ3ZHGq\nhtGvmDxZe5QCPPqolhLpjoEDte5btgiLuLCoe+MNbf+1ZIla4dauVUFXV6clSFIppCSGTDHX6lnS\nb+PjDMMwjKIgmVTLVW2tCiB/rKEh6E367rs63tamrbcefVR7mO7fr2U/KirSPzubIi6VsWM1Rm/i\nRBVx06Zp/J0v4nbt0i4OxUJRWuSMNJg1zjAMo9/RXXB/Y6OKMtBepGvWqLWqqQlefFGTBYYMCZ6T\nTKpLc9AgdWceOJDftfj43RZKSmDWLI2Xu/tuTWiYMUOtc21tel1/SWjoDrPIxYlERO81EZcfovp3\nTkTzWsMwoqe74P76+sAit2CBCp81a/TcJZdoAsHhw2p1q6hQC9yJE0FXhXww3Cv5HW7VBZopu2cP\nbNmiwvPBBwN3akVF524O/R2zyBmGYRhGP6W74P6amqBO3Nq1KoJaW4Okhhu9BnbHjwd128KxavnA\nz4RNfe9FF2kf1Rkz4Itf1DIp8+YF1sf+ltDQHUVnkbNEhxTMGpdf7N/bMIw80lXJkXBT+GRSi/+2\ntmqM2YIFKogGDdJry8qC+w4ezN/cIahH51NZqZ8TJzRrdvFi7TABgejLtMxKf8EscmeBJToYBUcC\nc7EahvFbfJdrezs0N6uIq6pSl+QDD6iFzndn5qs+XDoGDIDSUrUK1taqtbCpSWPg/FZdfq27rhIv\n+jtFZ5EXuQy7AAAgAElEQVSLLYkI3mnWoWiwf3fDMPJM2AIHaoGbNk1Fmt8b9Zxz4GtfC/qpjh0b\n3F9eriVIRPI779Ong24QV12lXRpmzercV/WDH9S1zZ7deY3Fggk5wzAMw+jnzJ2rFrh58/R4+XKN\nK6uoCCxae/aoiBs5Urs1hAXRkCGaWJDrfifhpAYRFZMTJ8JttwXvXrIEXntNxSbAeefp+pYv739d\nGzLBXKvFilmFio8E5l41jCJnzRoVaOGEgIYGuOUWLTcCWlYktbRIvkqNnD4d7DsH1dU6r4ED4d/+\nTQWmn6AxbZpa6Roa9LjYkhx8ikrIxTbRIZHn95mIix7r9GAYRh6ZM0cFkZ/d6Rx0dGiB30OH4De/\n0evKy9XFeviwZqrms9TIgAFnWvzGj9c5+Z0k1q9X4XbwoMbK1dVpvN/MmWqRS1cvr79TVEIuG1ii\ng2EYhlFo1NRoi6158+DVV7XxfCp+od/W1vzPDzpb40AL/Q4dquJz/HiNiztxQt2nviWxrU2PV6/W\n60T6XwuunjAhZxhRYVY5wzByQLibA3S2WDmnIq66WmPiQMXPiBH5Ly2Syrnndj7+7ndh1Srd9zNU\n9+1Tl2pDg4rTZDLo6LBiRfG5VcGEXPFhbtXiJoHFyRlGP8cvLSKiwm3+/KDl1qRJmvV56BC89JJa\ntJyLrt1WmL17g/3yct2uWaOFf998EzZtCrpQhNuO+Ra4qUX6d3HRCDmLjzNiiVnlDMPIMjNnqqtx\nxoygifzKlXpu0yYt8OsnNoQtc3Hi2DG47z518w4apPNfuDCIifOFarG5UdNh5UcMwzAMox/hlxZZ\nsUItVm+9pS7Jqiq1aPmdEIYMgXvu0fHKymjn7DNkiFoM6+rgqaeCenaPPqrWQwhq4M2YEe1c40LR\nWOSyQcEnOphb1QBzrxpGPySZVOtUR4ce19UF8WJPPqlN5UeM0Jizffu0Xtvhw/D3f6/WrwExMOtU\nVWlyw+23w5e/rB0nrrgCli4NrqmsVFewL1SL1Z0apiiE3LuMZmLUkzCMrjD3qmEYfaSxUctx+NTV\nBWU4pk7VjNUpU/Q4XOj35EndpmaMRsGJE/Duu3D33cHY9u1aEPiSS9QNXFenrmLfdWwUiZCLLYmo\nJ2AYhmH0B+rrtd3W6tUaB9ferqKno0PLeHR0aDJBVZUmPKxerfedOhXtvAcMCESk7zr1GTQIjhxR\n1/CttwbxcI2NZpELE3shJyLvAO3AKeCkc26KiJwD/CtwAfAOcKdzLgY5NzHG3KrxJt9WuQT2h4Rh\n9CNqalTgJJOaFNDW1tlCN9FzS915J+zeHc0cU6mt1Tnec4+Kz0mTgsb3N94IiYSeg87Wt2Lt4NAV\nMfCKZ8S1zrnLnHOeYZgG4CXn3ATgJe84pxR8fJxhGIbRL0kmOzeLd04TGoYMCYTRkSMaf3bBBfAf\n/xHZVAHNmgUtgXLfffDQQ5q88PTTMG6c7icSmuQwbJiKvBUrgvv9kiPF1sGhK2JvkeuCW4Dp3v5i\noBl4JKrJxB6zxhUGFitnGEVPuJhvd0LFT24AdZsuXaru1IoKLc0xdKgmM/iu1C1bVDg9/HB+1tEd\nx4/rvN56S48feEDntmSJxsL5blPnYO1aFXZmfeuaQrDIOeAnIrJeRO71xqqdc34Tkd1AdTRT6wOJ\nqCdgGIZhxA2/RtrChV1fk0zCHXeoW7KpSYv9gsa97dqlouerX4XBg7XZfHs7PPKI7vsMHAiXX57b\ntXTH4cOaRVtZqSKutlbn6e/PmKGdJurqNFHDrG9dUwhC7uPOucuAm4B6Ebk6fNI551Cx1wkRuVdE\n1onIuuPvtqWeNgwjEfUEDMNIpb5e3aTdWaAaG9VSVVurnz171A25aZNa5oYP1ybzR45oQd1Nm7Qm\n2113Bc84cQJeey336+mKw4fh/fc1oQHgqqvUjervL1+uInX4cBNxPRF716pzbqe33Ssiy4ErgT0i\nMsY51yoiY4C9ae5bBCwCqJxy0RlCzzAMwzDiRrjlVFf4GarOaamOFSvUgrVkiZ6fMQMWL9Y4Ob9H\n6bZt+okTpaXw2GMqKNvbdWz0aE3IAEtoyJRYW+REZKiIVPj7wCeB14HnAb/SzN3AD6KZoWFkGYtn\nNAyjB2pqNBauqUkL/c6YoRashgaYPVs7HzQ1qdUrrgwerDXstm7VtSxdqp9DhwIh62/DiRzGmcTd\nIlcNLBcR0Ll+zzm3SkR+DiwTkXuAXwN3RjjHeGPCwDAMo99RX68xcS0tcN11KoBEtHNDa6sKpT17\nNOnh0KGoZ3smt9+uGaq+xa29HdasUfHZ1KSxc3PnWl/VTIi1kHPObQMuTTO+H7gu/zMyDMMwjOip\nqYEFCwIRN3asiqK33oKNG4NCv1GKuMrKzkV+Bw/WeU+dqkJ08WLtoTpsGMyZo9f89Ked24tZzbie\nibWQMwzDKGRE5CHgT9GErF8CfwwMwQqaG1lg+XIVakOHwt/+rbpZX3hBzx0/3rlrQq4pK9N3+owc\nqQKtrU1j4UaM0B6vb72l8128uHPBYt8C94EPqHvYJ5OYwWIn1jFycSHrxYAT2X2cYRjxQ0TGAX8B\nTHHOTQZKgLuIoKC50T/wC/+uXavbj35U67EdOgRPPAHPPQdHj6oFCwIRV1KS+7mFRRxo0sJeLw1x\nxAhNaKit1eMNG3SOs2ZpjbvZszXOr6FBs2nDa7XYuJ4xIWcYhpE7SoHBIlKKWuJ2oQXNF3vnFwPW\n+tvICD9ebOZM3X72s2rlAnj7bXWvApx/fuf7Tp9WK1g+SSbh2DEtL1JRoS7UpqbAbdrQEHRtGDZM\nrYvz5wfiL5N6eoZirlXDiBv57PCQwCzEOcI5t1NEHgd+AxwBXnTOvSgihV/Q3IiEmTO1xEhrq7or\n/azU0lK1xPmibuxYLabrx6c5l/9YuSNH1BLonJZA2b5dBV17e+dyIz5+LNy553Y+tti4njEhZxiG\nkQNEZCRqfRsPvA/8XxH5XPga55wTkbR1Lr1ONvcCVFdX09zcnNF7Ozo6Mr620CmktZ44odamc8/t\n3GEhEzo6Ovjxj5vZuhX+8i/1/hMndDt4sIq4VNdm3BgxQuf77rtwqZfCOGQIXH89jBmjFsUbbgjW\n2toKH/4w/OpXeq6/kc3vXRNy/RkrPWL0I0SkBFgH7HTOfVpEzqGLpAERmQPcA5wC/sI59yNv/Arg\n28Bg4AXgAU9MlQNLgCuA/cBnnHPv9HHK1wPbnXPveu9+DvgoGRQ0h85FzadMmeKmT5+e0Uubm5vJ\n9NpCp5DW2tCgrsKGhsyD9/2+q9dd18xLL01n/nwdv+02Le47eTKsXw+bN+du3mdDebm6VcPMnq3u\n3Zde0oSHqiq1IE6b1rkFV3NzM6tWBWvtzb9XIZHN710TcoZhFAoPAG8Aw71jP2lgnog0eMePiMjF\naFLBJGAs2qt5onPuFNAEfAFYiwq5G4GVqOg74Jy7SETuAuYDn+njfH8DTBORIahr9TpUiB5CC5nP\nwwqaFw1n4yr048QuuEDdqr47sr1dEwY2bNDs0LiRKuJABeemTbr+W2/V5IYHH9Q6eAsXdhZrfucK\nMNdqJpiQMwwj9ojI+cCngMeAL3nDtwDTvf3FQDPwiDf+jHPuGLBdRLYCV4rIO8Bw51yL98wlaKLB\nSu+ehPesZ4Fvioh4vZzPCufcWhF5FngNOAlsQC1sw7CC5kVHT2U0fOtbfX1gnfKL/h46pG24Ght1\n/LbbdFtWBge8wjX5LDXSHSUlWsNu0iT40Id0/vv2weWXwx/8gQozf33LlqmISxVrNTXBWo2eMSFn\nGEbUVInIutDxIs+tGGYB8DBQERrrKmlgHNASum6HN3bC208d9+9JAjjnTopIGzAK2HdWK/Jwzn0V\n+GrK8DGsoLmRQroOBjU1KnZefjnoP5pMwiuv6L4fF1daqu2uoqS6Wudz4IDur1yp808mA7HmCzgf\nqxGXHUzIGUYcyWfmah95f/Bwnr90Wh+e8OI+59yUrs6KyKeBvc659SIyPd013SUNGEYh0JXrtaZG\nW1n5IqixUZMmBg/WzNCRIwOrXJTs2aNzPHAAPv7xYL41NbqmVGujkT2sjpxhGHHnY8DNnmv0GeAT\nIvIdvKQBgJSkgZ1A+NfF+d7YTm8/dbzTPV7Nt0o06cEw8oJvnfKFTjKpCQK1tVpGpK5Oj//7vzVR\n4CMf0W3YnVpWlt85V1QExYdBM1JBLXJhrCZcbjGLXL5JRD0BwygsnHNzgDkAnkXur5xznxORvyN9\n0sDzwPdE5BtossME4GfOuVMiclBEpqHJDrOB/xO6525gDXA78J99iY8zjL6wdq0mN7R6gQPbtnVu\nZwVBzThQMeWcfvKFyJm14I4e1SzUhpReJVYTLreYRa6/YqVHjExJRD2Bs2Ye8D9EZAta6mMegHNu\nE7AM2AysAuq9jFWAOuBbwFbgbTTRAeBpYJSXGPElrG2WkUN6aj/1wAMq4nwL2+nTan1LxW+95Qs4\nv71VPkgnGkeN0mLEjz6qos1vJQadrY1GdjGLXA9kvc+qYRhnjXOuGc1OxTm3ny6SBpxzj6EZrqnj\n64DJacaPAndkcaqG0SXpEhvCfPnL8MUvqlALi73p07VcR7ifqm+Nywfp6sNB0LFh/37t9+qzYYPO\nt6t1GtnBhJxhGIZh5BG/TlpbWyDU/GSAXbvgvvvUIlderudE1JX685+riAMVb6dOpX9+rujK4jd6\ntK5n4kR1rR46pO7gOXNgzRpzqeYac60aRlwx97hh9EtqatSK1dSkCQC+hW7evCA2rrQ0sH4NGKB1\n2Z58EsaPj27e6erUlZTAxz6m+9dfD4sXw0UXqTVuzRpzqeYDE3KGYRiGkWdmzlTr1YwZaolraFCr\nVmurZn0+9ZRmrFZVqeXtnXfU8rVrV9fPDGeQ9pUBKepgxIj01/lN7mtrNasWgrVddVX3sYBGdjAh\nZxiGYRh5ZvlyjR978EE9DseQVVVpH9Vp02DKFBVohw5pR4d0MWo+2YyVS7W+vf9++uvOOQeWLlUL\n3IoVOuavLZEILI1G7jAhZxiGYRh5JJmEgwfVitXSokKnrg5ee03Pb9oEn/qUul5XrQoEWlTdGyor\n9eMzdKgWJJ4+Xd2mVVUqMq+6SsXnRz+qlrjJXlpRe3tny1xPWbtG77Bkh/6IxVYZhmFESrreqT6N\njSrSZs3S4+Zm2LxZ92trdbthQ+/el8vs1SVLdHvHHdqG64YbYMECPW5u1nM7d8LXvqYlR+bO1fi4\nZFK7UuzcqZa59nZde09Zu0bvMCFnGIZhGFmmO7Eycya8+KJa4DZt0rHJk2HgQPjsZ+HrX+/9+3JZ\nguSee+Cmm4Leruedp+tbu1aTMMrKVNiBuor9fb9bRWrWqhUIzi4m5PJJIuoJFCZDOczTPMY9PMoh\nhkQ9nf5JAvv+NIws0p1YWbw4sLjV1qpL0jm10m3cmF6UlZere3Pv3jPP5Zp9+1S0AXzwg2pZ271b\n597UpEWAfbG6bNmZFsg5c3Tu/r+FL/CM7GAxckbsuY51fIaX+ATrop5K/jE3uWEUJKm9U9MxaZLG\nlPnZntXVKuJKSs7MGj12LP8iLpypOnCgbocM0eSG555TMfrgg7rOpqagnAqcGQdnDe9yh1nkjNgz\nk2YcMJPV/DtXRz0dwzCMPuFbqNraVPy0tKgouvVWLS8yYYKKpajxM1VF4KGH4Fvfgj/9UxVo+/Zp\nkkNLC1x+eWBt87dh17JzFhOXS0zIGTHH8WleQYA/4BXAAVkslmQYhnGWdJfQ0N1531qXTKqg27lT\nhdzQoSrimpvz23qrO/x5/MVfwOHDahnct0/PXX01bN+uXRx279bad/46U13LFhOXO0zIGbHmYrYz\nCI2wHcQxPsw7vEGEpc0NwzA8esq+7Ol8WND52Z1xsMSBxr0NG6ZJGC+/HIg3v7PEhRfC229rTJ/P\ngw9qtiqcGQdnlrjcYUKuG1a+fGvUUyh6fp9XKUErU5Zwmt/nv0zIGYYRC3rKvuxNdubOnfDCC2eO\n+7Fy+bbQHTigbt633tJYvn37dFtdrfFxoCJu0iT40IfUKudnqxr5xZId+hv9LDj+Tn7CYM8iN5jj\n3MlLEc/IMIxixw/kh+4TGtIlPISTAJJJFXnXX6+WuP37tZRHGL/DQj5FnEggIEeO1EzV2lqNk1uz\nRuvf+cV+y8rgiSe0lMrUqfmboxFgFjkjUp6lgdto7vL8MQZ2Or6UrTimdXn9vzGd2+ln/WB+uhau\ntZ+QhhEXunKZJpPB8Zw5gYDzY+VmzoQHHtBSHosWadstvzabz6hRmp166lR+1pIO53RuPr4F7v77\n4cgROHFC4+NqazW2b+FCc51GiQk5I1IaqONCdjKBJMM4esb5ck50e+zTwSDe4gM0YNG0hmHklnQu\n02RSOx349dYqKwNx4wu/1av1/NCh6rr0KS+HQYM0i/W996IVcamE53nkiG737NFs27o67fJgSQzR\nYq5VI1K28gGm8G2+yr0copyTvfyWPMkADlHO33AvU/g2W/lAjmZaBCSinoBhFAbpXKZz5wadDurq\nAnHj91Wtq1Mr3bRp8OSTmixQVqai7tgxjT2rrdX9ODF4sK4J1M06apTGy/n179K5fK2Xan4xIWdE\nzmlK+AZ/yGUs5Zf8Dh0Myui+DgbxCy7iMpbyBH+Is29nwzAi5pprVMQ0NgYu1aYmGD4cXn1V6641\nNurx8eNw8qTe99ZbGnd27bXRzh9UpPnFgK+8UosBT5qk1rn9+/X8smWwfLlaGv0iwD6+BTJ13MgN\n5lo1YoNvnXuEJXyFf/ltkkM6jlDG17ibedxtAi5bJICfRj0JwyhMwm2o/E4H7e1qtXrxRc3wTCa1\nfIffnqu6Wt2UYVavzv/cy8qCWL0LL9R5v/++irfXX1fx5lsaQYVqTU3XWbnWSzW/mJAzYsVpStjE\n73Ccgd0KueMM5HV+x0ScYRixIF3/0DVr1PXoCzfQWDhQ8TQk1Dq6rAx++MMgSzWfhBMuBg+GTZuC\nOe3fr/sigYDz6apnqvVSzS/2W9CIHTNppoLD3V5TwWFmEsGfroZhGF3gx4bdeCOMGaMC7uWXYeJE\nFTcVFYEr9fhx7YoAKpKOH++cWBAFlZVaOw5UcNbXq1WttlYtc+YqjScm5IyYoS25BhBE0J5kAIdT\nEiEG4EItu/o5VnrEMGJFV8H8fmzY3LnQ2qrdETZt0vi3ZFJdlr6QGxD67RtOGBgQwW/lkhLdDhwY\niMmjR3U9FRXqJm5oODNL1xIa4oG5Vo1YcTHbO7lU/bIij1DPfBqZyG9+W6ZksLXsMgwjArqqI+fH\nhs2YAUuWqHBbu1aF3NChnWuzdeVCHT36zLi5XHPqFJSWwl13wbe+pdmp55yj8Xzz5+s6Ghs739NT\n+zEjf5iQ629cO7WguztoS65TnGQAxxjI33AvC7gLxwB+lyk8yL/yt/wj5ZxggLXsMgwjAroK5g/H\nhi1frq7IkSP1ONOyIvkWcaBrOXkSnn5aLXGtrVq8uL1dz/vbMJbQEB/MtdoNN139XNRTKDru5CcM\n5FTasiKpZUrKOGktuwzDyDvp6silMnOmZqX6rsooXKaZUuqZdC67DM49N7N7Mvk3MPJDjL+1jGJk\nN6P4a/682+K+fpmSh/lz9nBOnmdoGIbRM8uXB9a1QYPg8ss7Z6nGhQEDtOUWqDVu3Tq1soXj9ioq\nopmbkRkm5IxYcTN/n1FxX986dzN/n6eZGYZh9MzatVowd8IErb02apQKpJYWOHw4fpY5P1avqkoL\nEoOKuKYm3W9o0I8RXyxGzjAMwzAywO/UUF+f3qWYTMLNN2vT+1/8IuhNGiaKOnFhBgxQ0Xb0qMa4\nffSjmtTgi7dx44JrX38dHnvM3Kdxx4ScYRiGYWRAV5mayaQer1mjIg7SizjQ5IeBA4Pr8omICkn/\n3UOGwH33qfhMJoPOFKA18FpaNGHDslLjjQk5wzAMw0gh1fqWTMLBgzBrFrS1BfXTGhthyxZ4zsuN\nq61VwfTaa2c+s6xMLWJRiDifWbOCkiiHD8Mf/RFs3qzn/Li4mhrtpbpwoWWlFgJnLeRE5BHn3Pxs\nTsbIHRdeWM6XvjSGz31uFBUVJbS3n+I739nPN77RyrZtGebFG/nHigEbRiSkWt8aG9X1OG2aWqoq\nK1X4zJ+v2amgFq6mJvj4x4PnTJyoHRxOnNDuDX7LqyhwTgXm1Kkq5EpLoaNDBVtbW9Af1q8Z54qg\n3np/IGMhJyLLwofAZUBkQk5EbgSeBEqAbznn5kU1l4xJeJ88c+ONlTz77AQGDhTKyjTStrKylC98\nYTSf/3wVt9++hVWr2vI/MSM+JKKeQNeIyCDgZaAc/Zn1rHPuqyLyd8AfAMeBt4E/ds69790zB7gH\nOAX8hXPuR974FcC3gcHAC8ADzjknIuXAEuAKYD/wGefcO3lbpBE7UuukhYv9rlgRjLe3w7Zt2uz+\n8GEtBPyxj8Err8CUKVp+xM8KjQObNmk27axZuqYlS1TEdXTo+fZ2TW44eFCFnRX8jT+9yZ856Jy7\n0/vcAfwkV5PqCREpARqBm4CLgc+KyMVRzSfOXHhhOc8+O4GhQ0t+K+J8ysoGMHRoCc8+O4ELLyyP\naIaG0SPHgE845y5F/4C8UUSmAT8GJjvnPgK8BcwB8H4W3AVMAm4EFno/MwCagC8AE7zPjd74PcAB\n59xFwBNE+EeqER/CFim/btrUqYGwaWyE3bth1SqNiRszRo9Xr9aSI74LMy6Uez/m9+2Dl17SFmJ+\nC66KChVww4YFlsjUtlxGPOnRIicig5xzR4HHUk49mpspZcSVwFbn3DYAEXkGuAXYHOGcYsmXvjSG\ngQOl22sGDhQeeug87r//13malWFkjnPOAZ69gIHexznnXgxd1gLc7u3fAjzjnDsGbBeRrcCVIvIO\nMNw51wIgIkuAGcBK757XRWQk8CzwTRER791GEdJdCyo/O3XjxqBzw4AB2hHhpz/V43A7rigRUUFa\nWQnXXadJDK2tsGsX3HknLFgQWB79WEA/6cGyVQuDTCxyPxORv0ddmL/FOfdebqaUEeOAcKveHd6Y\nAZ3iqj73uVFnWOJSKSsbwKxZVbmelWGcNSJSIiIbgb3Aj51zqX3o/gQVZND1z4dx3n7quH9PKfBz\n4Huou3ZUFuY9QkSeFZFficgbInKViJwjIj8WkS3edmRf32Nkn/r6ri1Sc+eqiAN1p0JQVsTv5FBW\nlvs5ZsL48ZqAMW6cJmRs366lR6qrNdZvyZLOHRqsY0PhkUmM3GXAp4AnRGQA6pr4j7j/pSoi9wL3\nAgz6QPGKlIqKkp4vAoYNy+w6w0jlXUbzFH/Whye8WCUi60IDi5xzi8JXOOdOAZeJyAhguYhMds69\nDiAijwInge/2YRIAfwc8CHwSDdv4mWftf9o59/ZZPvNJYJVz7nYRKQOGAF8GXnLOzRORBqABeKSP\nczeyTLhvaleUlmoP1cGDzyw3It07QvJCTY3G6w0bpu7T6mpNxKiu1li4pUu1ZEoyacKtkMnEIjcC\n2AT8T+A54OvAtlxOKgN2AuFvu/O9sd/inFvknJvinJtSNroyr5OLE+3tpzK6rqMjs+sMIwfs8/+v\nep9FXV3oJTP8FC+2TUQ+D3wa+KPQH5dd/XzY6e2njv/2Hu8Z76J/5B4HRgLPisjXe7soEakErgae\n9uZ+3Jv/LcBi77LFqHvXiCnJpFrl6uo05q2hAW68UePhTp7UmnAf+UhwfUWFCrsPfzi6OfscP65i\n7dAh7aG6Z48mZjQ0aKHf2lp1tc6Lf6qg0Q2ZWOT2AWuA/wLagUXAwVxOKgN+DkwQkfHoD+C7gD+M\ndkrx5Dvf2c8XvjC6W/fq8eOnWbp0Xx5nZRiZIyKjgRPOufdFZDDwP4D5Xub6w8A1zrnDoVueB74n\nIt8AxqJJDT9zzp0SkYNeosRaYDbwf0L3PO5lyJYCG7znnvA8EVu8d/WG8ago/BcRuRRYDzwAVDvn\nWr1rdgPVvXyukUf8siMQFMmdNk3jzEpLNSP1bc9eW1Kili7Q2nJRM2SIijXngtp1GzZowsby5bqO\nDRuinaPRdzIRclOA+4FLgG8By51zkTYZcc6dFJE/B36Exu79s3NuU5Rziivf+EYrn/98VbfxGidO\nOJ54Ynf+JmUYvWMMsNjLPB0ALHPO/dBLYigHfizqx2pxzt3nnNvklUvajLpc6z3XLEAdQfmRlQRx\ndU9754aicXifc86dAHDOnRaRT5/FvEuBy4H7nXNrReRJ1I36W7zSJ2nDVMLhIdXV1TQ3N2f00o6O\njoyvLXSysdYTJ1TknHuuWtfCYyNGwMUXw7/8C5w6pW7UP/1TjYe7807dDhyobtTjx/u+nq44//wO\nHn+8OePrS0v1c/SoHldUqKA7fTpIftiwAT71KbUm1tRAXL5liuX7N5vr7FHIOedeA/5YREYBfwq8\nLCIvOOe+lpUZnCXOuRfQOlBGN2zbdozbb99yRh05UEvciROO22/fYkWBjdjinPsFUJtm/KJu7nmM\nMzPtcc6tAyanGT+Klivp6nlvZDrfEDuAHaHEjGdRIbdHRMY451pFZAwqHNO9cxHqAWHKlClu+vTp\nGb20ubmZTK8tdLKx1oYGzU5taAhi4vwxv/jvtGkqijZu1PiyPXv0upISGD1aS47kkscfb+av/mp6\nt9dUVKi7F7TkSVWVlhkBtcwdPgxDh6qbdexYTXxYvvzMtUdNsXz/ZnOdmZQfWY3+lTrEGzqNpvlH\nKuSMzFm1qo2PfOSXPPTQecyaVcWwYSV0dJxi6dJ9PPHEbhNxccW6OhQ0zrndIpIUkQ86594ErkOt\nhJuBu4F53vYHEU6z6Ekt/JtMammO2lqYM0cFTksL3Hor7NgRZKmCWulyLeIypb1dP37Swr59MHmy\nWgzr69VFPH48nHcezJ6tIm7mzM5rNwqTTFyrs4H30YLAsc5UNbpm27Zj3H//r61WnGHkl/uB73oZ\nq9L7FUEAACAASURBVNuAP8ZzD4vIPcCvgTsjnJ9B58K/jY2aIADwox+poBs7Vjs17AuFEk+cqNtt\n2zTpAeCaa9Qa1tpKZOz00neqquD3fg/uvjuIh2tqUuubb4mzrg39g0xcq/ab3zAM4yxwzm1E44xT\nuS7fczHSk1r4t74+SFhwTsWP75IcPFhdqYcOwcMPwze/GYg40I4OpWfdwfzsGDBA5+mL0dOn1f37\nyU/q3P0Ejbq6znXxzBLXf8jzt1zhcdPVz7Hy5VujnoZhGIaRA1JdqzU1QdP4ZFJFkJ/ZeeSIul1P\nntSkh3SEhV2uqazUJI0tW4IOEwcOwG23qft0y5ZgnrNna7ZqMmlWuP6GCbn+yrVT4aepxe8NIw2J\nqCdgGLknLGDmzDmzk0FXhN2uIumF2sCBmumaa0pLO7//2LGgzMnAgZpp65cb+frXVYS2t8OmTbBi\nhQq5cDmVykoTdf0BE3KGYRhGvydTAZNM6rUzZ8J992mmamWlZq0e8/LCfFerTz5EHHQWcSUlQXmR\n8nIVcdXVmuDgd3HwaWiAGTN0O3Nm4Do212r/wIRcvklgFhDDMIw8E459607AzJ2rQujFF4N+qm1t\nuvVLeuQ7Di4dp0LNeHyB6ZdFaWiAq67StSxYoMkaN9+s62lvD1zHRv8gkxZdhmEYhlHQ+LFvjY2Z\n9RW95BKtvxbmmmtUzPnCLtdUVqrlbfBgtQKGCRd5LyuDQYN03y/4W1urfVR9d6ovStvbVeglk/lZ\ng5F7YvB3hWEYhmHEgzlzVEDV1cHVV6t79eRJmDQJ/t//61yCJNf4gvHIkcCVW1YGEyZo3Nv48WqF\nq66G7dvV8jZ06JmlRVIzca30SP/ChJxhxBErBmwYOcePh6uvPzP5Ye1a+MpXVMSNGRP0Ky0vD1yZ\nUXD8OFx+uQq648e1QLHfU/Wzn4XHH9fixWH3cWomri9Ujf6BuVYNwzCMosSvIbdwoQqcsMvxgQe0\nsO/QoboVUbF07bXRznn8eN1u2KBWuTFjdHvDDfDEEyo2W1q6dh/7QjUT97JRGJiQMwzDMIqS+vog\no/OOO1TU3Xmnirknn9RuCN/7nrpVN21S9+abbwb3D8jTb9ARI1REAtx0E7z7ru6PH69dGvw1XHWV\nxvB95CNqcbM4uOLAhJxhGIZRNIQtb751avlydaWOHavWrIULdf+aazT+zG979dZbGovmc/p07ubp\nJzNMnKgu1ERC593QAK+9pucOH9ZkBn8Nzz0HF10Eq1Zp5u3ChbmbnxEfLEauP2NFgQ3DMDrhu1Pb\n26GiQq1yfjLA7t0q1GbMgEcf1Z6rTz8N77+f/3n6NePee08F29y5sGyZzv9rX4O/+ZugLh4EHSpm\nzIAlS3TM4uCKAxNyhhE38pnokMjfqwwjDvii7dVXtSTH6tUqkCoqAgvWF7+oVjDQLNWRI7X1VZiS\nks613LJFWZm6bP1ivxUV+q733gvEZUNDYCX0CXeomGq5UkWFuVYz4Karn8vuAxPZfZxhGIaRGTU1\nmoG6caO6TVtaNC5u5swgDs3vrTppkro2U0Uc5EbEgQrID3xA3z1pkloIT51St+7rr3dufG8YYEKu\n/2NlLAzDMNJSWanJAS0t6o78wQ9UJPnJDddco7FyoFaxXM4DtLQJqGi75hpYuVLnM3KkisymJss4\nNc7EhJxhxAkT3oaRVVLLioAW/Z02TQWTX+D3+99X1+Xs2dqA3qelRbfZtMClisK2NhVqd96pIhLU\n5Tt3rs69pkbnu3hx53WkW5tRfFiMnGEUK4moJ2AYucdPbkjtZFBbq7Fymzbp8YEDGn/2k59o3biq\nKhVTl16qGa2plJZ2bmKfDr9dViqnTqlb1++NOmCAFhleulQtcBUVKiA3bVJr3eTJQWJDZWWwjq7W\nZhQXJuSiIoH9IjU6Y9Y4w8g6fjZnXZ0Ksvvu03pwW7bArFmaXODHxA0aFBT/3bdPPyJqEUu1evUk\n4kDF3okT6c+F+7iePg2bN6u4bGjQsXnzVGi2tWkdudmz4Ze/1KzUdGszihdzrRYDJhAMwyhSwp0M\nHnhAkxy2bNFzFRWd4+L8TNGwFc25s3NdVlV1X2fu8GEYNUo7M/ixcVddpfP0W2qNHauWuPff1+s2\nbIAVK9KvzSheTMhlSNYzVw3DMIy88uST6qacOFEtXJdfDlOmwLZt6S1n557b/fMGD+763L593Xd+\nePdd2L9ft8eOqWjz4938bX29isxTpzSrNtOMVYudKy5MyBlGHMi31TSR39cZRhyYOhU+9SlNchg7\nFr7yFe1NumqVjkFnl+fevZ3vF+l8fORI1+8aOlStcukYPFiF1pAh6qKtrtauDBC0Clu4UC1tFRUq\n9lasyNz6Fu4ha/R/TMhFSSKP7zL3qmEY/YCzsTalWrl8y9ZTT6mI8hvRV1fDP/yDxsqlI13iQlcc\nOaLxdqkMGqT9Ug8cUPcqwMc+piKzsVHj+KZNCyxv9fVw3nm9i4MLr9Ho/1iyg2EYhlEwhDM1b7gh\n/TXJpF5XXx/Em6W25fJj0Wpr1dLV0qIxaF//ehArl45MOzoMGhQItTBHj6r1bdYstcwdORJYA8PJ\nC77lraYGxo3rXRxcuMuD0f8pCiE3mnejnoJhdI25VQ0jY8Ji5+23018TFnt1dXDwoG7b29Xd2N6u\nFqu5c2HNGk2AmDRJRd22bcFzBg48M3Yu7F4tLVUrXVlZZzdrVyKushLOOUddqocOBfdMnKhbE2DG\n2WCu1V5Q8AkP5l41DKPAySRT008SaGvTa5uaYPjw4HxHh4q9piYVcSNHas22DRuCDFII9svKAgEX\nPn/ypFrnBg0KYuuqqjTDNB1tbeq+3bQJXn45GD/vvMzXbxipFI2Qu49/jHoKhnEmJq4N46xIJrVx\nfLpYOT9JoKlJLV+1tZ2bzA8bBhMmqEUtlXCCQ0eH3jthQhAfV1YWnB8zRgXcnDnq/gTNVt2+Xa1s\ndXXqQgW1+NXV6bVjxgQdJcK14wzjbCgaIRdbElFPwDAMo7BIJjW7c/fuzpmZ6Up3/OIXamlbulTF\nXUODfr7yFbWoDRkCo0fr/en6qR46FLhJKys1ScG/7vRpPff440FtOp/2dnj1Vb2/rk77pjY26lhr\nqwq4ujoVm42NZwpSKyFiZIoJuWLDLEDFTSLqCRhG3/GzO4cO7ZyZGS674VvlNm4MRNPs2YFl7amn\ntATJ1VdrssHgweomHTBAn+vz1ltqYYOgwO+pU2rV27NHXaWpZUpAxdrGjZrY8NprKiZra1Xw+QKu\nokL7p86fr31Ww6LNSogYmVIUyQ6GEUtMVBvGWeEnPPzO73SOlauvD9paJZNaRHf1aliwQMt7NDQE\n2avOwXXXBX1U/cSD06fVihamvFyL9ra36/GAAfDxj+t+c3Nw3aRJ8JvfBNf517a0wB/+oT5340ad\nx/LlOpfZs9XV2tKios1PdsgkqcMwwIRcr7np6udY+fKtUU/DMAyjaPETHsIiyh+vqFCB5FvAWlq0\nmO7UqYE4amsLmtB3hV8aRERdrzt2BOdOn9YiwqWl6p4tKYEPfQg++EFNZICgTMnv/Z5mzW7YoEkV\n48Zpv9SxY4O5tLZ2rh0XXiP0LORSy60YxYW5VuNAIs/vM0uQUUCISI2I/FRENovIJhF5IOX8X4qI\nE5Gq0NgcEdkqIm+KyA2h8StE5JfeuX8Q0VxEESkXkX/1xteKyAX5Wp+RXWbODCxcIp0L49bU6H5H\nh1rPwmU/ysu13IjPhz6kW+dUxFVWBhmrlZUq9E6e1ONTp1TA+S7Y8P2TJqlIA7jgAnj9dRWW/lxA\nt8uWnb0IMzdscVNUFrn7+Eee4s+inoZhRCOmE/l/ZZY4Cfylc+41EakA1ovIj51zm0WkBvgk8Bv/\nYhG5GLgLmASMBX4iIhOdc6eAJuALwFrgBeBGYCVwD3DAOXeRiNwFzAc+k78lGtli+fIgmWD3bk0u\nmDFDzzU2qnVs6VI9rquDW28NLHS33qpJCUeOwK9+1fm5bW26raoKMk59ixzo+5qaYMkSPZ49WwWb\nL9YqK3Ue4TG/BEpDQ98saWE3rFF8FJWQM0JcOxV+ujbqWRhGjzjnWoFWb79dRN4AxgGbgSeAh4Ef\nhG65BXjGOXcM2C4iW4ErReQdYLhzrgVARJYAM1AhdwuB1H0W+KaIiHO9acpkxAFf1OzcGQi2e+7R\nfqV796rAmjVLXZ3t7XqcSGj26v79Qazc1KnwxhvaiaGtLYiTGzxYz48cqdesWqXirqlJj8eOVYEG\nQWJF2E06NfQ3XLYEmBUSLm5MyBlGvjHX9lnjuTxrgbUicguw0zn339K5m/k4oCV0vMMbO+Htp477\n9yQBnHMnRaQNGAXsy/4qjFyQTKqY6ejQjFKf6mrd+pmlzmkm6uuv62fLFnXDArzySnDfxRer6Jo/\nX8XZtGmageo/Z/Ro/VRXa/bqgw+qe9R3c65eHbh3uxJZJsCMbGBCLi4kiCZWzqxyRh852DGirwlA\nVSKyLnS8yDm3KPUiERkG/BvwIOpu/TLqVjWKHL+u3NrQj7O6uiA+bsMGuPdejVv70Y9UjFVXw+WX\nw69/rYLt5z/XWLeJE+H664MivWGLmS8AfXyLX3V1kHVaXw+7dmnJkVmzzN1p5B4TcmeBZa4aBUci\n6gl0yz7n3JTuLhCRgaiI+65z7jkRuQQYD/jWuPOB10TkSmAnEI44Ot8b2+ntp44TumeHiJQClcD+\nvi7MyA9+XbnaWhg/XpMOZs8O3Jhz56rVDFTElZbq8fr1enzuuUGNuLa2zjFrc+fqs++7r3Odt4ED\nNZFh0ya44Qa1AvpxdG+9peMVFZZFauSeostatVZdKZibL7/Yv3ev8TJLnwbe+P/t3Xu0XGWd5vHv\nM0EBh6tEYghxEgV0AtPcIkaxMbQ0F7sXAZYysceQdtDIJF4Yu9cidK+e3mvarAFXt2M7cpFGljBN\nGzMKklEQGvVI20owKAiBZgyCJJH7xRBakcBv/ti7SHFSdU6dc6r2u3ft57PWWamza1ft366qc86T\n993v+0bEZwAi4q6I2D8i5kTEHPJu0qMi4hFgLbC4GIk6FzgYuK241m6rpAXFc57Fjmvr1gJLi9vv\nBb7j6+OqrX2JrhUr8vB13XX5clo/+Uk+qGDdurxLtBXijj02H9HaGqBw6KH590cdlX+/++75vhdc\nsOMYK1fmIe6OO1454GHDBnjXu/L7P/WpHUuCXXwx/O3f5sf97GfLfU2smdwiZ2ZVdyywBLhL0h3F\ntj+LiOs77RwRGyStIR8MsR1YUYxYBVgOfAnYnXyQww3F9i8C/7sYGPEU+ahXq7CLLsqvUWtNojt6\nIt2DDson7d2+PQ9sS5bk3Z1vfzvcd18exJ55Jh/hevrpeSBrHyDROkZr0t5f/jJvvTv00Dz4tZb7\narW4tQ9cmD0bfvjD8l8TayYHuSrJSNMF5mvlypGqNS5Lc9h+iYjvAxpnnzmjvl8FrOqw33rgsA7b\nfwO8b0qFWqlWrIBbbsmXtmrXGkBwwAE7Wt6OOmpHd+eGDXmo23PPfAH7G2/MB0Ccdlq+XFbr2rrW\nMVrh7FOfylvqfvCDPOyNnjJkKgMXPKGvTYWDnJmZ1c7s2fkqCd2Cz6WX5gMcjj0WVq3aMeDhyCPz\nlrkNG/I531qL2P/kJ/mAhZkz8xY42Dlcta/d2loGrB/Bq9XyN9YIV7NuHOQmaegGPLhVzsxq5oUX\n8paxFSvy71sh6Pzz87D1x3+8I4hddFF+/dujj+5YRuuf/invLp0+HZ56CnbbLQ91556bX/82OlyN\nXuJr7737E7w8oa9NhYOcWRk8yKGxJE0D1pPPefeHkl4LfAWYAzwInBkRT6ersL4ee2xH2IrYsX6q\nlI9IXbduRxBrnyi4tQ5rluVfDz2Ud71CPvr0Qx/KH798eef1TzdtykPc8uX96Rb1fHI2FY0btQoe\nudqVw8bwyVIXYMAngHvbvl8JfDsiDga+XXxvE7RpUz7vWytsnX56Hs6WLMlXbGhNR3LaaTuueVu+\nPA9qS5bko0qPPBJOPDFf0WHGjHwgw7ZtcPnleSjca6/O4awVvFotfV7n1FJyi1zVZPiPr9mQkHQg\n8AfkAy8+WWxeBCwsbl8JjADnlV1bXbRWbIC8y7QVrFqjVlth66KL8pa2XXfNpyCBfITqtdfu3Gq3\nYEF+Pdzee+/crXnxxTuviToWd4taaqriVEmSMvKFrR8vNr081YCk88kXuH4R+HhE3Dje8x00f+/4\nzPoFr9h2KR+Zcp0Du0YuG8zT9szXyvVXypbObIL7v0u3jzc572h6y/zgsvXj79jHY9aFpK8C/wPY\nE/jTomv1mYjYp7hfwNOt70c9dhmwDGDGjBlHr169uqdjbtu2jT3a16iquS1b4JFH8tuvf30+wAHy\n6+O2bt3Gc8/twcyZ+bb774fnnssD3rRp+US/kF/3BrDffvmUI/vsk/+7//75xL5VN2zv6Viacq7j\nnefxxx/f8+/FKrfI/c+I+Ov2DZLmkc/vdChwAHCzpEPa5ogq1dANeDCzvpH0h8BjEXG7pIWd9omI\nkNTxf9PFMmWXAcyfPz8WLuz4FDsZGRmh133rYNOmHRP0nnnmK7s6r756hKVLF7JyZd5q95a35C1q\no/dbuTJvlWvt1+txR1/7lmqakGF7T8fSlHPt53lWOch1sghYHRHPAw8Uk3ceA3jqxX7yCNb+qVNr\nnPXbscCpkt4D7AbsJenvgUclzYyIhyXNBB5LWmXFtbpNYcdKC61Rqu3XyLX27RTUWt2frevlWkFs\nrGDWaUqQ1rZnn82nIvG8b1YFVR7s8DFJP5V0haR9i22zgLbV7thcbNuJpGWS1ktav/Xx3+50f6UH\nPGSpC8ADH8ymKCLOj4gDi8mKF5Mv+/UBXrkc2FJ2LBNm42gfWHDRRfD44zuukWuFvE2bXnkbdgS8\n1vVyrYEJYw1UaC371X7tW2tbhAc4WHUka5GTdDPw+g53/TlwCfBXQBT//g3wnyfy/O3dEgfN37t6\nFwLWgVvmpsZh2Dq7AFgj6WzgF8CZ4+xvhdEDC9pXdmiFsptuyoPWHXfsPMHu6MePNVChU+tep+lH\nzFJLFuQi4oRe9pP0d8A3im+3AO0N2QcW25IZ2HVyGdVpmXOYm7jUIS5Le3h7pYgYIR+dSkQ8Cbw7\nZT11NTpcta/ssGIFfO97+WhUyEemdgpa7eP7Jjt/m+d9syqpZNdqcd1Iy+nA3cXttcBiSbtKmgsc\nDNw22eNUunvV6it1iDNroNmzYc2aHdfMrVnT/bq3qXaJju66NUupqoMdPi3pCPKu1QchnyskIjZI\nWgPcA2wHVqQasdoobpXrXRVCXJa6ALM02gdGdNKvOd+8NqpVSSVb5CJiSUT8h4j4nYg4NSIebrtv\nVUS8KSLeHBE3pKyz5ZTjrhnME2eDedpJqUJAqTq/Rmalaq212mvLWPuKDFPRaSCEWSqVDHJlqnz3\napa6gDYOKt1V5bXJUhdgVp7WWqutrtKyujz7FQjN+qHxQa5fBtYqVzVVCSxV4tfErO96CWX77//K\nljGve2pN5CBXB1nqAkZxcMkd/7ZqvRZZ6gLM+qfXUNY+CnUiXZ4esGDDwkGOGnSvVlGVAkwKTT9/\nswHrJZSN7lqdSJenW+9sWDjI9dFAu1ezwT31pDU1zFTxvLPUBZj1Vy+hbHTX6kR4wIINi6pOP2JW\nTVUMcWYN9apXTX76D0/qa8PCLXKFfnWvulVuiDXpXM3MrBYc5GzqmhBwqnyOWeoCzKrLgxps2DnI\n1U2WuoAuqhx0pmqYz81syHlQgw07B7kBGPicctlgn37Shi3wVG16kU6y1AWY9Ve/W9A8qMGGnYNc\nG09D0gd1CD+9GIZzMKuhfregeRUGG3YOcgPS2Fa5ljoHurrUnaUuwKz/xmpB8/VuZjvz9CM2WK1Q\n9N11aevoVV1CnNmQGmtakFZrneSpQ8xa3CI3Sj+7VxvfKteuDi10Va+vXZa6ALPy+Xo3s525Rc7K\nVdUWujqFOLOG8iS+Zjtzi1zdZakLmKRWC10VAlQVapiILHUBZmZWFQ5yHdSqe3UYlBno2gNkVYKk\nWcN5EIPZ5LlrdRhkDEcrTb+7XYcxpGWpCzDrPw9iMJs8t8iVoJRWuWzwhyjNZFrK3NI21CRdIekx\nSXeP2v4xSf8iaYOkT7dtP1/SRkn3STqpbfvRku4q7vucJBXbd5X0lWL7Oklzyjo38yAGs6lwi1wX\n5/AFLuUjqctotm4tdE0NaVnqApL6EvB54KrWBknHA4uAwyPieUn7F9vnAYuBQ4EDgJslHRIRLwKX\nAB8G1gHXAycDNwBnA09HxEGSFgMXAv+xpHNrPA9iMJs8B7lhkjGcf+ybGtzaZakLSCsibunQSvZf\ngAsi4vlin8eK7YuA1cX2ByRtBI6R9CCwV0TcCiDpKuA08iC3iB2v8leBz0tSRMTATsrMrA/ctVoS\nD3qwqkv4GZ0uaX3b17IeH3cI8LtFV+j3JL212D4LaL9sfnOxbVZxe/T2VzwmIrYDvwL2m9zpmJmV\nxy1yY6hl92pG41tvhk6WuoBx/JKp1vhERMyfxON2AV4LLADeCqyR9MYpVWJmVjNukSuRW+VswrJy\nDlPTz+Zm4JrI3Qa8BEwHtgDtS6QfWGzbUtwevZ32x0jaBdgbeHKg1ZuZ9YGD3DDKUhdgVoqvA8cD\nSDoEeDXwBLAWWFyMRJ0LHAzcFhEPA1slLShGq54FXFc811pgaXH7vcB3fH2cmdWBg9w4+jk5sNmE\nZKkLqA5JXwZ+CLxZ0mZJZwNXAG8spiRZDSwtWuc2AGuAe4BvASuKEasAy4HLgY3A/eQDHQC+COxX\nDIz4JLCypFMzM5sSXyNXslOOu4Ybbjlj8AfKcBCos6y8Q9WhWzUi3t/lrg902X8VsKrD9vXAYR22\n/wZ431RqNDNLwS1ywyxLXYCZmZkNkoNcD/rdvVqHFhBLKCvvUP4smpnVm4PcsMtSF2ATkqUuwMzM\n6sRBzqyh3BpnZlZ/DnI9qnX3albeoWwKstQFmJlZ3TjIJeQwZy/Lyj2cW+PMzIZDI4LcPr/e2pfn\nqf2cclnqAqyjrNzDOcSZmQ2PRgQ5gFPvvCl1CR35j2rDZakLMDOzOmtMkLNClroAe1lW/iH9Hwcz\ns+HSqCDXj1a5QXSvlv7HNSv3cNZBVv4hHeLKJWm2pO9KukfSBkmfKLa/VtI/SvpZ8e++qWs1s/pq\nVJCzNhkOdKlkqQuwkmwH/iQi5gELgBWS5pGv4/rtiDgY+DZe19XMpqBxQc6tcqNkaQ7bWFmaw7o1\nrnwR8XBE/Li4/SxwLzALWARcWex2JXBamgrNbBg0LshVmcPckMvSHNYhLj1Jc4AjgXXAjIh4uLjr\nEWBGorLMbAjskrqAujqHL3ApH0ldRv9kONANUpa6AEtF0h7A14BzI2KrpJfvi4iQFF0etwxYBjBj\nxgxGRkZ6Ot62bdt63rfumnKuTTlPaM659vM8GxnkTr3zJtYefmLqMjo65bhruOGWM9IcPBv1r9We\nW+PSkvQq8hB3dUS03oxHJc2MiIclzQQe6/TYiLgMuAxg/vz5sXDhwp6OOTIyQq/71l1TzrUp5wnN\nOdd+nqe7Vqeg9hMEd5OlLmDIZGkO6xCXlvKmty8C90bEZ9ruWgssLW4vBa4ruzYzGx6NDXJVnSAY\nKvIHOEtdwJDIUhdgCR0LLAF+T9Idxdd7gAuA35f0M+CE4nszs0lpZNdqPw3dtXLtMhxEpiJLd+hK\n/Geg4SLi+4C63P3uMmsxs+GVtEVO0vuKiTJfkjR/1H3nS9oo6T5JJ7VtP1rSXcV9n1P7lcMT5Fa5\nHmQ4zE1Uhl8zMzMrRequ1buBM4Bb2jcWk2YuBg4FTgYuljStuPsS4MPAwcXXyaVV28WgrpWrTJgD\nB5NeZFTidarU58bMzAYqaZCLiHsj4r4Ody0CVkfE8xHxALAROKYY4bVXRNwaEQFcxRQn06xyqxxU\n7I9ylrqACstSF5Cr1OfFzMwGLnWLXDezgE1t328uts0qbo/entzQjmAdLUtdQMVk+DUxM7NkBh7k\nJN0s6e4OX4sGfNxlktZLWv/404M80uBVrpUlw+EFKvcaVO5zYmZmAzfwIBcRJ0TEYR2+xpo7aQsw\nu+37A4ttW4rbo7d3Ou5lETE/Iua/bt+xa+xX9+ogW+Uq+Uc6S11AIhmVO/dKfj7MzGzgqtq1uhZY\nLGlXSXPJBzXcVqxPuFXSgmK06llUbDJNh7khltGs8zUzs8pLPf3I6ZI2A28HvinpRoCI2ACsAe4B\nvgWsiIgXi4ctBy4nHwBxP3BDP2qp+qCHFoe5RLLUBXRXyc+EmZmVIumEwBFxLXBtl/tWAas6bF8P\nHDbg0qZkqCcJ7iYb9e+wyFIXMDaHODOzZqtq12oSbpXrg4zKh5+eZAzHeZiZ2VBzkBuQQU9HUukw\nBzuCUJa0isnJUhfQm8p/BszMbOAc5EapS6sc1OgPeUY9Ql1G9Ws0MzNr4yA3QI2ZJHgiMqoZmLLU\nBUxMbUK8mZkNlINcB/1slWt8F+tYMtKFuozqhspx1Po9NzOzvko6atX645TjruGGW85IXcbUZF1u\n9+s5h0RTQ5yk/wp8CAjgLuCDwGuArwBzgAeBMyPi6WL/84GzgReBj0fEjcX2o4EvAbsD1wOfKNZt\nNjOrJQe5EpQxHclQhLmWrMvt8fYdcg0OcbOAjwPzIuLXktYAi4F5wLcj4gJJK4GVwHmS5hX3Hwoc\nANws6ZBiLspLgA8D68iD3Mn0aS5KM7MUHOS6OPXOm1h7+Impy5iQoQpzLVnqAqqhqSGuzS7A7pJe\nIG+J+yVwPrCwuP9KYAQ4D1gErI6I54EHJG0EjpH0ILBXRNwKIOkq4DQc5MysxnyNXEk88MEmq6wQ\nl/AzOl3S+ravZe13RsQW4K+Bh4CHgV9FxE3AjGLZPoBHgBnF7VnApran2Fxsm1XcHr3dzKy2z93h\neQAADklJREFU3CI3BrfKmfXg2efgu+um8gxPRMT8bndK2pe8lW0u8AzwfyR9oH2fiAhJvtbNzBrH\nLXIlKqvFw91ww6MBrXG9OAF4ICIej4gXgGuAdwCPSpoJUPz7WLH/FmB22+MPLLZtKW6P3m5mVlsO\ncuPo9wTBDnPWK4e4lz0ELJD0GkkC3g3cC6wFlhb7LAWuK26vBRZL2lXSXOBg4LaiG3arpAXF85zV\n9hgzs1pykBtiDnP15fduh4hYB3wV+DH51CP/BrgMuAD4fUk/I2+1u6DYfwOwBrgH+BawohixCrAc\nuBzYCNyPBzqYWc05yPWgrq1y4EBQR2W+ZzVojQMgIv4yIt4SEYdFxJKIeD4inoyId0fEwRFxQkQ8\n1bb/qoh4U0S8OSJuaNu+vniON0XERz2HnJnVnYNcIg5zNtopx13jEGdmZhPiINejfrfKlc1hrtrK\nfn8c4szMhkMzgtwj/XmaOnexgsNcVTnEmZnZZDUjyAFcmLqAzhzmms0hzszMpqI5Qa5PBtHF6jDX\nTH4fzMxsqpoV5CraKpeCQ0Q6ZQ9qaHFrnJnZ8GlWkIO+hLlhaJWDdIGiyVK93g5xZmbDqXlBrsJS\n/bF1oCuHQ5yZmfVbM4NcRVvlIO0fXYe5wXGIMzOzQWhmkOuTus8t14lb5/rPr6eZmQ1Kc4NchQc+\nVKEVxeFj6lKH4ip8jszMbLCaG+T6ZBi7WFtSB5E6S/26VeHzY2Zmg9fsINenVrlhDnPgQDcRVXit\nqvK5MTOzwWt2kINKd7FCtf4opw4oVVaFAAfV+ryYmdng7ZK6gGFx6p03sfbwEwfy3OfwBS7lIwN5\n7olqhZUbbjkjcSXpVSG4tXOIMzNrHrfIQeW7WKF6f6SrFmLKVJXWNzMzMwe5PmtamGtSoKny+Vbt\ns2FmZuVwkGup+LVyLVX8g13lgNMPVT+/Kn4mbGySTpZ0n6SNklamrsfM6stBrl0Nulihun+4qxx2\nJqPqAQ6q+1mw7iRNAy4CTgHmAe+XNC9tVWZWVx7sMCCDHPwA1RoA0W508KnjoIiqh7cWh7jaOgbY\nGBE/B5C0GlgE3DPlZz73XI4YGYF99pnyU9XBEc8804hzbcp5wpCf6xFHwGc/2/endZAb7ULgvP48\nVVPDXLs6Bbu6BDhwiKu5WcCmtu83A28bvZOkZcAygBkzZjAyMjLuEx+0eTO7v/gizzzzTH8qrbgX\nG3KuTTlPGO5z3bZ5MxuLn+Nt27b19DPdCwe5mqtDmGtXxWBXpwBnzRERlwGXAcyfPz8WLlw4/oMW\nLmRkZISe9h0CTTnXppwnDPe57gMcWNzu53k6yHVSo1Y5qF+Ya1dGsBumoOaWuKGwBZjd9v2BxTYz\nswlzkCuBw1zvJhrshimkjcchbmj8CDhY0lzyALcY+KO0JZlZXTnIddPHVrmyDEuYa9ekoDYWh7jh\nERHbJX0UuBGYBlwRERsSl2VmNeXpR8bSx7nlBj0lSYv/4A+fst7Tsj6jBhFxfUQcEhFviohVqesx\ns/pykCuRw5xNlEOcmZmNxUFuPH1e8cFhznpxDl9wiDMzs3E5yA0xh7l6KvN9c4gzM6s3B7le1LRV\nDhzm6sYhzszMJsJBrlcOczZgfp/MzGyikgY5Se+TtEHSS5Lmt22fI+nXku4ovi5tu+9oSXdJ2ijp\nc5KUpvqpc5izlrLfn7q1xkk6WdJ9xc/9ytT1mJlVReoWubuBM4BbOtx3f0QcUXyd07b9EuDDwMHF\n18m9HOifvzzVUul7q1zZHOaqySFubJKmARcBpwDzgPdLmpe2KjOzakga5CLi3oi4r9f9Jc0E9oqI\nWyMigKuA08Z94NyjJ1/kgJX9R9VhrjrKHJnaUrcQVzgG2BgRP4+I3wKrgUWJazIzq4TULXJjmVt0\nq35P0u8W22YBm9v22VxsK88AWuUc5ponxXtQ0xAH+c/4prbvy/+5NzOrqIEv0SXpZuD1He7684i4\nrsvDHgbeEBFPSjoa+LqkQyd43GXAsuLbDe8E+DK/mchzdDX5btrpwBOd7yr1j+x0uKlLHaUa4/Uo\nVel13FCROjp488Qf8i83woLpUzjmbpLWt31/WURcNoXnGzq33377E5J+0ePuVfgclaUp59qU84Tm\nnOt45/nven2igQe5iDhhEo95Hni+uH27pPuBQ8gXmD6wbdcDi22dnuMy4OU/BpLWR8T8TvuWpQo1\nuA7XMV4NE31MRPR0neoUbAFmt33f9ed+WEXE63rdtwqfo7I05Vybcp7QnHPt53lWsmtV0uuKC5yR\n9EbyQQ0/j4iHga2SFhSjVc8CurXqmdlw+BFwsKS5kl4NLAbWJq7JzKwSUk8/crqkzcDbgW9KurG4\n6zjgp5LuAL4KnBMRTxX3LQcuBzYC99O1l8rMhkFEbAc+CtwI3AusiYgNaasyM6uGgXetjiUirgWu\n7bD9a8DXujxmPXDYJA5XhWtuqlADuI7RXMcOVahhJxFxPXB96jpqopLv4YA05Vybcp7QnHPt23kq\nn8XDzMzMzOqmktfImZmZmdn4hi7IdVv2q7jv/GKJn/skndS2faDLfknKJG1pW3LsPePVNCipljqS\n9GDxGt/RGhkp6bWS/lHSz4p/9x3Aca+Q9Jiku9u2dT3uoN6PLnWU/rmQNFvSdyXdU/ycfKLYXvpr\nYlPT6TM16v7/JOmnxc/dDyQdXnaN/TDeebbt91ZJ2yW9t6za+qmX85S0sPhdsUHS98qsr596+Ozu\nLen/SrqzONcPll1jP3T7fTtqHxW5Y2Px83rUhA8UEUP1Bfx78rmwRoD5bdvnAXcCuwJzyQdKTCvu\nuw1YAIh88MQpfa4pA/60w/auNQ3otZlWHOONwKuLY88r6X15EJg+atungZXF7ZXAhQM47nHAUcDd\n4x13kO9HlzpK/1wAM4Gjitt7Av+vOF7pr4m/+v+ZGnX/O4B9i9unAOtS1zyI8yz2mQZ8h/w6yvem\nrnlA7+c+wD3kc6wC7J+65gGe65+1/Q56HfAU8OrUdU/iPDv+vh21z3vIc4fIc8iEf06HrkUuui/7\ntQhYHRHPR8QD5KNej9Fkl/3qj441DfB4VVvqaBFwZXH7SgbwukfELeS/BHo57sDejy51dDPIOh6O\niB8Xt58lHwU6iwSviU3NeJ+piPhBRDxdfHsrr5yDszZ6/Nn5GPkAuccGX9Fg9HCefwRcExEPFfsP\n87kGsGfRO7ZHse/2MmrrpzF+37ZbBFwVuVuBfYpc0rOhC3Jj6LbMT1nLfn2saDa9oq3bquylh1Iu\ndRTAzZJuV77qBsCMyOcGBHgEmFFSLd2Om+L1Sfa5kDQHOBJYR7VeE+u/sxnSqZokzQJOBy5JXcuA\nHQLsK2mk+D16VuqCBujz5L1rvwTuAj4RES+lLWlqRv2+bTfl37G1DHKSbpZ0d4evZK1L49R0CXl3\n5hHky4/9Tao6E3pnRBxB3sWzQtJx7XcWraGlD6FOddxCss+FpD3IWzDOjYit7fclfk2szyQdTx7k\nzktdy4B8Fjiv7n/oe7ALcDTwB8BJwF9IOiRtSQNzEnAHcAD578fPS9orbUmTN9bv235IOo/cZMUk\nlv2i+zI/PS/71Y+aJP0d8I1xahqUZEsdRcSW4t/HJF1L3j33qKSZEfFw0ZRcVldBt+OW+vpExKOt\n22V+LiS9ivyXytURcU2xuRKvifWXpN8hn0D9lIh4MnU9AzIfWJ33wjEdeI+k7RHx9bRl9d1m4MmI\neA54TtItwOHk110Nmw8CFxT/qdwo6QHgLeTXs9dKl9+37ab8O7aWLXKTtBZYLGlXSXPJl/26LUpY\n9mtUf/fpQGukTsea+nnsUZIsdSTp30ras3UbOJH8NVgLLC12W0p5y611O26p70eKz0XxGf8icG9E\nfKbtrkq8JtY/kt4AXAMsiYhh/GMPQETMjYg5ETGHfCWg5UMY4iD/mXynpF0kvQZ4G/k1V8PoIeDd\nAJJmkA9g/HnSiiZhjN+37dYCZxWjVxcAv2q7zKUntWyRG4uk04H/RT7S5ZuS7oiIkyJig6Q15KN+\ntgMrIuLF4mHLgS8Bu5NfR9Lva0k+LekI8u6qB4GPAIxTU99FxHZJraWOpgFXRDlLHc0Ari3+x7wL\n8A8R8S1JPwLWSDob+AVwZr8PLOnLwEJguvLl4P4SuKDTcQf5fnSpY2GCz8WxwBLgLuVL4EE+Qqz0\n18Smpstn6lUAEXEp8N+A/YCLi5+97VHDxch7OM+hMN55RsS9kr4F/BR4Cbg8IsackqWqenhP/wr4\nkqS7yEdznhcRTyQqdyq6/b59A7x8rteTj1zdCPwreWvkhHhlBzMzM7OaalLXqpmZmdlQcZAzMzMz\nqykHOTMzM7OacpAzMzMzqykHOTMzM7OacpAzMzMzqykHOTMzM7OacpCzgZM0p1hOBklHSQpJ0yVN\nk3RXMUu5mZkBkt4q6aeSditWxtkg6bDUdVk1Dd3KDlZJzwB7FLc/BtwK7AO8A7g5Iv41VWFmZlUT\nET+StBb4FPmKQ39f11UcbPAc5KwMW4HXSJoOzAT+GdgXWAZ8slh/9WLgt8BIRFydrFIzs2r47+Tr\nY/8G+HjiWqzC3LVqAxcRL5GvJ/oh8gWEnwUOB6YVi3mfAXw1Ij4MnJqsUDOz6tiPvCdjT2C3xLVY\nhTnIWVleIg9p15K30P0J0Frw+kBgU3HbC7KbmcEXgL8ArgYuTFyLVZiDnJXlBeCGiNhO0dUKfKO4\nbzN5mAN/Js2s4SSdBbwQEf8AXAC8VdLvJS7LKkoRkboGa7jiGrnPk18L8n1fI2dmZtYbBzkzMzOz\nmnI3lpmZmVlNOciZmZmZ1ZSDnJmZmVlNOciZmZmZ1ZSDnJmZmVlNOciZmZmZ1ZSDnJmZmVlNOciZ\nmZmZ1ZSDnJmZmVlN/X8C0u4aUzb+lAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x114dd2b70>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Time Visualization\n",
+    "from ipywidgets import IntSlider, interact\n",
+    "\n",
+    "def plot_figure(n_iter):\n",
+    "    fig = gradient_descent_visualization(\n",
+    "        gradient_losses, gradient_ws, grid_losses, grid_w0, grid_w1, mean_x, std_x, height, weight, n_iter)\n",
+    "    fig.set_size_inches(10.0, 6.0)\n",
+    "\n",
+    "interact(plot_figure, n_iter=IntSlider(min=1, max=len(gradient_ws)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 4 Stochastic gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def compute_stoch_gradient(y, tx, w):\n",
+    "    \"\"\"Compute a stochastic gradient from just few examples n and their corresponding y_n labels.\"\"\"\n",
+    "    # ***************************************************\n",
+    "    return compute_gradient(t, tx, w)\n",
+    "\n",
+    "\n",
+    "def stochastic_gradient_descent(\n",
+    "        y, tx, initial_w, batch_size, max_iters, gamma):\n",
+    "    \"\"\"Stochastic gradient descent algorithm.\"\"\"\n",
+    "    ws = [initial_w]\n",
+    "    losses = []\n",
+    "    w = initial_w\n",
+    "    num_batches = int(np.shape(tx)[0]/batch_size)\n",
+    "    for epoch_num in range(max_iters):\n",
+    "        for batch_idx in range(num_batches-1):\n",
+    "            tx_batch = tx[batch_idx * batch_size : (batch_idx + 1)*batch_size]\n",
+    "            y_batch = y[batch_idx * batch_size : (batch_idx + 1)*batch_size]\n",
+    "            dw = compute_gradient(y_batch, tx_batch, w)\n",
+    "            w = w - gamma * dw\n",
+    "            # store w and loss\n",
+    "            loss = compute_loss(y, tx, w)\n",
+    "        ws.append(w)\n",
+    "        losses.append(loss)\n",
+    "        print(\"Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}\".format(\n",
+    "              bi=epoch_num, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))\n",
+    "\n",
+    "    return losses, ws"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Gradient Descent(0/49): loss=149.23111693710902, w0=62.56993588158218, w1=11.620824895012472\n",
+      "Gradient Descent(1/49): loss=36.43137243583583, w0=70.94488894272497, w1=13.103361024581373\n",
+      "Gradient Descent(2/49): loss=32.314559738515754, w0=72.0660926029723, w1=13.2920452628946\n",
+      "Gradient Descent(3/49): loss=31.96001127518039, w0=72.21622428225437, w1=13.315995721883963\n",
+      "Gradient Descent(4/49): loss=31.91609383500287, w0=72.23633122826242, w1=13.319026864925306\n",
+      "Gradient Descent(5/49): loss=31.910281263464345, w0=72.23902466019712, w1=13.319409210315216\n",
+      "Gradient Descent(6/49): loss=31.909504627473964, w0=72.23938553135955, w1=13.319457258216254\n",
+      "Gradient Descent(7/49): loss=31.909400708458584, w0=72.2394338911883, w1=13.31946327045237\n",
+      "Gradient Descent(8/49): loss=31.909386798347704, w0=72.23944037311061, w1=13.319464019078492\n",
+      "Gradient Descent(9/49): loss=31.909384935997032, w0=72.23944124208992, w1=13.3194641117658\n",
+      "Gradient Descent(10/49): loss=31.90938468660687, w0=72.23944135861021, w1=13.319464123164956\n",
+      "Gradient Descent(11/49): loss=31.909384653203958, w0=72.2394413742374, w1=13.319464124555802\n",
+      "Gradient Descent(12/49): loss=31.909384648729223, w0=72.23944137633363, w1=13.319464124723872\n",
+      "Gradient Descent(13/49): loss=31.909384648129652, w0=72.23944137661488, w1=13.319464124743941\n",
+      "Gradient Descent(14/49): loss=31.909384648049326, w0=72.23944137665261, w1=13.319464124746302\n",
+      "Gradient Descent(15/49): loss=31.909384648038515, w0=72.2394413766577, w1=13.319464124746574\n",
+      "Gradient Descent(16/49): loss=31.909384648037033, w0=72.23944137665839, w1=13.319464124746597\n",
+      "Gradient Descent(17/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746617\n",
+      "Gradient Descent(18/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(19/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(20/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(21/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(22/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(23/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
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+      "Gradient Descent(25/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(26/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(27/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(28/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(29/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(30/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
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+      "Gradient Descent(33/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(34/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(35/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(36/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(37/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(38/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(39/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(40/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(41/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(42/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(43/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(44/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(45/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(46/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(47/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(48/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "Gradient Descent(49/49): loss=31.90938464803682, w0=72.23944137665849, w1=13.319464124746615\n",
+      "SGD: execution time=0.691 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "# from stochastic_gradient_descent import *\n",
+    "\n",
+    "# Define the parameters of the algorithm.\n",
+    "max_iters = 50\n",
+    "gamma = 0.01\n",
+    "batch_size = 100\n",
+    "\n",
+    "# Initialization\n",
+    "w_initial = np.array([0, 0])\n",
+    "\n",
+    "# Start SGD.\n",
+    "start_time = datetime.datetime.now()\n",
+    "sgd_losses, sgd_ws = stochastic_gradient_descent(\n",
+    "    y, tx, w_initial, batch_size, max_iters, gamma)\n",
+    "end_time = datetime.datetime.now()\n",
+    "\n",
+    "# Print result\n",
+    "exection_time = (end_time - start_time).total_seconds()\n",
+    "print(\"SGD: execution time={t:.3f} seconds\".format(t=exection_time))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "6cd1325533394f5aaf3bbb98549b6dbc"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<function __main__.plot_figure>"
+      ]
+     },
+     "execution_count": 112,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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oIV3D5Mnq9i3EbNRMMSHXB/ptf1Wzxhnx4mPAzSLy+8AgYLiIfAf4AzRuDuD/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\nmZmZ1ZSDnJmZmVlN/X8C0u4aUzb+lAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x115f72eb8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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rg/vu08Xee++RLySJZK1FLhE02/6qZo0z0osvA5dGXaNPAl8TkT+j9dlmRK/5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\nWgtdqYQ4Edm212qDWsZuuIH2N/4Evv512t15Qxhs10TazUHSRC1yNeR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uO72LiCSrMoIc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\nAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1156c5ac8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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lZevYJaJgqwwTcoZRX5gQjhoichzwfeDJsGEHtPO204BN3va3tdqcc+uBdcC5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\nOeecc65AeSLnnHPOOVeg/h+nNv+6AGPELgAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x115290ac8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Time Visualization\n",
+    "from ipywidgets import IntSlider, interact\n",
+    "def plot_figure(n_iter):\n",
+    "    fig = gradient_descent_visualization(\n",
+    "        sgd_losses, sgd_ws, grid_losses, grid_w0, grid_w1, mean_x, std_x, height, weight, n_iter)\n",
+    "    fig.set_size_inches(10.0, 6.0)\n",
+    "\n",
+    "interact(plot_figure, n_iter=IntSlider(min=1, max=len(gradient_ws)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 5 Effect of Outliers and MAE Cost Function, and Subgradient Descent"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercise 5\n",
+    "\n",
+    "Load and plot data containing outliers"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Gradient Descent(0/499): loss=3811.1447934585167, w0=14.07288311243601, w1=2.0966300245379426\n",
+      "Gradient Descent(1/499): loss=2545.839255152703, w0=25.471918433509178, w1=3.7949003444136755\n",
+      "Gradient Descent(2/499): loss=1715.6722914702589, w0=34.705137043578446, w1=5.170499303513016\n",
+      "Gradient Descent(3/499): loss=1170.9997465982074, w0=42.18404411773455, w1=6.28473446038348\n",
+      "Gradient Descent(4/499): loss=813.6400899076541, w0=48.241958847801, w1=7.187264937448556\n",
+      "Gradient Descent(5/499): loss=579.1764191529824, w0=53.14886977915482, w1=7.9183146238712645\n",
+      "Gradient Descent(6/499): loss=425.34480477084236, w0=57.123467633551414, w1=8.510464869873658\n",
+      "Gradient Descent(7/499): loss=324.4158825747201, w0=60.34289189561266, w1=8.990106569135595\n",
+      "Gradient Descent(8/499): loss=258.1964167218445, w0=62.95062554788226, w1=9.378616345537763\n",
+      "Gradient Descent(9/499): loss=214.7498251757728, w0=65.06288980622064, w1=9.69330926442352\n",
+      "Gradient Descent(10/499): loss=186.2445164623953, w0=66.77382385547472, w1=9.948210528720983\n",
+      "Gradient Descent(11/499): loss=167.54218341554815, w0=68.15968043537053, w1=10.154680552801926\n",
+      "Gradient Descent(12/499): loss=155.27158270351174, w0=69.28222426508614, w1=10.32192127230749\n",
+      "Gradient Descent(13/499): loss=147.22084157634464, w0=70.19148476715579, w1=10.457386255106996\n",
+      "Gradient Descent(14/499): loss=141.93875032281034, w0=70.92798577383219, w1=10.567112891174597\n",
+      "Gradient Descent(15/499): loss=138.47317025136647, w0=71.52455158924009, w1=10.655991466389354\n",
+      "Gradient Descent(16/499): loss=136.19940316649212, w0=72.00776989972049, w1=10.727983112313307\n",
+      "Gradient Descent(17/499): loss=134.70758458210608, w0=72.39917673120961, w1=10.786296345511708\n",
+      "Gradient Descent(18/499): loss=133.7288024088904, w0=72.71621626471578, w1=10.833530064402414\n",
+      "Gradient Descent(19/499): loss=133.08662342504363, w0=72.97301828685579, w1=10.871789376703886\n",
+      "Gradient Descent(20/499): loss=132.6652897937417, w0=73.1810279247892, w1=10.902779419668077\n",
+      "Gradient Descent(21/499): loss=132.3888527982445, w0=73.34951573151527, w1=10.927881354469072\n",
+      "Gradient Descent(22/499): loss=132.20748248549884, w0=73.48599085496338, w1=10.948213921657878\n",
+      "Gradient Descent(23/499): loss=132.0884854233064, w0=73.59653570495634, w1=10.964683301080811\n",
+      "Gradient Descent(24/499): loss=132.01041145080194, w0=73.68607703345064, w1=10.978023498413387\n",
+      "Gradient Descent(25/499): loss=131.9591871174418, w0=73.75860550953104, w1=10.988829058252772\n",
+      "Gradient Descent(26/499): loss=131.92557883232413, w0=73.81735357515615, w1=10.997581561722674\n",
+      "Gradient Descent(27/499): loss=131.90352843645843, w0=73.86493950831249, w1=11.004671089533295\n",
+      "Gradient Descent(28/499): loss=131.88906117173102, w0=73.90348411416913, w1=11.010413607059897\n",
+      "Gradient Descent(29/499): loss=131.8795691993433, w0=73.934705244913, w1=11.015065046256446\n",
+      "Gradient Descent(30/499): loss=131.87334151625976, w0=73.95999436081554, w1=11.01883271200565\n",
+      "Gradient Descent(31/499): loss=131.86925553338864, w0=73.98047854469661, w1=11.021884521262507\n",
+      "Gradient Descent(32/499): loss=131.8665747200269, w0=73.99707073364026, w1=11.02435648676056\n",
+      "Gradient Descent(33/499): loss=131.86481583838025, w0=74.01051040668462, w1=11.026358778813982\n",
+      "Gradient Descent(34/499): loss=131.86366183613188, w0=74.02139654185055, w1=11.027980635377254\n",
+      "Gradient Descent(35/499): loss=131.86290469525673, w0=74.03021431133494, w1=11.029294339193505\n",
+      "Gradient Descent(36/499): loss=131.86240793512857, w0=74.03735670461732, w1=11.030358439284669\n",
+      "Gradient Descent(37/499): loss=131.86208201080842, w0=74.04314204317603, w1=11.031220360358512\n",
+      "Gradient Descent(38/499): loss=131.861868171862, w0=74.0478281674086, w1=11.031918516428325\n",
+      "Gradient Descent(39/499): loss=131.86172787212928, w0=74.05162392803697, w1=11.032484022844873\n",
+      "Gradient Descent(40/499): loss=131.8616358214746, w0=74.05469849414595, w1=11.032942083042277\n",
+      "Gradient Descent(41/499): loss=131.86157542704012, w0=74.05718889269423, w1=11.033313111802174\n",
+      "Gradient Descent(42/499): loss=131.86153580225164, w0=74.05920611551834, w1=11.03361364509769\n",
+      "Gradient Descent(43/499): loss=131.8615098044279, w0=74.06084006600587, w1=11.033857077067058\n",
+      "Gradient Descent(44/499): loss=131.86149274725574, w0=74.06216356590076, w1=11.034054256962246\n",
+      "Gradient Descent(45/499): loss=131.8614815560451, w0=74.06323560081563, w1=11.034213972677348\n",
+      "Gradient Descent(46/499): loss=131.86147421349176, w0=74.06410394909668, w1=11.034343342406581\n",
+      "Gradient Descent(47/499): loss=131.86146939604257, w0=74.06480731120432, w1=11.03444813188726\n",
+      "Gradient Descent(48/499): loss=131.86146623531414, w0=74.0653770345115, w1=11.034533011366609\n",
+      "Gradient Descent(49/499): loss=131.8614641615602, w0=74.06583851039032, w1=11.034601763744883\n",
+      "Gradient Descent(50/499): loss=131.86146280097026, w0=74.06621230585218, w1=11.034657453171285\n",
+      "Gradient Descent(51/499): loss=131.86146190828717, w0=74.06651508017627, w1=11.03470256160667\n",
+      "Gradient Descent(52/499): loss=131.86146132259782, w0=74.06676032737879, w1=11.034739099439332\n",
+      "Gradient Descent(53/499): loss=131.86146093832704, w0=74.06695897761283, w1=11.034768695083788\n",
+      "Gradient Descent(54/499): loss=131.86146068620698, w0=74.0671198843024, w1=11.034792667555797\n",
+      "Gradient Descent(55/499): loss=131.861460520791, w0=74.06725021872096, w1=11.034812085258125\n",
+      "Gradient Descent(56/499): loss=131.86146041226158, w0=74.06735578959999, w1=11.03482781359701\n",
+      "Gradient Descent(57/499): loss=131.86146034105542, w0=74.067441302012, w1=11.034840553551506\n",
+      "Gradient Descent(58/499): loss=131.86146029433706, w0=74.06751056706572, w1=11.034850872914648\n",
+      "Gradient Descent(59/499): loss=131.86146026368516, w0=74.06756667175924, w1=11.034859231598793\n",
+      "Gradient Descent(60/499): loss=131.86146024357444, w0=74.067612116561, w1=11.03486600213295\n",
+      "Gradient Descent(61/499): loss=131.8614602303798, w0=74.06764892685041, w1=11.03487148626562\n",
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+     "name": "stdout",
+     "output_type": "stream",
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+     ]
+    },
+    {
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dUM1c1l5pTBt02J6xl9cMtxzOX14R9WRtNj6udL7I7Ozx7Of4nut9FzKq9i/1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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1149a0128>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "height, weight, gender = load_data(sub_sample=True, add_outlier=True)\n",
+    "x, mean_x, std_x = standardize(height)\n",
+    "y, tx = build_model_data(x, weight)\n",
+    "plt.plot(tx[:, 1], y, 'o')\n",
+    "\n",
+    "\n",
+    "# Define the parameters of the algorithm.\n",
+    "max_iters = 500\n",
+    "gamma = 0.05\n",
+    "batch_size = 100\n",
+    "\n",
+    "# Initialization\n",
+    "w_initial = np.array([0, 0])\n",
+    "\n",
+    "# Start SGD.\n",
+    "start_time = datetime.datetime.now()\n",
+    "sgd_losses, sgd_ws = stochastic_gradient_descent(\n",
+    "    y, tx, w_initial, batch_size, max_iters, gamma)\n",
+    "end_time = datetime.datetime.now()\n",
+    "w = sgd_ws[-1]\n",
+    "y_MSE = w[0] + w[1] * np.linspace(-2, 2, 100)\n",
+    "plt.plot(np.linspace(-2,2,100), y_MSE)\n",
+    "# Print result\n",
+    "exection_time = (end_time - start_time).total_seconds()\n",
+    "print(\"SGD: execution time={t:.3f} seconds\".format(t=exection_time))\n",
+    "\n",
+    "def compute_MAE(y, tx, w):\n",
+    "    N = np.shape(tx)[0]\n",
+    "    cost = 1/N * np.sum(np.abs((y - tx @ w)))\n",
+    "    return cost\n",
+    "\n",
+    "def compute_gradient_MAE(y, tx, w):\n",
+    "    N = np.shape(tx)[0]\n",
+    "    gradient = -1/np.shape(tx)[0] * tx.T @ np.sign(y - tx @ w)\n",
+    "    return gradient\n",
+    "\n",
+    "def stochastic_gradient_descent_MAE(\n",
+    "        y, tx, initial_w, batch_size, max_iters, gamma):\n",
+    "    \"\"\"Stochastic gradient descent algorithm.\"\"\"\n",
+    "    ws = [initial_w]\n",
+    "    losses = []\n",
+    "    w = initial_w\n",
+    "    num_batches = int(np.shape(tx)[0]/batch_size)\n",
+    "    for epoch_num in range(max_iters):\n",
+    "        for batch_idx in range(num_batches):\n",
+    "            tx_batch = tx[batch_idx * batch_size : (batch_idx + 1)*batch_size]\n",
+    "            y_batch = y[batch_idx * batch_size : (batch_idx + 1)*batch_size]\n",
+    "            dw = compute_gradient_MAE(y, tx, w)\n",
+    "            w = w - gamma * dw\n",
+    "            # store w and loss\n",
+    "        loss = compute_MAE(y, tx, w)\n",
+    "        ws.append(w)\n",
+    "        losses.append(loss)\n",
+    "        print(\"Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}\".format(\n",
+    "              bi=epoch_num, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))\n",
+    "\n",
+    "    return losses, ws\n",
+    "    \n",
+    "max_iters = 500\n",
+    "gamma = 0.8\n",
+    "batch_size = 100\n",
+    "\n",
+    "# Initialization\n",
+    "w_initial = np.array([0, 0])\n",
+    "\n",
+    "# Start SGD.\n",
+    "start_time = datetime.datetime.now()\n",
+    "sgd_losses, sgd_ws = stochastic_gradient_descent_MAE(\n",
+    "    y, tx, w_initial, batch_size, max_iters, gamma)\n",
+    "end_time = datetime.datetime.now()\n",
+    "w = sgd_ws[-1]\n",
+    "y = w[0] + w[1] * np.linspace(-2, 2, 100)\n",
+    "plt.plot(np.linspace(-2,2,100), y)\n",
+    "# Print result\n",
+    "exection_time = (end_time - start_time).total_seconds()\n",
+    "print(\"SGD: execution time={t:.3f} seconds\".format(t=exection_time))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercise 6"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Modify the function `compute_loss(y, tx, w)` for the Mean Absolute Error cost function [here](#compute_loss)"
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/src/implementations/gradient descent.py b/src/implementations/gradient descent.py
new file mode 100644
index 0000000..72f6b3f
--- /dev/null
+++ b/src/implementations/gradient descent.py	
@@ -0,0 +1,50 @@
+# -*- coding: utf-8 -*-
+"""Gradient Descent"""
+import datetime
+import numpy as np
+
+def compute_gradient(y, tx, w, type='mse'):
+    """Compute the gradient."""
+    if type == 'mse':
+        gradient = -2/np.shape(tx)[0] * tx.T @ (y - tx @ w)
+    elif type == 'mae':
+        gradient = -1 / np.shape(tx)[0] * tx.T @ np.sign(y - tx @ w)
+    else:
+        raise ValueError('type not implemented')
+    assert np.shape(w) == gradient
+    return gradient
+
+
+def gradient_descent(y, tx, initial_w, loss_func, gradient_func, max_iters, gamma):
+    """Gradient descent algorithm."""
+    # Define parameters to store w and loss
+    ws = [initial_w]
+    losses = []
+    w = initial_w
+    for n_iter in range(max_iters):
+        loss = loss_func(y, tx, w)
+        dw = gradient_func(y, tx, w)
+        w = w - gamma * dw
+        # store w and loss
+        ws.append(w)
+        losses.append(loss)
+        print("Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}".format(
+              bi=n_iter, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))
+
+    return losses, ws
+
+def train():
+    max_iters = 50
+    gamma = 0.1
+
+    # Initialization
+    w_initial = np.array([0, 0])
+
+    # Start gradient descent.
+    start_time = datetime.datetime.now()
+    gradient_losses, gradient_ws = gradient_descent(y, tx, w_initial, max_iters, gamma)
+    end_time = datetime.datetime.now()
+
+    # Print result
+    exection_time = (end_time - start_time).total_seconds()
+    print("Gradient Descent: execution time={t:.3f} seconds".format(t=exection_time))
\ No newline at end of file
diff --git a/src/implementations/grid_search.py b/src/implementations/grid_search.py
new file mode 100644
index 0000000..f53359a
--- /dev/null
+++ b/src/implementations/grid_search.py
@@ -0,0 +1,27 @@
+# -*- coding: utf-8 -*-
+""" Grid Search"""
+
+import numpy as np
+import costs
+
+
+def generate_w(num_intervals):
+    """Generate a grid of values for w0 and w1."""
+    w0 = np.linspace(-100, 200, num_intervals)
+    w1 = np.linspace(-150, 150, num_intervals)
+    return w0, w1
+
+
+def get_best_parameters(w0, w1, losses):
+    """Get the best w from the result of grid search."""
+    min_row, min_col = np.unravel_index(np.argmin(losses), losses.shape)
+    return losses[min_row, min_col], w0[min_row], w1[min_col]
+
+
+def grid_search(y, tx, w0, w1, loss_func):
+    """Algorithm for grid search."""
+    losses = np.zeros((len(w0), len(w1)))
+    for idx_0, w0_elem in enumerate(w0):
+        for idx_1, w1_elem in enumerate(w1):
+            losses[idx_0, idx_1] = loss_func(y, tx, np.asarray([w0_elem, w1_elem]))
+    return losses
\ No newline at end of file
diff --git a/src/implementations/helpers.py b/src/implementations/helpers.py
new file mode 100644
index 0000000..782c3a1
--- /dev/null
+++ b/src/implementations/helpers.py
@@ -0,0 +1,74 @@
+# -*- coding: utf-8 -*-
+"""some helper functions."""
+import numpy as np
+
+
+def load_data(sub_sample=True, add_outlier=False):
+    """Load data and convert it to the metrics system."""
+    path_dataset = "height_weight_genders.csv"
+    data = np.genfromtxt(
+        path_dataset, delimiter=",", skip_header=1, usecols=[1, 2])
+    height = data[:, 0]
+    weight = data[:, 1]
+    gender = np.genfromtxt(
+        path_dataset, delimiter=",", skip_header=1, usecols=[0],
+        converters={0: lambda x: 0 if b"Male" in x else 1})
+    # Convert to metric system
+    height *= 0.025
+    weight *= 0.454
+
+    # sub-sample
+    if sub_sample:
+        height = height[::50]
+        weight = weight[::50]
+
+    if add_outlier:
+        # outlier experiment
+        height = np.concatenate([height, [1.1, 1.2]])
+        weight = np.concatenate([weight, [51.5/0.454, 55.3/0.454]])
+
+    return height, weight, gender
+
+
+def standardize(x):
+    """Standardize the original data set."""
+    mean_x = np.mean(x)
+    x = x - mean_x
+    std_x = np.std(x)
+    x = x / std_x
+    return x, mean_x, std_x
+
+
+def build_model_data(height, weight):
+    """Form (y,tX) to get regression data in matrix form."""
+    y = weight
+    x = height
+    num_samples = len(y)
+    tx = np.c_[np.ones(num_samples), x]
+    return y, tx
+
+
+def batch_iter(y, tx, batch_size, num_batches=1, shuffle=True):
+    """
+    Generate a minibatch iterator for a dataset.
+    Takes as input two iterables (here the output desired values 'y' and the input data 'tx')
+    Outputs an iterator which gives mini-batches of `batch_size` matching elements from `y` and `tx`.
+    Data can be randomly shuffled to avoid ordering in the original data messing with the randomness of the minibatches.
+    Example of use :
+    for minibatch_y, minibatch_tx in batch_iter(y, tx, 32):
+        <DO-SOMETHING>
+    """
+    data_size = len(y)
+
+    if shuffle:
+        shuffle_indices = np.random.permutation(np.arange(data_size))
+        shuffled_y = y[shuffle_indices]
+        shuffled_tx = tx[shuffle_indices]
+    else:
+        shuffled_y = y
+        shuffled_tx = tx
+    for batch_num in range(num_batches):
+        start_index = batch_num * batch_size
+        end_index = min((batch_num + 1) * batch_size, data_size)
+        if start_index != end_index:
+            yield shuffled_y[start_index:end_index], shuffled_tx[start_index:end_index]
diff --git a/src/implementations/plots.py b/src/implementations/plots.py
new file mode 100644
index 0000000..d434771
--- /dev/null
+++ b/src/implementations/plots.py
@@ -0,0 +1,80 @@
+# -*- coding: utf-8 -*-
+"""function for plot."""
+import matplotlib.pyplot as plt
+import numpy as np
+from grid_search import get_best_parameters
+
+
+def prediction(w0, w1, mean_x, std_x):
+    """Get the regression line from the model."""
+    x = np.arange(1.2, 2, 0.01)
+    x_normalized = (x - mean_x) / std_x
+    return x, w0 + w1 * x_normalized
+
+
+def base_visualization(grid_losses, w0_list, w1_list,
+                       mean_x, std_x, height, weight):
+    """Base Visualization for both models."""
+    w0, w1 = np.meshgrid(w0_list, w1_list)
+
+    fig = plt.figure()
+
+    # plot contourf
+    ax1 = fig.add_subplot(1, 2, 1)
+    cp = ax1.contourf(w0, w1, grid_losses.T, cmap=plt.cm.jet)
+    fig.colorbar(cp, ax=ax1)
+    ax1.set_xlabel(r'$w_0$')
+    ax1.set_ylabel(r'$w_1$')
+    # put a marker at the minimum
+    loss_star, w0_star, w1_star = get_best_parameters(
+        w0_list, w1_list, grid_losses)
+    ax1.plot(w0_star, w1_star, marker='*', color='r', markersize=20)
+
+    # plot f(x)
+    ax2 = fig.add_subplot(1, 2, 2)
+    ax2.scatter(height, weight, marker=".", color='b', s=5)
+    ax2.set_xlabel("x")
+    ax2.set_ylabel("y")
+    ax2.grid()
+
+    return fig
+
+
+def grid_visualization(grid_losses, w0_list, w1_list,
+                       mean_x, std_x, height, weight):
+    """Visualize how the trained model looks like under the grid search."""
+    fig = base_visualization(
+        grid_losses, w0_list, w1_list, mean_x, std_x, height, weight)
+
+    loss_star, w0_star, w1_star = get_best_parameters(
+        w0_list, w1_list, grid_losses)
+    # plot prediciton
+    x, f = prediction(w0_star, w1_star, mean_x, std_x)
+    ax2 = fig.get_axes()[2]
+    ax2.plot(x, f, 'r')
+
+    return fig
+
+
+def gradient_descent_visualization(
+        gradient_losses, gradient_ws,
+        grid_losses, grid_w0, grid_w1,
+        mean_x, std_x, height, weight, n_iter=None):
+    """Visualize how the loss value changes until n_iter."""
+    fig = base_visualization(
+        grid_losses, grid_w0, grid_w1, mean_x, std_x, height, weight)
+
+    ws_to_be_plotted = np.stack(gradient_ws)
+    if n_iter is not None:
+        ws_to_be_plotted = ws_to_be_plotted[:n_iter]
+
+    ax1, ax2 = fig.get_axes()[0], fig.get_axes()[2]
+    ax1.plot(
+        ws_to_be_plotted[:, 0], ws_to_be_plotted[:, 1],
+        marker='o', color='w', markersize=10)
+    pred_x, pred_y = prediction(
+        ws_to_be_plotted[-1, 0], ws_to_be_plotted[-1, 1],
+        mean_x, std_x)
+    ax2.plot(pred_x, pred_y, 'r')
+
+    return fig
diff --git a/src/implementations/stochastic_gradient_descent.py b/src/implementations/stochastic_gradient_descent.py
new file mode 100644
index 0000000..31a9281
--- /dev/null
+++ b/src/implementations/stochastic_gradient_descent.py
@@ -0,0 +1,33 @@
+# -*- coding: utf-8 -*-
+"""Stochastic Gradient Descent"""
+import numpy as np
+
+def compute_stoch_gradient(y, tx, w):
+    """Compute a stochastic gradient from just few examples n and their corresponding y_n labels."""
+    # ***************************************************
+    # INSERT YOUR CODE HERE
+    # TODO: implement stochastic gradient computation.It's same as the gradient descent.
+    # ***************************************************
+    raise NotImplementedError
+
+
+def stochastic_gradient_descent(y, tx, initial_w, grad_func, loss_func, batch_size, max_iters, gamma):
+    """Stochastic gradient descent algorithm."""
+    ws = [initial_w]
+    losses = []
+    w = initial_w
+    num_batches = int(np.shape(tx)[0]/batch_size)
+    for epoch_num in range(max_iters):
+        for batch_idx in range(num_batches):
+            tx_batch = tx[batch_idx * batch_size : (batch_idx + 1)*batch_size]
+            y_batch = y[batch_idx * batch_size : (batch_idx + 1)*batch_size]
+            dw = grad_func(y_batch, tx_batch, w)
+            w = w - gamma * dw
+            # store w and loss
+        loss = loss_func(y, tx, w)
+        ws.append(w)
+        losses.append(loss)
+        print("Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}".format(
+              bi=epoch_num, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))
+
+    return losses, ws
\ No newline at end of file
diff --git a/src/logistic_regression.py b/src/logistic_regression.py
new file mode 100644
index 0000000..8c98e7b
--- /dev/null
+++ b/src/logistic_regression.py
@@ -0,0 +1,61 @@
+import numpy as np
+from utils import batch_iter, dataloader, split_data, standardize
+
+num_epochs = 10
+batch_size = 100
+learning_rate = 10**-3
+
+x, y = dataloader(mode='train', reduced=False)
+x = standardize(x)
+train_dataset, test_dataset = split_data(x, y, ratio=0.9)
+test_data, test_target = test_dataset
+train_data, train_target = train_dataset
+num_batches = int(np.shape(train_data)[0]/batch_size)
+
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
+
+def sigmoid_prime(x):
+    return sigmoid(x)*(1-sigmoid(x))
+
+def loss_mse(weights, x, target):
+    g_x = sigmoid(x @ weights)
+    return 1/np.shape(target)[0] * (target - g_x).T @ (target - g_x)
+
+def gradient_mse(weights, x, target):
+    g_x = sigmoid(x @ weights)
+    return (g_x - target) * g_x * (1 - g_x) * x
+
+def loss_ce(weights, x, target):
+    g_x = sigmoid(x @ weights)
+    return 1/np.shape(x)[0] * np.sum(target * np.log(g_x) + (1-target)*np.log(1-g_x))
+
+def gradient_ce(weights, x, target):
+    g_x = sigmoid(x @ weights)
+    return 1/np.shape(target)[0] * x.T @ (target - g_x)
+
+def train_logistic_regression(loss_func, grad_func):
+    weights = np.zeros(30)
+    for epoch in range(num_epochs):
+        for batch_label, batch_input in batch_iter(
+                train_target, train_data, batch_size, num_batches=num_batches):
+            grad = grad_func(weights, batch_input, batch_label)
+            weights -= learning_rate * grad
+        train_loss = loss_func(weights, train_data, train_target)
+        print("Epoch : ", epoch)
+        print("Train loss : ", train_loss)
+        test_logistic_regression(weights, loss_func)
+
+
+def test_logistic_regression(weights, loss_func):
+    loss = loss_func(weights, test_data, test_target)
+    output = sigmoid(test_data @ weights)
+    predicted = output > 0.5
+    correct = np.sum(predicted == test_target)
+    accuracy = correct/np.shape(test_data)[0]
+    print("Test loss :", loss)
+    print('Test accuracy :', accuracy)
+
+if __name__ == '__main__':
+    train_logistic_regression(loss_ce, gradient_ce)
+
diff --git a/src/neural_network_torch.py b/src/neural_network_torch.py
new file mode 100644
index 0000000..a8c0087
--- /dev/null
+++ b/src/neural_network_torch.py
@@ -0,0 +1,93 @@
+from torch import optim
+import torch
+import torch.utils.data
+import numpy as np
+from torch.autograd import Variable
+from torch import nn
+import torch.nn.functional as f
+from utils import dataloader, standardize, split_data
+
+x, y = dataloader(mode='train', reduced=False)
+x = standardize(x)
+train_dataset, test_dataset = split_data(x, y, ratio=0.9)
+test_data, test_target = test_dataset
+train_data, train_target = train_dataset
+
+
+train = torch.utils.data.TensorDataset(torch.from_numpy(train_data).type(torch.FloatTensor),
+                                       torch.from_numpy(train_target).type(torch.LongTensor))
+train_loader = torch.utils.data.DataLoader(train, batch_size=128, shuffle=True)
+test = torch.utils.data.TensorDataset(torch.from_numpy(test_data).type(torch.FloatTensor),
+                                      torch.from_numpy(test_target).type(torch.LongTensor))
+test_loader = torch.utils.data.DataLoader(test, batch_size=128, shuffle=True)
+
+class SimpleNN(torch.nn.Module):
+    def __init__(self, batch_size=128, learning_rate=10**-4, num_epochs= 10, load_weights=False):
+        super().__init__()
+        self.batch_size = batch_size
+        self.learning_rate = learning_rate
+        self.load_weights = load_weights
+        self.num_epochs = num_epochs
+        # architecture
+        self.fc_1 = nn.Linear(30, 256)
+        self.fc_2 = nn.Linear(256, 256)
+        self.fc_3 = nn.Linear(256, 2)
+
+    def forward(self, x):
+        x = f.relu(self.fc_1(x))
+        x = f.dropout(x)
+        x = f.relu(self.fc_2(x))
+        x = f.dropout(x)
+        x = f.tanh(self.fc_3(x))
+        return x
+
+    def init_optimizer(self):
+        self.optimizer = optim.Adam(self.parameters(), lr=self.learning_rate, weight_decay=10**-3)
+
+    def loss(self, outputs, targets):
+        self.loss_func = nn.CrossEntropyLoss()
+        loss = self.loss_func(outputs, targets)
+        return loss
+
+def new_train(model, epoch):
+    log_interval = 250
+    model.init_optimizer()
+    train_loss = 0
+    for batch_idx, (data, target) in enumerate(train_loader):
+        data, target = Variable(data), Variable(target)
+        # target = preprocess_target(target)
+        model.optimizer.zero_grad()
+        output = model(data)
+        loss = model.loss(output, target)
+        train_loss += loss
+        loss.backward()
+        model.optimizer.step()
+        if batch_idx % log_interval == 0:
+            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
+                epoch, batch_idx * len(data), len(train_loader.dataset),
+                       100. * batch_idx / len(train_loader), loss.data[0]))
+    print("Train loss :", 100*train_loss/np.shape(train_data)[0])
+
+
+def test(model):
+    model.eval()
+    test_loss = 0
+    correct = 0
+    for data, target in test_loader:
+        data, target = Variable(data, volatile=True), Variable(target)
+        output = model(data)
+        test_loss += model.loss(output, target)
+        pred = output.data.max(1, keepdim=True)[1]
+        correct += pred.eq(target.data.view_as(pred)).cpu().sum()
+
+    print('\nTest set: Accuracy: {}/{} ({})\n'.format(
+        correct, np.shape(test_data)[0],
+        100. * correct / np.shape(test_data)[0]))
+    print("Test loss : {}" .format(100*test_loss[0]/np.shape(test_data)[0]))
+
+if __name__ == '__main__':
+    net = SimpleNN()
+    num_epochs = 100
+    for epoch in range(num_epochs):
+        new_train(net, epoch)
+        test(net)
\ No newline at end of file
diff --git a/src/utils.py b/src/utils.py
new file mode 100644
index 0000000..4270513
--- /dev/null
+++ b/src/utils.py
@@ -0,0 +1,69 @@
+import numpy as np
+
+
+
+def dataloader(mode= 'train', reduced=False):
+    table = np.genfromtxt('dataset/' + mode + '.csv', dtype=float, delimiter=',', skip_header=1,
+                          converters={1: lambda x: float(x == b's')})
+
+    if reduced:
+        features = table[:10000, 2:]
+        labels = table[:10000, 1]
+    else:
+        features = table[:, 2:]
+        labels = table[:, 1]
+    if mode == 'train':
+        return features, labels
+    else:
+        return features
+
+def standardize(x):
+    x = (x-np.mean(x, axis=0))/(np.std(x, axis=0))
+    return x
+
+def split_data(x, y, ratio, seed=1):
+    """
+    split the dataset based on the split ratio. If ratio is 0.8
+    you will have 80% of your data set dedicated to training
+    and the rest dedicated to testing
+    """
+    # set seed
+    np.random.seed(seed)
+    num_train_samples = int(np.shape(x)[0]*ratio)
+    indeces = np.arange(np.shape(x)[0])
+    random_indeces = np.random.permutation(indeces)
+    train_idx, test_idx = random_indeces[:num_train_samples], random_indeces[num_train_samples:]
+    train_x, train_y = x[train_idx], y[train_idx]
+    test_x, test_y = x[test_idx], y[test_idx]
+    return (train_x, train_y), (test_x, test_y)
+
+
+
+def batch_iter(y, tx, batch_size, num_batches=1, shuffle=True):
+    """
+    Generate a minibatch iterator for a dataset.
+    Takes as input two iterables (here the output desired values 'y' and the input data 'tx')
+    Outputs an iterator which gives mini-batches of `batch_size` matching elements from `y` and `tx`.
+    Data can be randomly shuffled to avoid ordering in the original data messing with the randomness of the minibatches.
+    Example of use :
+    for minibatch_y, minibatch_tx in batch_iter(y, tx, 32):
+        <DO-SOMETHING>
+    """
+    data_size = len(y)
+
+    if shuffle:
+        shuffle_indices = np.random.permutation(np.arange(data_size))
+        shuffled_y = y[shuffle_indices]
+        shuffled_tx = tx[shuffle_indices]
+    else:
+        shuffled_y = y
+        shuffled_tx = tx
+    for batch_num in range(num_batches):
+        start_index = batch_num * batch_size
+        end_index = min((batch_num + 1) * batch_size, data_size)
+        if start_index != end_index:
+            yield shuffled_y[start_index:end_index], shuffled_tx[start_index:end_index]
+
+
+if __name__ == '__main__':
+    pass
\ No newline at end of file
diff --git a/test/__pycache__/test_utils.cpython-36.pyc b/test/__pycache__/test_utils.cpython-36.pyc
new file mode 100644
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diff --git a/test/test_utils.py b/test/test_utils.py
new file mode 100644
index 0000000..459fbd6
--- /dev/null
+++ b/test/test_utils.py
@@ -0,0 +1,18 @@
+import unittest
+import numpy.testing as npt
+import numpy as np
+from utils import dataloader, standardize
+
+class TestUtils(unittest.TestCase):
+
+    @unittest.skip
+    def test_dataloader(self):
+        x, y = dataloader(mode='train')
+        self.assertEqual(np.shape(x), (250000, 30))
+        self.assertEqual(np.shape(y), (250000,))
+
+    def test_stardardize(self):
+        x, y = dataloader(mode='train', reduced=False)
+        x = standardize(x)
+        npt.assert_array_almost_equal(np.mean(x, axis=0), np.zeros(30))
+        npt.assert_array_almost_equal(np.std(x, axis=0), np.ones(30))