{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "source": [ "# PageRank\n", "Dans ce notebook, vous approfondirez vos connaissances des vecteurs propres et des valeurs propres en explorant l'algorithme PageRank.\n", "\n", "Le notebook est divisé en deux parties : la première est une feuille de travail pour vous familiariser avec le fonctionnement de l'algorithme - ici, nous examinerons un micro-internet avec moins de 10 sites Web et verrons ce qu'il fait et ce qui peut mal se passer.\n", "\n", "La deuxième est une évaluation qui testera votre application de la théorie des valeurs propres à ce problème et en calculant le PageRank d'un grand réseau représentant une sous-section de l'internet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partie 1\n", "### Introduction\n", "\n", "PageRank (développé par Larry Page et Sergey Brin) a révolutionné la recherche sur le Web en générant une liste classée de pages Web basée sur la connectivité sous-jacente du Web. L'algorithme PageRank est basé sur un surfeur Web idéal qui, lorsqu'il atteint une page, se rend sur la page suivante en cliquant sur un lien. Le surfeur a la même probabilité de cliquer sur n'importe quel lien de la page et, lorsqu'il atteint une page sans lien, a la même probabilité de se rendre sur n'importe quelle autre page en tapant son URL. De plus, le surfeur peut occasionnellement choisir de taper une URL aléatoire au lieu de suivre les liens d'une page. \n", "\n", "Le PageRank est l'ordre classé des pages, de la page la plus probable à la moins probable que le surfeur visualisera." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Chargement des bibliothèques nécessaires\n", "%matplotlib notebook\n", "import numpy as np\n", "import numpy.linalg as la\n", "\n", "# Génération d'un graph\n", "def generate_internet(n) :\n", " c = np.full([n,n], np.arange(n))\n", " c = (abs(np.random.standard_cauchy([n,n])/2) > (np.abs(c - c.T) + 1)) + 0\n", " c = (c+1e-10) / np.sum((c+1e-10), axis=0)\n", " return c\n", " \n", "np.set_printoptions(suppress=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PageRank en tant que problème d'algèbre linéaire\n", "Imaginons un micro-internet, avec seulement 6 sites Web (**A**vocado, **B**ullseye, **C**atBabel, **D**romeda, **e**Tings et **F**aceSpace).\n", "\n", "Chaque site Web est lié à certains des autres, ce qui forme un réseau comme indiqué,\n", "\n", "![Image du micro-internet](./dOXTNcTHBZIsmBeE.png)\n", "\n", "Le principe de conception de PageRank est que les sites Web importants seront liés par des sites Web importants.\n", "\n", "Ce principe quelque peu récursif formera la base de notre réflexion.\n", "\n", "Imaginez que nous avons 100 *utilisateurs* sur notre micro-internet, chacun visualisant un seul site Web à la fois.\n", "\n", "Chaque minute, les utilisateurs suivent un lien sur leur site Web vers un autre site sur le micro-internet.\n", "\n", "Après un certain temps, les sites Web qui sont les plus liés auront plus de utilisateurs qui les visitent, et à long terme, pour chaque utilisateur qui quitte un site Web, un autre entrera, gardant le nombre total de utilisateurs sur chaque site Web constant.\n", "\n", "Le PageRank est simplement le classement des sites Web en fonction du nombre de utilisateurs qu'ils ont sur eux à la fin de ce processus.\n", "\n", "Nous représentons le nombre de utilisateurs sur chaque site Web avec le vecteur,\n", "$$\\mathbf{r} = \\begin{bmatrix} r_A \\\\ r_B \\\\ r_C \\\\ r_D \\\\ r_E \\\\ r_F \\end{bmatrix}$$\n", "\n", "Et disons que le nombre de utilisateurs sur chaque site Web à la minute $i+1$ est lié à ceux à la minute $i$ par la transformation matricielle\n", "\n", "$$ \\mathbf{r}^{(i+1)} = L \\,\\mathbf{r}^{(i)}$$\n", "avec la matrice $L$ de la forme suivante,\n", "$$ L = \\begin{bmatrix}\n", "L_{A→A} & L_{B→A} & L_{C→A} & L_{D→A} & L_{E→A} & L_{F→A} \\\\\n", "L_{A→B} & L_{B→B} & L_{C→B} & L_{D→B} & L_{E→B} & L_{F→B} \\\\\n", "L_{A→C} & L_{B→C} & L_{C→C} & L_{D→C} & L_{E→C} & L_{F→C} \\\\\n", "L_{A→D} & L_{B→D} & L_{C→D} & L_{D→D} & L_{E→D} & L_{F→D} \\\\\n", "L_{A→E} & L_{B→E} & L_{C→E} & L_{D→E} & L_{E→E} & L_{F→E} \\\\\n", "L_{A→F} & L_{B→F} & L_{C→F} & L_{D→F} & L_{E→F} & L_{F→F} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "où les colonnes représentent la probabilité de quitter un site Web pour n'importe quel autre site Web et somment à un.\n", "\n", "Les lignes déterminent la probabilité que vous avez d'entrer sur un site Web à partir de n'importe quel autre, bien que celles-ci n'aient pas besoin de s'additionner à un.\n", "\n", "Le comportement à long terme de ce système est donné par $ \\mathbf{r}^{(i+1)} = \\mathbf{r}^{(i)}$. En supprimant les exposants nous pouvons écrire,\n", "$$ L \\,\\mathbf{r} = \\mathbf{r}$$\n", "\n", "qui est une équation de valeur propre pour la matrice $L$, avec la valeur propre 1 (ceci est garanti par la structure probabiliste de la matrice $L$).\n", "\n", "Complétez la matrice $L$ ci-dessous.\n", "\n", "N'oubliez pas que c'est la probabilité de cliquer sur un autre site Web à partir de celui-ci, donc chaque colonne doit s'additionner à un (en mettant à l'échelle par le nombre de liens)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Remplacer les ??? par la probabilité de cliquer sur un lien pour chaque site.\n", "L = np.array([[0, 1/2, 1/3, 0, 0, 0 ],\n", " [1/3, 0, 0, 0, 1/2, 0 ],\n", " [1/3, 1/2, 0, 1, 0, 1/2 ],\n", " [1/3, 0, 1/3, 0, 1/2, 1/2 ],\n", " [0, 0, 0, 0, 0, 0 ],\n", " [0, 0, 1/3, 0, 0, 0 ]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En principe, nous pourrions utiliser une bibliothèque d'algèbre linéaire, comme ci-dessous, pour calculer les valeurs propres et les vecteurs.\n", "\n", "Et cela fonctionnerait pour un petit système. Mais cela devient ingérable pour les grands systèmes.\n", "\n", "Et puisque nous ne nous soucions que du vecteur propre principal (celui avec la plus grande valeur propre, qui sera 1 dans ce cas), nous pouvons utiliser la *méthode de la puissance itérée* qui évoluera mieux et sera plus rapide pour les grands systèmes.\n", "\n", "Utilisez le code ci-dessous pour jeter un œil au PageRank de ce micro-internet." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([16. , 5.33333333, 40. , 25.33333333, 0. ,\n", " 13.33333333])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eVals, eVecs = la.eig(L) # Gets the eigenvalues and vectors\n", "order = np.absolute(eVals).argsort()[::-1] # Orders them by their eigenvalues\n", "eVals = eVals[order]\n", "eVecs = eVecs[:,order]\n", "\n", "r = eVecs[:, 0] # Sets r to be the principal eigenvector\n", "100 * np.real(r / np.sum(r)) # Make this eigenvector sum to one, then multiply by 100 Procrastinating Pats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons voir à partir de cette liste, le nombre de utilisations Procrastinateurs que nous nous attendons à trouver sur chaque site Web après un long temps.\n", "\n", "En les mettant dans l'ordre de *popularité* (basé sur cette métrique), le PageRank de ce micro-internet est :\n", "\n", "**C**, **D**, **A**, **F**, **B**, **E**\n", "\n", "En se référant au diagramme du micro-internet, est-ce ce à quoi vous vous attendiez ?\n", "\n", "Convaincez-vous que, en fonction des pages qui semblent importantes compte tenu des autres qui y sont liées, il s'agit d'un classement raisonnable.\n", "\n", "Essayons maintenant d'obtenir le même résultat en utilisant la méthode de la puissance itérée qui a été abordée dans la vidéo.\n", "\n", "Cette méthode sera beaucoup meilleure pour gérer les grands systèmes.\n", "\n", "Tout d'abord, définissons notre vecteur initial, $\\mathbf{r}^{(0)}$, afin que nous ayons les 100 utilisateurs répartis uniformément sur chacun des 6 sites Web." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([16.66666667, 16.66666667, 16.66666667, 16.66666667, 16.66666667,\n", " 16.66666667])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 100 * np.ones(6) / 6 # Répartition uniforme des utilisateurs\n", "r # Affiche la valeur de r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ensuite, mettons à jour le vecteur à la minute suivante, avec la matrice $L$.\n", "Exécutez la cellule suivante plusieurs fois, jusqu'à ce que la réponse se stabilise." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([13.88888889, 13.88888889, 38.88888889, 27.77777778, 0. ,\n", " 5.55555556])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = L @ r # Multiplication de la r par la matrice d'itération\n", "r # Affiche la valeur de r\n", "# Rexécuter cette fonction plusieurs fois" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons automatiser l'application de cette matrice plusieurs fois comme suit," ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([16. , 5.33333333, 40. , 25.33333333, 0. ,\n", " 13.33333333])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 100 * np.ones(6) / 6 # Vecteur initial\n", "for i in np.arange(100) : # Répéter 100 fois\n", " r = L @ r\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ou mieux encore, nous pouvons continuer à exécuter jusqu'à ce que nous atteignions la tolérance requise." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "18 iterations pour converger.\n" ] }, { "data": { "text/plain": [ "array([16.00149917, 5.33252025, 39.99916911, 25.3324738 , 0. ,\n", " 13.33433767])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 100 * np.ones(6) / 6 # Sets up this vector (6 entries of 1/6 × 100 each)\n", "lastR = r\n", "r = L @ r\n", "i = 0\n", "while la.norm(lastR - r) > 0.01 :\n", " lastR = r\n", " r = L @ r\n", " i += 1\n", "print(str(i) + \" iterations pour converger.\")\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Paramètre d'amortissement\n", "\n", "Le système que nous venons d'étudier a convergé assez rapidement vers la bonne réponse.\n", "\n", "Considérons une extension de notre micro-internet où les choses commencent à mal tourner.\n", "Disons qu'un nouveau site Web est ajouté au micro-internet : le site Web de *G*.\n", "\n", "Ce site Web est lié par *G* et ne relie que lui-même.\n", "\n", "![Image du micro-internet](./fNyblyvXfGKKIQeZ.png)\n", "\n", "Intuitivement, seul *G*, qui se trouve dans la moitié inférieure du classement des pages, est lié à ce site Web parmi les deux autres auxquels il est lié, nous pouvons donc nous attendre à ce que le site de *G* ait un score PageRank correspondant faible.\n", "\n", "Construisez la nouvelle matrice $L$ pour le micro-internet étendu et utilisez Power-Iteration sur le vecteur utilisations Procrastinateurs.\n", "\n", "Voyez ce qui se passe..." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Afin de distinguer les matrices, nous appelerons cette matrice L2.\n", "L2 = np.array([[0, 1/2, 1/3, 0, 0, 0, 0 ],\n", " [1/3, 0, 0, 0, 1/2, 0, 0 ],\n", " [1/3, 1/2, 0, 1, 0, 1/3, 0 ],\n", " [1/3, 0, 1/3, 0, 1/2, 1/3, 0 ],\n", " [0, 0, 0, 0, 0, 0, 0 ],\n", " [0, 0, 1/3, 0, 0, 0, 0 ],\n", " [0, 0, 0, 0, 0, 1/3, 1 ]])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "131 iterations pour converger.\n" ] }, { "data": { "text/plain": [ "array([ 0.03046998, 0.01064323, 0.07126612, 0.04423198, 0. ,\n", " 0.02489342, 99.81849527])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 100 * np.ones(7) / 7 #\n", "lastR = r\n", "r = L2 @ r\n", "i = 0\n", "while la.norm(lastR - r) > 0.01 :\n", " lastR = r\n", " r = L2 @ r\n", " i += 1\n", "print(str(i) + \" iterations pour converger.\")\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ce n'est pas bon ! *G* semble prendre tout le trafic sur le micro-internet et, d'une manière ou d'une autre, arrive en tête du PageRank.\n", "\n", "Ce comportement peut être compris, car une fois qu'un Pat arrive sur le site Web de *G*, il ne peut pas partir, car tous les liens retournent vers Geoff.\n", "\n", "Pour lutter contre cela, nous pouvons ajouter une petite probabilité que les utilisations ne suivent aucun lien sur une page Web, mais visitent plutôt un site Web sur le micro-internet au hasard.\n", "\n", "Nous dirons que la probabilité qu'ils suivent un lien est $d$ et la probabilité de choisir un site Web aléatoire est donc $1-d$.\n", "\n", "Nous pouvons utiliser une nouvelle matrice pour déterminer où les utilisations visitent chaque minute.\n", "\n", "$$ M = d \\, L + \\frac{1-d}{n} \\, J $$\n", "où $J$ est une matrice $n\\times n$ où chaque élément est un.\n", "\n", "Si $d$ est égal à un, nous avons le cas que nous avions précédemment, alors que si $d$ est égal à zéro, nous visiterons toujours une page Web aléatoire et par conséquent toutes les pages Web seront également probables et également classées.\n", "\n", "Pour que cette extension fonctionne au mieux, $1-d$ doit être quelque peu petit - bien que nous n'entrerons pas dans une discussion sur la taille exacte.\n", "\n", "Réessayons ce PageRank avec cette extension.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "d = 0.5 # Vous pouvez tester différentes valeurs pour ce paramètre\n", "M = d * L2 + (1-d)/7 * np.ones([7, 7]) # np.ones() est la matrice contenant uniquement des 1." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "8 iterations to convergence.\n" ] }, { "data": { "text/plain": [ "array([13.68217054, 11.20902965, 22.41964343, 16.7593433 , 7.14285714,\n", " 10.87976354, 17.90719239])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = 100 * np.ones(7) / 7 # Sets up this vector (6 entries of 1/6 × 100 each)\n", "lastR = r\n", "r = M @ r\n", "i = 0\n", "while la.norm(lastR - r) > 0.01 :\n", " lastR = r\n", " r = M @ r\n", " i += 1\n", "print(str(i) + \" iterations to convergence.\")\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "C'est certainement mieux, le PageRank donne des nombres raisonnables pour les utilisations Procrastinateurs qui finissent sur chaque page Web.\n", "\n", "Cependant, cette méthode prédit toujours que Geoff a une page Web de haut rang.\n", "\n", "Cela pourrait être considéré comme une conséquence de l'utilisation d'un petit réseau. Nous pourrions également contourner le problème en ne comptant pas les auto-liens lors de la production de la matrice L (et si un site Web n'a pas de liens sortants, faites-le lier à tous les sites Web de manière égale).\n", "\n", "Nous n'irons pas plus loin dans cette voie, car cela relève plutôt du domaine des améliorations de PageRank que des problèmes de valeurs propres.\n", "\n", "Vous êtes maintenant dans une bonne position, ayant acquis une compréhension de PageRank, pour produire votre propre code afin de calculer le PageRank d'un site Web avec des milliers d'entrées.\n", "\n", "Bonne chance!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partie 2 - Exercice\n", "\n", "Il vous est demandé de produire une fonction capable de calculer le PageRank pour une matrice de probabilité arbitrairement grande\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def pageRank(linkMatrix, d) :\n", " shape = linkMatrix.shape\n", " M = d * linkMatrix + (1-d)/7 * np.ones(shape) # np.ones() est la matrice contenant uniquement des 1.\n", " r = 100 * np.ones(shape[0]) / (shape[0])\n", " lastR = r\n", " r = M @ r\n", " i = 0\n", " while la.norm(lastR - r) > 0.01 :\n", " lastR = r\n", " r = M @ r\n", " i += 1 \n", " return r\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tester votre code" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0. , 0.33333333, 0.2 , 0. ],\n", " [0. , 0. , 0. , 0.2 , 0. ],\n", " [1. , 0. , 0.33333333, 0.2 , 0. ],\n", " [0. , 1. , 0. , 0.2 , 0. ],\n", " [0. , 0. , 0.33333333, 0.2 , 1. ]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Généré des réseaux de taille diffférents\n", "generate_internet(5)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Comparer votre algorithme à celui donner par défaut pour des résaux plus grands \n", "L = generate_internet(10)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([99.70283456, 0.06932741, 0.01855446, 0.0182651 , 0.09856206,\n", " 0.00899638, 0.00899638, 0.03765285, 0.02781443, 0.00899638])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pageRank(L, 1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([99.9999969, 0.0000007, 0.0000002, 0.0000002, 0.000001 ,\n", " 0.0000001, 0.0000001, 0.0000004, 0.0000003, 0.0000001])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Do note, this is calculating the eigenvalues of the link matrix, L,\n", "# without any damping. It may give different results that your pageRank function.\n", "# If you wish, you could modify this cell to include damping.\n", "# (There is no credit for this though)\n", "eVals, eVecs = la.eig(L) # Obtention des valeurs et vecteurs propres\n", "order = np.absolute(eVals).argsort()[::-1] # Tri des valeurs propres\n", "eVals = eVals[order]\n", "eVecs = eVecs[:,order]\n", "\n", "r = eVecs[:, 0]\n", "100 * np.real(r / np.sum(r))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "/* global mpl */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function () {\n", " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert(\n", " 'Your browser does not have WebSocket support. ' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.'\n", " );\n", " }\n", "};\n", "\n", "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = this.ws.binaryType !== undefined;\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById('mpl-warnings');\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent =\n", " 'This browser does not support binary websocket messages. ' +\n", " 'Performance may be slow.';\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = document.createElement('div');\n", " this.root.setAttribute('style', 'display: inline-block');\n", " this._root_extra_style(this.root);\n", "\n", " parent_element.appendChild(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message('supports_binary', { value: fig.supports_binary });\n", " fig.send_message('send_image_mode', {});\n", " if (fig.ratio !== 1) {\n", " fig.send_message('set_device_pixel_ratio', {\n", " device_pixel_ratio: fig.ratio,\n", " });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = document.createElement('div');\n", " titlebar.classList =\n", " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", " var titletext = document.createElement('div');\n", " titletext.classList = 'ui-dialog-title';\n", " titletext.setAttribute(\n", " 'style',\n", " 'width: 100%; text-align: center; padding: 3px;'\n", " );\n", " titlebar.appendChild(titletext);\n", " this.root.appendChild(titlebar);\n", " this.header = titletext;\n", "};\n", "\n", "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", "\n", "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", "\n", "mpl.figure.prototype._init_canvas = function () {\n", " var fig = this;\n", "\n", " var canvas_div = (this.canvas_div = document.createElement('div'));\n", " canvas_div.setAttribute('tabindex', '0');\n", " canvas_div.setAttribute(\n", " 'style',\n", " 'border: 1px solid #ddd;' +\n", " 'box-sizing: content-box;' +\n", " 'clear: both;' +\n", " 'min-height: 1px;' +\n", " 'min-width: 1px;' +\n", " 'outline: 0;' +\n", " 'overflow: hidden;' +\n", " 'position: relative;' +\n", " 'resize: both;' +\n", " 'z-index: 2;'\n", " );\n", "\n", " function on_keyboard_event_closure(name) {\n", " return function (event) {\n", " return fig.key_event(event, name);\n", " };\n", " }\n", "\n", " canvas_div.addEventListener(\n", " 'keydown',\n", " on_keyboard_event_closure('key_press')\n", " );\n", " canvas_div.addEventListener(\n", " 'keyup',\n", " on_keyboard_event_closure('key_release')\n", " );\n", "\n", " this._canvas_extra_style(canvas_div);\n", " this.root.appendChild(canvas_div);\n", "\n", " var canvas = (this.canvas = document.createElement('canvas'));\n", " canvas.classList.add('mpl-canvas');\n", " canvas.setAttribute(\n", " 'style',\n", " 'box-sizing: content-box;' +\n", " 'pointer-events: none;' +\n", " 'position: relative;' +\n", " 'z-index: 0;'\n", " );\n", "\n", " this.context = canvas.getContext('2d');\n", "\n", " var backingStore =\n", " this.context.backingStorePixelRatio ||\n", " this.context.webkitBackingStorePixelRatio ||\n", " this.context.mozBackingStorePixelRatio ||\n", " this.context.msBackingStorePixelRatio ||\n", " this.context.oBackingStorePixelRatio ||\n", " this.context.backingStorePixelRatio ||\n", " 1;\n", "\n", " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", " 'canvas'\n", " ));\n", " rubberband_canvas.setAttribute(\n", " 'style',\n", " 'box-sizing: content-box;' +\n", " 'left: 0;' +\n", " 'pointer-events: none;' +\n", " 'position: absolute;' +\n", " 'top: 0;' +\n", " 'z-index: 1;'\n", " );\n", "\n", " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", " if (this.ResizeObserver === undefined) {\n", " if (window.ResizeObserver !== undefined) {\n", " this.ResizeObserver = window.ResizeObserver;\n", " } else {\n", " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", " this.ResizeObserver = obs.ResizeObserver;\n", " }\n", " }\n", "\n", " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", " var nentries = entries.length;\n", " for (var i = 0; i < nentries; i++) {\n", " var entry = entries[i];\n", " var width, height;\n", " if (entry.contentBoxSize) {\n", " if (entry.contentBoxSize instanceof Array) {\n", " // Chrome 84 implements new version of spec.\n", " width = entry.contentBoxSize[0].inlineSize;\n", " height = entry.contentBoxSize[0].blockSize;\n", " } else {\n", " // Firefox implements old version of spec.\n", " width = entry.contentBoxSize.inlineSize;\n", " height = entry.contentBoxSize.blockSize;\n", " }\n", " } else {\n", " // Chrome <84 implements even older version of spec.\n", " width = entry.contentRect.width;\n", " height = entry.contentRect.height;\n", " }\n", "\n", " // Keep the size of the canvas and rubber band canvas in sync with\n", " // the canvas container.\n", " if (entry.devicePixelContentBoxSize) {\n", " // Chrome 84 implements new version of spec.\n", " canvas.setAttribute(\n", " 'width',\n", " entry.devicePixelContentBoxSize[0].inlineSize\n", " );\n", " canvas.setAttribute(\n", " 'height',\n", " entry.devicePixelContentBoxSize[0].blockSize\n", " );\n", " } else {\n", " canvas.setAttribute('width', width * fig.ratio);\n", " canvas.setAttribute('height', height * fig.ratio);\n", " }\n", " /* This rescales the canvas back to display pixels, so that it\n", " * appears correct on HiDPI screens. */\n", " canvas.style.width = width + 'px';\n", " canvas.style.height = height + 'px';\n", "\n", " rubberband_canvas.setAttribute('width', width);\n", " rubberband_canvas.setAttribute('height', height);\n", "\n", " // And update the size in Python. We ignore the initial 0/0 size\n", " // that occurs as the element is placed into the DOM, which should\n", " // otherwise not happen due to the minimum size styling.\n", " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " this.resizeObserverInstance.observe(canvas_div);\n", "\n", " function on_mouse_event_closure(name) {\n", " /* User Agent sniffing is bad, but WebKit is busted:\n", " * https://bugs.webkit.org/show_bug.cgi?id=144526\n", " * https://bugs.webkit.org/show_bug.cgi?id=181818\n", " * The worst that happens here is that they get an extra browser\n", " * selection when dragging, if this check fails to catch them.\n", " */\n", " var UA = navigator.userAgent;\n", " var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n", " if(isWebKit) {\n", " return function (event) {\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We\n", " * want to control all of the cursor setting manually through\n", " * the 'cursor' event from matplotlib */\n", " event.preventDefault()\n", " return fig.mouse_event(event, name);\n", " };\n", " } else {\n", " return function (event) {\n", " return fig.mouse_event(event, name);\n", " };\n", " }\n", " }\n", "\n", " canvas_div.addEventListener(\n", " 'mousedown',\n", " on_mouse_event_closure('button_press')\n", " );\n", " canvas_div.addEventListener(\n", " 'mouseup',\n", " on_mouse_event_closure('button_release')\n", " );\n", " canvas_div.addEventListener(\n", " 'dblclick',\n", " on_mouse_event_closure('dblclick')\n", " );\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " canvas_div.addEventListener(\n", " 'mousemove',\n", " on_mouse_event_closure('motion_notify')\n", " );\n", "\n", " canvas_div.addEventListener(\n", " 'mouseenter',\n", " on_mouse_event_closure('figure_enter')\n", " );\n", " canvas_div.addEventListener(\n", " 'mouseleave',\n", " on_mouse_event_closure('figure_leave')\n", " );\n", "\n", " canvas_div.addEventListener('wheel', function (event) {\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " on_mouse_event_closure('scroll')(event);\n", " });\n", "\n", " canvas_div.appendChild(canvas);\n", " canvas_div.appendChild(rubberband_canvas);\n", "\n", " this.rubberband_context = rubberband_canvas.getContext('2d');\n", " this.rubberband_context.strokeStyle = '#000000';\n", "\n", " this._resize_canvas = function (width, height, forward) {\n", " if (forward) {\n", " canvas_div.style.width = width + 'px';\n", " canvas_div.style.height = height + 'px';\n", " }\n", " };\n", "\n", " // Disable right mouse context menu.\n", " canvas_div.addEventListener('contextmenu', function (_e) {\n", " event.preventDefault();\n", " return false;\n", " });\n", "\n", " function set_focus() {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "};\n", "\n", "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", " var toolbar = document.createElement('div');\n", " toolbar.classList = 'mpl-toolbar';\n", " this.root.appendChild(toolbar);\n", "\n", " function on_click_closure(name) {\n", " return function (_event) {\n", " return fig.toolbar_button_onclick(name);\n", " };\n", " }\n", "\n", " function on_mouseover_closure(tooltip) {\n", " return function (event) {\n", " if (!event.currentTarget.disabled) {\n", " return fig.toolbar_button_onmouseover(tooltip);\n", " }\n", " };\n", " }\n", "\n", " fig.buttons = {};\n", " var buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'mpl-button-group';\n", " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'mpl-button-group';\n", " continue;\n", " }\n", "\n", " var button = (fig.buttons[name] = document.createElement('button'));\n", " button.classList = 'mpl-widget';\n", " button.setAttribute('role', 'button');\n", " button.setAttribute('aria-disabled', 'false');\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", "\n", " var icon_img = document.createElement('img');\n", " icon_img.src = '_images/' + image + '.png';\n", " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", " icon_img.alt = tooltip;\n", " button.appendChild(icon_img);\n", "\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " var fmt_picker = document.createElement('select');\n", " fmt_picker.classList = 'mpl-widget';\n", " toolbar.appendChild(fmt_picker);\n", " this.format_dropdown = fmt_picker;\n", "\n", " for (var ind in mpl.extensions) {\n", " var fmt = mpl.extensions[ind];\n", " var option = document.createElement('option');\n", " option.selected = fmt === mpl.default_extension;\n", " option.innerHTML = fmt;\n", " fmt_picker.appendChild(option);\n", " }\n", "\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "};\n", "\n", "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", " // which will in turn request a refresh of the image.\n", " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", "};\n", "\n", "mpl.figure.prototype.send_message = function (type, properties) {\n", " properties['type'] = type;\n", " properties['figure_id'] = this.id;\n", " this.ws.send(JSON.stringify(properties));\n", "};\n", "\n", "mpl.figure.prototype.send_draw_message = function () {\n", " if (!this.waiting) {\n", " this.waiting = true;\n", " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " var format_dropdown = fig.format_dropdown;\n", " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", " fig.ondownload(fig, format);\n", "};\n", "\n", "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", " var size = msg['size'];\n", " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", " fig._resize_canvas(size[0], size[1], msg['forward']);\n", " fig.send_message('refresh', {});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", " var x0 = msg['x0'] / fig.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", " var x1 = msg['x1'] / fig.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / fig.ratio,\n", " fig.canvas.height / fig.ratio\n", " );\n", "\n", " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", "};\n", "\n", "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", " // Updates the figure title.\n", " fig.header.textContent = msg['label'];\n", "};\n", "\n", "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", " fig.canvas_div.style.cursor = msg['cursor'];\n", "};\n", "\n", "mpl.figure.prototype.handle_message = function (fig, msg) {\n", " fig.message.textContent = msg['message'];\n", "};\n", "\n", "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", " // Request the server to send over a new figure.\n", " fig.send_draw_message();\n", "};\n", "\n", "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", " fig.image_mode = msg['mode'];\n", "};\n", "\n", "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", " for (var key in msg) {\n", " if (!(key in fig.buttons)) {\n", " continue;\n", " }\n", " fig.buttons[key].disabled = !msg[key];\n", " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", " if (msg['mode'] === 'PAN') {\n", " fig.buttons['Pan'].classList.add('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " } else if (msg['mode'] === 'ZOOM') {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.add('active');\n", " } else {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " }\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Called whenever the canvas gets updated.\n", " this.send_message('ack', {});\n", "};\n", "\n", "// A function to construct a web socket function for onmessage handling.\n", "// Called in the figure constructor.\n", "mpl.figure.prototype._make_on_message_function = function (fig) {\n", " return function socket_on_message(evt) {\n", " if (evt.data instanceof Blob) {\n", " var img = evt.data;\n", " if (img.type !== 'image/png') {\n", " /* FIXME: We get \"Resource interpreted as Image but\n", " * transferred with MIME type text/plain:\" errors on\n", " * Chrome. But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " img.type = 'image/png';\n", " }\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src\n", " );\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " img\n", " );\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " } else if (\n", " typeof evt.data === 'string' &&\n", " evt.data.slice(0, 21) === 'data:image/png;base64'\n", " ) {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig['handle_' + msg_type];\n", " } catch (e) {\n", " console.log(\n", " \"No handler for the '\" + msg_type + \"' message type: \",\n", " msg\n", " );\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\n", " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", " e,\n", " e.stack,\n", " msg\n", " );\n", " }\n", " }\n", " };\n", "};\n", "\n", "function getModifiers(event) {\n", " var mods = [];\n", " if (event.ctrlKey) {\n", " mods.push('ctrl');\n", " }\n", " if (event.altKey) {\n", " mods.push('alt');\n", " }\n", " if (event.shiftKey) {\n", " mods.push('shift');\n", " }\n", " if (event.metaKey) {\n", " mods.push('meta');\n", " }\n", " return mods;\n", "}\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * https://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys(original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object') {\n", " obj[key] = original[key];\n", " }\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function (event, name) {\n", " if (name === 'button_press') {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " // from https://stackoverflow.com/q/1114465\n", " var boundingRect = this.canvas.getBoundingClientRect();\n", " var x = (event.clientX - boundingRect.left) * this.ratio;\n", " var y = (event.clientY - boundingRect.top) * this.ratio;\n", "\n", " this.send_message(name, {\n", " x: x,\n", " y: y,\n", " button: event.button,\n", " step: event.step,\n", " modifiers: getModifiers(event),\n", " guiEvent: simpleKeys(event),\n", " });\n", "\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", " // Handle any extra behaviour associated with a key event\n", "};\n", "\n", "mpl.figure.prototype.key_event = function (event, name) {\n", " // Prevent repeat events\n", " if (name === 'key_press') {\n", " if (event.key === this._key) {\n", " return;\n", " } else {\n", " this._key = event.key;\n", " }\n", " }\n", " if (name === 'key_release') {\n", " this._key = null;\n", " }\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.key !== 'Control') {\n", " value += 'ctrl+';\n", " }\n", " else if (event.altKey && event.key !== 'Alt') {\n", " value += 'alt+';\n", " }\n", " else if (event.shiftKey && event.key !== 'Shift') {\n", " value += 'shift+';\n", " }\n", "\n", " value += 'k' + event.key;\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", " if (name === 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message('toolbar_button', { name: name });\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "\n", "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", "// prettier-ignore\n", "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n", "\n", "mpl.default_extension = \"png\";/* global mpl */\n", "\n", "var comm_websocket_adapter = function (comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. Currently this is a non binary\n", " // socket, so there is still some room for performance tuning.\n", " var ws = {};\n", "\n", " ws.binaryType = comm.kernel.ws.binaryType;\n", " ws.readyState = comm.kernel.ws.readyState;\n", " function updateReadyState(_event) {\n", " if (comm.kernel.ws) {\n", " ws.readyState = comm.kernel.ws.readyState;\n", " } else {\n", " ws.readyState = 3; // Closed state.\n", " }\n", " }\n", " comm.kernel.ws.addEventListener('open', updateReadyState);\n", " comm.kernel.ws.addEventListener('close', updateReadyState);\n", " comm.kernel.ws.addEventListener('error', updateReadyState);\n", "\n", " ws.close = function () {\n", " comm.close();\n", " };\n", " ws.send = function (m) {\n", " //console.log('sending', m);\n", " comm.send(m);\n", " };\n", " // Register the callback with on_msg.\n", " comm.on_msg(function (msg) {\n", " //console.log('receiving', msg['content']['data'], msg);\n", " var data = msg['content']['data'];\n", " if (data['blob'] !== undefined) {\n", " data = {\n", " data: new Blob(msg['buffers'], { type: data['blob'] }),\n", " };\n", " }\n", " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", " ws.onmessage(data);\n", " });\n", " return ws;\n", "};\n", "\n", "mpl.mpl_figure_comm = function (comm, msg) {\n", " // This is the function which gets called when the mpl process\n", " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", "\n", " var id = msg.content.data.id;\n", " // Get hold of the div created by the display call when the Comm\n", " // socket was opened in Python.\n", " var element = document.getElementById(id);\n", " var ws_proxy = comm_websocket_adapter(comm);\n", "\n", " function ondownload(figure, _format) {\n", " window.open(figure.canvas.toDataURL());\n", " }\n", "\n", " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", "\n", " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", " // web socket which is closed, not our websocket->open comm proxy.\n", " ws_proxy.onopen();\n", "\n", " fig.parent_element = element;\n", " fig.cell_info = mpl.find_output_cell(\"
\");\n", " if (!fig.cell_info) {\n", " console.error('Failed to find cell for figure', id, fig);\n", " return;\n", " }\n", " fig.cell_info[0].output_area.element.on(\n", " 'cleared',\n", " { fig: fig },\n", " fig._remove_fig_handler\n", " );\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / fig.ratio;\n", " fig.cell_info[0].output_area.element.off(\n", " 'cleared',\n", " fig._remove_fig_handler\n", " );\n", " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable();\n", " fig.parent_element.innerHTML =\n", " '';\n", " fig.close_ws(fig, msg);\n", "};\n", "\n", "mpl.figure.prototype.close_ws = function (fig, msg) {\n", " fig.send_message('closing', msg);\n", " // fig.ws.close()\n", "};\n", "\n", "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", " // Turn the data on the canvas into data in the output cell.\n", " var width = this.canvas.width / this.ratio;\n", " var dataURL = this.canvas.toDataURL();\n", " this.cell_info[1]['text/html'] =\n", " '';\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Tell IPython that the notebook contents must change.\n", " IPython.notebook.set_dirty(true);\n", " this.send_message('ack', {});\n", " var fig = this;\n", " // Wait a second, then push the new image to the DOM so\n", " // that it is saved nicely (might be nice to debounce this).\n", " setTimeout(function () {\n", " fig.push_to_output();\n", " }, 1000);\n", "};\n", "\n", "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", " var toolbar = document.createElement('div');\n", " toolbar.classList = 'btn-toolbar';\n", " this.root.appendChild(toolbar);\n", "\n", " function on_click_closure(name) {\n", " return function (_event) {\n", " return fig.toolbar_button_onclick(name);\n", " };\n", " }\n", "\n", " function on_mouseover_closure(tooltip) {\n", " return function (event) {\n", " if (!event.currentTarget.disabled) {\n", " return fig.toolbar_button_onmouseover(tooltip);\n", " }\n", " };\n", " }\n", "\n", " fig.buttons = {};\n", " var buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " var button;\n", " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " continue;\n", " }\n", "\n", " button = fig.buttons[name] = document.createElement('button');\n", " button.classList = 'btn btn-default';\n", " button.href = '#';\n", " button.title = name;\n", " button.innerHTML = '';\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message pull-right';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "\n", " // Add the close button to the window.\n", " var buttongrp = document.createElement('div');\n", " buttongrp.classList = 'btn-group inline pull-right';\n", " button = document.createElement('button');\n", " button.classList = 'btn btn-mini btn-primary';\n", " button.href = '#';\n", " button.title = 'Stop Interaction';\n", " button.innerHTML = '';\n", " button.addEventListener('click', function (_evt) {\n", " fig.handle_close(fig, {});\n", " });\n", " button.addEventListener(\n", " 'mouseover',\n", " on_mouseover_closure('Stop Interaction')\n", " );\n", " buttongrp.appendChild(button);\n", " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", "};\n", "\n", "mpl.figure.prototype._remove_fig_handler = function (event) {\n", " var fig = event.data.fig;\n", " if (event.target !== this) {\n", " // Ignore bubbled events from children.\n", " return;\n", " }\n", " fig.close_ws(fig, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", "};\n", "\n", "mpl.figure.prototype._canvas_extra_style = function (el) {\n", " // this is important to make the div 'focusable\n", " el.setAttribute('tabindex', 0);\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " } else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which === 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " fig.ondownload(fig, null);\n", "};\n", "\n", "mpl.find_output_cell = function (html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i = 0; i < ncells; i++) {\n", " var cell = cells[i];\n", " if (cell.cell_type === 'code') {\n", " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", " var data = cell.output_area.outputs[j];\n", " if (data.data) {\n", " // IPython >= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] === html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "};\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel !== null) {\n", " IPython.notebook.kernel.comm_manager.register_target(\n", " 'matplotlib',\n", " mpl.mpl_figure_comm\n", " );\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Représentation graphique du page rank\n", "from matplotlib import pyplot as plt\n", "\n", "r = pageRank(generate_internet(100), 1.)\n", "plt.bar(np.arange(r.shape[0]), r);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "coursera": { "course_slug": "linear-algebra-machine-learning", "graded_item_id": "Sfbnp", "launcher_item_id": "aPxf3" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.3" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": true, "autocomplete": false, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }