{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TP0 : Notebooks et Python\n", "\n", "## 1. Introduction aux notebooks\n", "\n", "Pour lancer Jupyter, il faut, dans un terminal, lancer la commande\n", "\n", "`jupyter-notebook`\n", "\n", "Cela ouvrira automatiquement un navigateur Web dans lequel on peut travailler. L'onglet principal représente l’arborescence des fichiers depuis le fichier où la commande à été lancé.\n", "\n", "Les notebooks sont composés de cellules contenant du code (en python) ou du texte (simple ou formaté avec les balisages Markdown). Ces notebooks permettent de faire des calculs interactifs en Python, et constituent un outil de choix pour l'enseignement.\n", "\n", "On peut éditer une cellule en double-cliquant dessus, et l’évaluer en tapant **Ctrl+Entrée** (on utilisera aussi souvent **Maj.+Entrée** pour évaluer et passer à la cellule suivante). Les boutons dans la barre d’outil vous seront très utiles, survolez-les pour faire apparaître une infobulle si leur pictogramme n’est pas assez clair. N’oubliez pas de sauvegarder de temps en temps votre travail, même si Jupyter fait des sauvegardes automatiques régulières." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercice** : Cliquer sur *Help -> User Interface Tour*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercice** : Supprimer la cellule suivante (On pourra regarder *Help -> Keyboard Shortcuts*) :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----- Supprimer moi !!! ------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cellule Markdown\n", "Le *Markdown* est un format de texte qui accepte un minimum de formattage. Il permet de rapidement :\n", "- faire des liste.\n", "- faire des *italiques*, du **gras**, du ~~barré~~, etc.\n", "- faire des [liens](https://fr.wikipedia.org/wiki/Markdown)\n", "- écrire des formules mathématiques avec $\\LaTeX$ (voir [ici](http://www.tuteurs.ens.fr/logiciels/latex/maths.html#s2) pour une rapide introduction à $\\LaTeX$).\n", "\n", "__Fun fact__ : L'application **WhatsApp** reconnaît le Markdown." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercice** : Transformer ce *mot* de italique à gras (indice : double cliquer sur la cellule précédente)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cellule Python\n", "La cellule suivante est une cellule python. On peut l'évaluer avec **Maj.+Entrée**." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a = 8 et 2*a = 16\n" ] } ], "source": [ "# Ceci est un commentaire Python\n", "# On prendra l'habitude de commenter son code :\n", "# Un code doit être lisible et compréhensible par d'autres utilisateurs\n", "#\n", "a = 8\n", "print(\"a =\", a, \"et 2*a =\", 2*a)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m **Exercice 4** : Cette cellule doit être formaté en Markdown, pas en Python...\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "**Exercice 4** : Cette cellule doit être formaté en Markdown, pas en Python..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut obtenir de l’aide interactivement avec *Jupyter*. Par exemple, si on veut connaître ce que fait une fonction (par exemple `abs`), on peut taper soit `help(abs)`, soit `abs?`, ou encore `abs`, puis **Maj+Tab** ou **Maj+2xTab**. Cette dernière option permet aussi de connaître les différents arguments que prend la fonction.\n", "\n", "**Exercice** : Que prend en entrée `str()` ? Quelle est la différence entre `2` et `str(2)` ?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "str?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### La première cellule !\n", "\n", "Au début de chaque TP, on commencera toujours par valider la cellule\n", "\n", "`%pylab inline`\n", "\n", "Cette cellule permet de charger toutes les fonctions mathématiques (librairie numpy) et d'affichage (librairie matplotlib) de Python." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Bases de Python\n", "\n", "### Structure du Python\n", "\n", "Un code python est structuré par *l’indentation*.\n", "\n", "**ATTENTION** : Les indices en Python commencent à **ZÉRO** !\n", "\n", "**ATTENTION** : On n'utilise pas de boucle *While* dans ce cours !\n", "\n", "Dans le code suivant, la commande `range(N)` renvoie la liste `[0, 1, ..., N-1]`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "J'ai 10 morceaux de chocolat\n", "Si je mange 0 morceau de chocolat,\n", " il en reste 10 .\n", "Si je mange 1 morceau de chocolat,\n", " il en reste 9 .\n", "Si je mange 2 morceaux de chocolat,\n", " il en reste 8 .\n", "Si je mange 3 morceaux de chocolat,\n", " il en reste 7 .\n", "Si je mange 4 morceaux de chocolat,\n", " il en reste 6 .\n", "Si je mange 5 morceaux de chocolat,\n", " il en reste 5 .\n", "Si je mange 6 morceaux de chocolat,\n", " il en reste 4 .\n", "Si je mange 7 morceaux de chocolat,\n", " il en reste 3 .\n", "Si je mange 8 morceaux de chocolat,\n", " il en reste 2 .\n", "Si je mange 9 morceaux de chocolat,\n", " il en reste 1 .\n", "On est sorti de la boucle for\n" ] } ], "source": [ "N = 10\n", "print(\"J'ai\", N, \"morceaux de chocolat\")\n", "\n", "for i in range(N):\n", " \n", " # Boucle for, l'indentation commence après les deux points\n", " if i < 2: \n", " \n", " #Boucle if. De nouveau les deux points\n", " print(\"Si je mange\", i, \"morceau de chocolat,\")\n", " else: \n", " #else, au même niveau d'indentation que if\n", " print(\"Si je mange\", i, \"morceaux de chocolat,\") # Pluriel !!!\n", " # On revient à l'indentation précédente, on est encore dans la boucle for\n", " print(\" il en reste\", N-i, \".\")\n", "\n", "# On revient à l’indentation précédente, on quitte la boucle for\n", "print(\"On est sorti de la boucle for\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercice** : La cellule suivante a des erreurs de code. Corrigez les ! (On lira attentivement les messages d'erreurs)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m for i in [12,15,6,20]\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "for i in [12,15,6,20]\n", " if i > 12:\n", " print(i,\"est vraiment plus grand que 12\")\n", " else:\n", " print(\"12 est plus grand que\",i)\n", "print(\"Bravo\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Déclaration de variables" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a = 3 et b = 4\n", "a = 4 et b = 3\n" ] } ], "source": [ "a, b = 3, 4 #Raccourci pour a = 3 puis b = 4\n", "print(\"a = \", a, \"et b = \", b)\n", "a, b = b, a #Pas besoin de variables temporaires\n", "print(\"a = \", a, \"et b = \", b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Les types\n", "Python connait plusieurs types (cf cellule suivante). nous reviendrons sur les types plus tard." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a = 4 \t\t\t\t est de type \n", "a = 3.5 \t\t\t est de type \n", "a = 10000000.0 \t\t est de type \n", "a = 3.141592653589793 \t\t est de type \n", "a = True \t\t\t est de type \n", "a = Hello World! \t\t est de type \n", "a = [1, 2, 3] \t\t\t est de type \n", "a = (1.5, [1, 2], 'coucou') \t est de type \n" ] } ], "source": [ "#Entier\n", "a = 4\n", "print(\"a = \", a, \"\\t\\t\\t\\t est de type\", type(a))\n", "\n", "# Floatant\n", "a = 3.5\n", "print(\"a = \", a, \"\\t\\t\\t est de type\", type(a))\n", "a = 1e7 # Raccourci pour 10^7, --> float\n", "print(\"a = \", a, \"\\t\\t est de type\", type(a))\n", "a = pi # Python connait certaines variables standards\n", "print(\"a = \", a, \"\\t\\t est de type\", type(a))\n", "\n", "# Boolean\n", "a = True\n", "print(\"a = \", a, \"\\t\\t\\t est de type\", type(a))\n", "\n", "# String\n", "a = \"Hello World!\"\n", "print(\"a = \", a, \"\\t\\t est de type\", type(a))\n", "\n", "# Listes (taille variable)\n", "a = [1,2,3]\n", "print(\"a = \", a, \"\\t\\t\\t est de type\", type(a))\n", "\n", "# Tuples (taille fixe)\n", "a = (1.5, [1,2], \"coucou\")\n", "print(\"a = \", a, \"\\t est de type\", type(a))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En plus de ces types de base, nous travaillons avec la librairie numpy, qui introduit le type array (= matrice)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a = \n", " [[ 1 2]\n", " [90 4]] \t\t\t est de type \n" ] } ], "source": [ "# Array (matrices)\n", "a = array([[1,2], [90,4]])\n", "print(\"a = \\n\", a, \"\\t\\t\\t est de type\", type(a))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Opérations de base\n", "\n", "Python connait les opérations `+,-,/,*`, et plein d'autres encore. Voici quelques astuces et pièges" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sqrt{2} = 1.4142135623730951\n", "17 modulo 3 = 2\n", "3/2 = 1.5 est un float\n", "a = 4\n", "a = 6\n" ] } ], "source": [ "print(\"sqrt{2} = \", 2**.5) # La puissance se fait avec **\n", "print(\"17 modulo 3 = \", 17%3) # Avec %\n", "print(\"3/2 = \", 3/2, \"est un float\")\n", "\n", "a = 4\n", "print(\"a = \", a)\n", "a += 2 #Raccourci pour a = a+2 (marche aussi avec *=, /=, etc.)\n", "print(\"a = \", a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Print\n", "La fonction `print` permet d'afficher des chaines de charactères (string), et les valeurs des variables." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "On peut mettre les arguments à la suite : pi = 3.141592653589793 et e = 2.718281828459045\n", "C'est (presque) équivalent au formattage : pi = 3.141593 et e = 2.718282\n", "Le formattage permet d'afficher seulement 3 chiffres : pi = 3.142, et e =2.718\n", "Le print d'une liste est la liste des prints : ['pi', 3.141592653589793]\n", "\n", " On peut faire des sauts à la ligne avec \n", " et des tabulations avec \t.\n" ] } ], "source": [ "print(\"On peut mettre les arguments à la suite : pi =\", pi, \"et e = \", e)\n", "\n", "#On peut formatter une ligne avec le symbole %\n", "print(\"C'est (presque) équivalent au formattage : pi = %f et e = %f\"%(pi, e))\n", "#%f pour float, %d pour int, %s pour string, etc.\n", "print(\"Le formattage permet d'afficher seulement 3 chiffres : pi = %.3f, et e =%.3f\"%(pi, e))\n", "\n", "print(\"Le print d'une liste est la liste des prints : \", [\"pi\", pi])\n", "\n", "print(\"\\n On peut faire des sauts à la ligne avec \\n et des tabulations avec \\t.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Booleans\n", "\n", "Les booleans ont la valeur True ou False. La commande if prend un boolean en entrée. Voici **quelques astuces**" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cette phrase est lue\n", "celle là aussi\n" ] }, { "ename": "AssertionError", "evalue": "Attention, il y a un problème", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;31m# l'assertion permet d'arréter un code si une hypothèse n'est pas vérifiée\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0;32massert\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Attention, il y a un problème\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m: Attention, il y a un problème" ] } ], "source": [ "a = 2\n", "if a == 2: # Attention, 2 signes == pour créer un boolean\n", " print(\"cette phrase est lue\")\n", "\n", "if not (a != 2): # la négation se fait avec not, != signifie \"n'est pas égale à\"\n", " print(\"celle là aussi\")\n", "\n", "# l'assertion permet d'arréter un code si une hypothèse n'est pas vérifiée\n", "assert (a == 2) and (1 < 0), \"Attention, il y a un problème\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Liste\n", "Le code en Python se veut très lisible, voici les choses à connaître :" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "La liste vide : L = [] \n", "\n", "range(5) = range(0, 5)\n", "mais aussi\n", "range(5) = [0, 1, 2, 3, 4] \n", "\n", "Les puissances de 2 sont [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]\n", "Les puissances de 2 sont [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048] \n", "\n", "Il y a 12 éléments dans cette liste.\n" ] } ], "source": [ "#La liste vide\n", "L = []\n", "print(\"La liste vide : L =\", L, \"\\n\")\n", "\n", "# range(n) ou range(0, n) renvoie la liste (0, 1, ..., n-1) sous forme \"compacte\"\n", "print(\"range(5) = \", range(5))\n", "print(\"mais aussi\")\n", "print(\"range(5) =\", [i for i in range(5)], \"\\n\")\n", "\n", "# Création de liste par compréhension (plus lisible ET plus rapide !)\n", "puissanceDe2 = [2**n for n in range(0,11)]\n", "print(\"Les puissances de 2 sont\", puissanceDe2)\n", "\n", "# Ajouter un élément à une liste avec .append()\n", "puissanceDe2.append(2**11)\n", "print(\"Les puissances de 2 sont\", puissanceDe2, \"\\n\")\n", "\n", "# Connaitre la taille de la liste avec len\n", "print(\"Il y a\", len(puissanceDe2),\"éléments dans cette liste.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On accède à un élément d'une liste avec des crochets.\n", "\n", "**Remarque :** En Python, \n", "- les parenthèses servent à évaluer une fonction ;\n", "- les crochets servent à accéder à une mémoire.\n", "\n", "On rappele que les indices commencent à 0 en Python." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L = [1, 2, 3, 4, 5]\n", "Le premier élément est 1\n", "Le dernier élément est 5\n", "L contient la sous liste [2, 3, 4]\n" ] } ], "source": [ "L = [1,2,3,4,5]\n", "print(\"L =\", L)\n", "print(\"Le premier élément est\", L[0])\n", "print(\"Le dernier élément est\", L[-1]) #raccourci pour le dernier élément !\n", "\n", "# On peut aussi accéder à une sous liste \n", "print(\"L contient la sous liste\", L[1:4]) # Ici, [1:4] est un raccourci pour range(1,4), et vaut [1, 2, 3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Les matrices\n", "\n", "Nous attaquons maintenant le calcul matriciel, les liste de Python ne conviennent pas (cf exemple suivant). Le bon type à utiliser est l'array. Celui-ci se trouve dans la librarie `numpy`, qu'on a déjà chargé avec notre commande `%pylab inline`." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L = [1, 2, 3] \t\t\t\t Larray = [1 2 3]\n", "2*L = [1, 2, 3, 1, 2, 3] \t\t 2*Larray = [2 4 6]\n", "2\n" ] } ], "source": [ "L = [1,2,3]\n", "Larray = array(L)\n", "print(\"L =\", L, \"\\t\\t\\t\\t Larray =\", Larray)\n", "print(\"2*L =\", 2*L, \"\\t\\t 2*Larray =\", 2*Larray)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comme pour les listes, on accède aux éléments avec des crochets. Cependant, pour une matrice, il faut maintenant 2 paires de crochets !" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A = \n", " [[1 2 3]\n", " [4 5 6]\n", " [7 8 9]]\n", "L'élément au milieu du bas est 8\n" ] } ], "source": [ "A = array([[1, 2, 3], [4, 5, 6], [7,8,9]])\n", "print(\"A = \\n\", A)\n", "print(\"L'élément au milieu du bas est\", A[2][1]) # de la forme A[i][j]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Création d'array\n", "Nous décrivons maintenant les différentes façons de créer un array\n", "\n", "#### Création à partir de liste" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A = \n", " [[1 2 3]\n", " [4 5 6]\n", " [7 8 9]] \n", "\n", "et\n", "\n", "A.transpose() = \n", " [[1 4 7]\n", " [2 5 8]\n", " [3 6 9]]\n", "\n", " A = \n", " [[1 1 1]\n", " [1 2 4]\n", " [1 3 9]]\n" ] } ], "source": [ "# Creation à partir d'une liste\n", "x = array([1,2,3]) #Ici, une seule dimension --> un vecteur\n", "\n", "# On obtient une matrice avec une liste de liste\n", "# Dans ce cas, les matrices sont définies \"lignes par lignes\"\n", "A = array([[1,2,3], [4,5,6], [7,8,9]])\n", "print(\"A = \\n\", A, \"\\n\\net\\n\\nA.transpose() = \\n\", A.transpose())\n", "\n", "# On peut aussi définir \"par compréhension\" (plus lisible et plus rapide)\n", "# Ici, une matrice de Vandermonde\n", "A = array([[i**j for j in range(3)] for i in range(1,4)])\n", "print(\"\\n A = \\n\", A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Les matrices de base\n", "Python connait un certain nombre de matrices de référence. Nous utiliserons souvent les matrices suivantes." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A = \n", " [[0. 0. 0.]\n", " [0. 0. 0.]]\n", "\n", "B = \n", " [[1. 1. 1.]\n", " [1. 1. 1.]]\n", "\n", " A = \n", " [[1. 0. 0.]\n", " [0. 1. 0.]\n", " [0. 0. 1.]]\n" ] } ], "source": [ "# La matrice nulle prend des dimensions en entrée :\n", "A = zeros([2,3]) #de taille 2 x 3.\n", "print (\"A = \\n\", A)\n", "\n", "# La matrice avec que des 1 :\n", "B = ones([2,3]) \n", "print (\"\\nB = \\n\", B)\n", "\n", "# La matrice identité est carrée et ne prend qu'un seul paramètre :\n", "A = eye(3) \n", "print(\"\\n A = \\n\", A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Le calcul matriciel.\n", "\n", "**ATTENTION**, le produit de base de Python est le produit terme à terme, alors que le produit matriciel se fait avec dot." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = [1 2 3] y = [4 5 6] , x*y = [ 4 10 18] et dot(x,y) = 32\n" ] } ], "source": [ "x = array([1,2,3])\n", "y = array([4,5,6])\n", "print (\"x =\", x, \"y =\", y, \", x*y =\", x*y, \"et dot(x,y) =\", dot(x,y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**ATTENTION** Python fait la différence entre 1 et la matrice identité." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 1 =\n", " [[ 2. 1. 1.]\n", " [ 1. 2. 1.]\n", " [ 1. 1. 2.]]\n" ] } ], "source": [ "A = eye(3)\n", "print(\"A + 1 =\\n\", A + 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python connait les fonctions \"usuelles\", à savoir déterminant, trace, norm, inv, ... On peut aussi résoudre des systèmes avec solve." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "On a bien | Ax - b | = 0.0\n" ] } ], "source": [ "A = array([[(i-j)**2 for j in range(3)] for i in range(3)])\n", "b = array([0,0,1])\n", "x = solve(A,b) # La solution de Ax = b\n", "\n", "print(\"On a bien | Ax - b | = \", norm(dot(A,x) - b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercice** : Que vaut exp(eye(3)) ? Comment créer l'exponentielle de eye(3) ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Les graphiques\n", "On utilise matplotlib pour tracer les graphiques. Là aussi, les fonctions sont directement accessible grâce à la directive `%pylab` initiale.\n", "\n", "La commande de base est `plot(x,y)` où $x$ et $y$ sont des listes/array de même taille. En pratique, si on veut que $x$ représente l'intervalle $[a,b]$, on pourra utiliser la commande `linspace`." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "linspace?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voici un exemple complet pour afficher le graphe d'une fonction $f$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'x')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x) : return x**4 - cos(2*pi*x) # La fonction f\n", "\n", "xx=linspace(-1,1,100) # 100 points entre -1 et 1\n", "plot(xx, f(xx), 'r') # 'r' pour red\n", "\n", "axis('equal') # pour avoir la même échelle dans les deux axes\n", "title(\"le graphe de $f$\") # Les titres acceptent le Latex !\n", "legend(\"f\")\n", "xlabel(\"x\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Remarque** : Ici, j'utilise la convention `xx` pour désigner l'intervalle dans lequel vit `x`\n", ". C'est une convention personnelle : pour moi, une variable doublée signifie toujours l'espace dans lequel vit la variable non doublée." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut aussi tracer facilement des courbes paramétrées. Pour tracer la courbe\n", "$$\n", " c(t) = (\\sin^3(t), \\cos(t) - \\cos^4(t)),\n", "$$\n", "on peut utiliser le code suivant." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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P8fhVOYxMibY7kvIAV7uAlgBXW8+vBv7dcQYRiReRUOt5EnAc8I2L7Sovd/Lo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\np1cCK9WJyelxJESG8PHm/b3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt = linspace(0, 2*pi, 100)\n", "xx = sin(tt)**3 # f(liste) = liste(f) !\n", "yy = cos(tt) - cos(tt)**4\n", "\n", "plot(xx,yy)\n", "axis(\"equal\")\n", "title(\"Le coeur de Laporte (1993)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Enfin, on peut tracer les courbes de niveau d'une fonction à deux variables avec `contour`. Ici, on trace par exemple les courbes de niveau de \n", "$$\n", "f(x,y) = e^{-y^2} \\sin(x-y)\n", "$$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TwrnMihlcYd1S1FkI/sbhIwatEHybycieimJ2lBXxTUUxOosFF4WSqSER3Dt6ItNDIwh3\nG9rC3k98JUk618/zlhDirUvsazXwuRDivCgFSZKCgA+AHwkh7JfYd2dfA+GjP2tUJJDalY++i7al\nwHghROPF2vXFZ9YXhBB8WZjDnw9/g8lm5dnpC1geMzjFOz7LPcVvd27jztFjeOIKF4Ro0OpIzS0g\nNbeAkzW1AET7eDM3Lpp5cTGMDAoYEm88Q4FjldU8sXUXBQ2NrJk0nodnTh2UvO55DfWs+mwdCb5+\nfHzDzVfUVaa3mNleVsSmM/nsqyzBYrfj56xhTng0CyJjmRwcjtMgue6GoI9+MvCUEGLB2c+PAggh\nnu2ibRZwnxDi0Dnb3IFvgL8IIT7vy/foiivyV5EkKRCoE0KIs68iMqDpSpy7G3u4MS6JqSERPLBr\nE7/Yk0pRaxO/HDf1io5AMmuqeHz3TqaGhfP76bOuyDmNFiu7Cs+w/lQe+4tLsQnBiEB/Hpk1jQXx\nMUR6e10RO642xoYG88Wdt/Lnnd/w1uEM8uoa+NeN1+OkvHLC1qjXsyZ1Ax5qJ95YsvyKiLxdCI7U\nVPBVYS5fl+Sjs1gI1rhx54ixLIqKJ9k/yDEY6Jp0IFaSpCigis5R+23fbyRJUgLgBaSds00FfEVn\ncEu/RR4GSOglSVoHzKLzdaaSzkkFJYAQ4g1gFXCvJElWwACsFgP1KtEPAjVufLz0Fh4/sJNXstJQ\nyeQ8MHbyFTl3VUc796RuIMjNjVcWXf6qP7l19XySlc3G3Hy0JjMBbq7cNWk8K0YmEu0zNCbyhjpq\nhYI/LZzLyMAA/rBlJ/d/lcq/blyG6gqkpjDbbNz79QaaDHrW3XgLfpd5fqRW18EnBdl8WpBNlbYd\njVLJ4qh4VsUlkRIY6hD3HhBCWCVJuh/YRmd45VohRI4kSU8DGUKIjWebrgb++z09vBmYAfhIknTn\n2W13CiGOX6o9AxV1c2sP+18FXh2Icw00Spmcv0yfj9lm5cXMA4S7e152N47BYuHe1A2YbDb+u2wF\nnk6XJ6LDYrOx8/QZ3s/IIqOyGrVCzsL4WG4YNYKJ4aFDLuTxauHm5JHYheDxrbv4y869PLXg8rrc\nhBD8ce9uMmuqeXnhEkYHBF6282TUVfFezjG2lRRiFXamhUTwm5QZzI+MwVkxNCLBrhaEEJuBzd/b\n9sT3Pj/VxXEfAh8OpC1XRyzcZUYmSTw/cyHlHW08fnAHU0PCL9vqWiEEv96xlZyGet5atoJo74Gf\nCG7WG1iXdZKPj52gXqsj1NOdR+fM4MaRI66qxUBDmdVjRlHa3Mq/j2YyPz6GKZGXr0bAf05kse7U\nSe4ZN4GlcQkD3r/JZmVDUR5rT2WS39yAm0rNj5PG8oPEMYS7OwrcXAs4hP4sSpmc56YvYOEX7/H8\n0X38deaiy3Kef2UcYXPRaX43dQZzoqIHtO/aDi3vHM7gk+PZGK1WZgyL5M+L5jJjWOSQGL1bbXY6\nTCb0JjM6swWTxYrZZsNmt5+zKlKGUi5DrVDgolbiqlbh7qRGNQTj8x+eOYXtp4v44/Y9pP70jsuS\nXfRQRTnP7P+GuVHRPDJl2oD2rbeY+TjvBG9lp1Ov15Hg7cuz0+ezPHo4LsrBDyO1C4HWYqLDYsJg\ntWCwWjDbbVjsduxng1BkkoRS5sjq2hND7+4ZRGK8fPhx0ljeyc7goXFTCXEd2Hj2bWcKeTHtINfH\nJ3DX2H4FCJxHaXMLbx3OYH12LnYhuH5EAndNGk+s35WrEdqiN1DR3EZFcxvVre3UtndQ166lUaun\nWaunRW9AazL33FE3aNQqfDQuBLi7EuThRriPJ5E+XsT6+xDp64VKceVvdrVCwWNzZ3LP5xvZml/I\nshEDO9oubW3hvs2bGOblzYvzFw2YX7zNZOTdU5m8l3OMVpORyUHhvDRrMVODI65YMILeaqaso5UK\nbSuVulaqdR3UGTqoN2hpMOhoMelpMxsZ9Im8a4QhLfR1Bi2HaksZ5xd6xVay/iBxDG9nZ7CxKI97\nk7tc33BJ5Dc28KvtWxgdEMhzc+YPyA1V3dbOKwcO81V2Lgq5jFuSR/KTieMI87x8SZ60RhN5tQ3k\n1zRQWN9IUX0TxQ0ttBmM57Vzc1Lj76bBz03D6LAgvDTOeDg74e6kRqNW4aJSolYqUMnlKGSy734P\nu7BjsdkxWqwYzBa0JjPtBiPNegMNHTrq27UcLalg44m8786llMsZHuRHclgQ4yNDmRgVivsVclHN\njhlGkLsbG3LyB1ToO0wm1mxajyTB28tWDEgheJ3FzL+zM3g7O4MOs4m5ETHcO3oC4wIuX0pjk83K\n6dYGclvqKWit53RbI8XtTdToO85r5yRXEOjihr+zK8O9/PFWdyYs81A546pU4apQ4aRQdl4vkgyZ\n1PmGKoTAbLcxi9/329YWcwWfl/2y3/0MRYa00NcbtNy+ax0uCiXTAqNYFB7P3NBYXJWXb9l0uLsn\nY/2D+bqkYMCEvkmv5+7UDbiqVLyxZDlO/ZzUatLpef3QUdZlnQTgB+OTuXtyyoCvVDVarJyqquVE\nZS2nKmvJramnvPl/eUo8XZyI8fdhwYhYony9CPf2JNTbgxBPdzTqy/vqb7RYKWtqobCuibzaerIr\n6/g0I5v307KQyySSw4KZlxjDwqQ4AtxdL5sdMkliaWI8a49k0m404u7U/weMzW7n4bOF4P+zYhXh\nHv3zk5tsVj7MPc7rJ47QaNAzPyKGh8dNZbiPf79tPReb3U5BWwPHG6s50VRDdnMNha2NWM+6WZzl\nSmI9fJgUEMEwd28i3bwJd/UkVOOBl9r5Wl5cNegMaaFP9ArgrzNXsbe6mJ2VhWyvPI2LQsnSiER+\nFD+ORK+Ay3LeycHhvHniKGabrd+hcxabjfu3bKJOp+WTG28hwPXSRcdktbL26DHeTEvHaLGwcmQi\nD0ybRLDHwLiYjBYrx8qrOHymgvTSSnKq67DYOm/SEE93RgT7s3LMCIYH+zM80A8/t8HL7e6kVBAf\n6Ed8oB9LR3eOpM1WG9lVtewvLOWb/GKe27KXF7buY3psJLdOHM2M2MjLYu+k8DDePpxBfn0jE8L7\nv7L5xbSD7C4t5o+z5vSrELwQgtTiAp4/uo9KbRtTg8N5a950xgYE99tG6BT2nJY6DtaWcqSunMyG\nSrTWTvecl9qZJO9AZg2PZoR3ACO8Awh39RrSYZleqjBWRbzUy9Z/v6y2DDRDWujlksTc0Fjmhsby\nx5T5ZDZU8nnxSTaV5vLpmRPMCh7Gr0fPItF7YAU/wdsPq7BzprWpX6MeIQR/3LeHI1WVvDR/EaMD\ngy65n635hbzwzX4qW9uZFxfNI7OmMayf8e9CCArrmthfVMqhojIyy6owWW0oZDKSQgL44eSxjA0P\nZnRYED6uQz/9gUohZ1xECOMiQnho7lRKGprZcCKPL4/lcM8H64n19+HBOVOYMzx6QAU/3r9zLqRg\nAIR+Q0Eeb2T2vxD8yYZa/nx4D0drK0n08efDGTcxLSSyX7YB1Ojb2Vddwr6aYtLqymgxdWYujfXw\nZUXUCMb5hTLWN4Qw12s6/cFVx5AW+nORSRIp/mGk+Ifx2Ng5fHj6GO/kH2XplrWsjknmd2Nm464a\nGL9sgEvnqLvJqO9XPx9ln+Dj7BOsGZfCioTES+rjdEMjT2/fw5HySuL9fPnPrTf2K5TParOTXlrJ\nzrwi9uQXU9PW6SuN8ffh5pRRTIuJYFxEyGV3vVwJovy8eWjuVO6bPYnN2QW8tTedB9ZtYmJUGE8u\nu44ov4FZKObv2ukya9b373o5UVfLb3duY0JwKE9eYjqMZqOeF47u55OCk3g7ufDMtHmsjh91yVFX\nQgjyWuvZVlHAjspC8lrqAQhwduW6kBimB0YxJTASv6u82M+1zlUj9OfirnLi50lTuD12DC+fOsh/\nCjLYU3WGv0+9nkkB/Y9n/jZfh9FqveQ+DldW8PS+PcyOHMavJ/c9LM5gsfD6oaO8fTgDV5WKPy64\njluSR17SDfutuG/LOc32nCJa9AaclQqmxETw89mTmB4beVn92IONUi5neXIiS0Ym8GlGNi/vOsjK\nf33IbxbO5NYJo/o98pQkCbVC3q/rpU6r5d7UDfi5aPjXkr6vtv02f9MzR76h3WTiZyPH8+DYKZeU\nBlgIQX5rA5vL80gty6O0owWZJDHWN4TfJs9mdkg0cR6+jhH7VcRVKfTf4qF25vFxc7k+MpGHD27i\nh7vX8bfJS7k+sn81M632Tr+0XLq0UVBFWxs/37yRSA9P/r5gcZ/F+UBJGY9v3Ullazsrkobz6JyZ\nfc6HLoQgt6aeDcfz2JJdQKNWj4tKycy4KBYmxTE9NhJn1f+vlY4KuYzbJo5mbmI0f/hqB39K3U1Z\nUwu/XTgTmezSRUsIgd0uLtn/bLJauefrDbSbTXy6ajXezn1zkxW3NvP7A9s5XFPBGP8gnp2+gATv\nvtcZrta1s77kFF+VnKKovQmZJDHJP5y7hk9kflgcvk6OUfvVylUt9N8y2ieY9Qt/xJq9X/CLgxtp\nN5u4I27sJffXfNZl4+3c99QEWrOZNanrEQLeXrYS9z6ExXUYTTy/Zx+fHD9FlLcXH962iokRYX06\nf7vBSOrJAj7PyCavtgGlXM7s+CgWj4xnRlzUgIu7EIJ2g4n6Nm1nvLzOQLveiNZoRmsyYzRbMVut\nWG2di6JkkoRMJqFSyHFWKdGoVbg7q/HQOOPnpsHfw5UAT9fLsvjoW/zdXHnjjhU8t3Uv76dl0aI3\n8NwNCy9Z7DtMJix2O96XkMZZCMEf9uzkRF0try+5nkS/3s8J2ex23s05xl/T96OWy3l2+nxuiR/V\npweOxW5jd1UR/y06zt7qYgSQ4hfGn1PGszA8AR+ngZ+b0VnN1Bs6aDbpaDbraDMb6LAY0VnN6K1m\nTHYrVrsNq7AjISGXJFQyBWq5Ao1CjZtSjZfKBR8nV/yd3AhydtSM7YlrQuih053zn+tu4ef7v+LJ\njO1Eu/swOTDikvqq0XX6rf2d++bOsAvBw9u+pqi5ibXLbyDCs/dhcfuLS3l08w7qO7SsmTSeB6dP\n7lN2wpOVtXx85DhbT53GZLWREOjH40uvY8mo+H6nPbDbBVUtbRTXNVNa30JZYwuVTW1UN7dT29qB\nyWrr8jiZJOGkUqBWKFDIz8bKC4HVLjBbrRjN1u/enr5/XJCXG9EBPsQG+ZIY6s+oiCACPd369T3O\nO4dM4tFFM/F0duKV3WlE+/lw98wJl9RXTbsW+J+vvi+8fSyDL/Jy+MXEySyI7rJEQ5cUtzbzq72b\nyaqvYU54NM9On4+/S++v10ptKx8XHufT4hM0GfUEOLtyX9IUbho2inC3/mUwFULQZNJR1NFAcUcj\nZdomKnQtVOlbqda3obWauj3WSa5ALVOilMmRn31g2YTAYrdisHWujHXQd64ZoQdQyxW8PHU51299\nl18c3MDXi396SZNEeU0NuKvUBGr6JvT/OHyIXSXFPDlzNtPDI3t1jNFi5fnd+/jw2AlifL157YZb\nGR3cu6RVVpudXXlFrD2YycnKWlxUSlaMSWTVuCRGBAdckg/VZrdTXNfMqYo6cirqyK+q53RNIwaz\n5bs2Hi5OhPl4kBDiz6wR0QR4uuLnpsHHzQVPjTMeLk64OqlxVikuaoMQApPVRrveSIvOQFOHntrW\nDqqa2ylvbOFMXTOHCsq+exiEeLszOS6CGcOjmBIfgbqfKYIlSeLeWRMpaWzh5V2HGBMexISovr1B\nAeTXNwD/i77pLXtLS3j+4D6WxMbx4ITeZU0VQvBR3gn+fHgPaoWCf8xewvLo4b36WwshyGqs4u28\no2yv7KxWNyckhtUxycwIGnZJGVSFEFQb2jjVUk12SxW5rbUUtNXSbP7fxLSzXEmYxosQF09SfCMI\ncHbH38kNXydXvFQueKpccFOq0SjUPb6NWOw2OixGWkx6mkw66oztVOlbuZen+mz792kwVfNG0ZP9\n7mcock0JPYBGqeK1aStZse0/PJu1m5emLOtzH6ca6xju498noUw9nc+r6Ye5KTGJH44a06tjcmrr\n+NXGrZxpaubHKWP51aypvRrF60xmPss8xQdpWVS3thPu7cEflsxmefJwXJ36NvmmN1k4XlpNRnEl\nJ0pryC7JIPUCAAAgAElEQVSv/U7UXZ1UJIT4c8PEEcQG+hId4ENUgDceLgMT3SRJEk5KBU4ervh7\ndP1QNVutnK5uJKu0mvSiSjZn5fP54WxcnVTMGRnDTZNHMSo88JInBiVJ4qnr55BTXcfj63fw9YN3\nopD3TfByautRyuVE9SGXf1FzEw9sTWW4rx/Pz13YK/sb9Dp+t38bu8rPMD0kkr/OXEigpue3HJvd\nztaKAt7JO8rxpmrcVU7cPXwSt8eNIUTTN7eHxW4jt7WGjMYyjjVVcKKlkiaTDgClJCPWI4BZQXHE\nuwcQ4+5PtJsv/k5uAzZxq5TJ8VZr8FZriOZ/8xD3Dkjv1y7XnNADJHj5c0fsGN4ryOChkdP69Cra\nZjJyqqmO+8dM6vUxp+rr+M3ObYwPDuFPs+f2eFELIfgw8wTP7t6Ht4sza2+5genDenYzdRhNvJ+W\nxQdpx2gzmBgfGcKji2YyO2FYryd87XZBXlUd+/NLSTtdzsnSGqx2O3KZRFywH8tTEhkVHsiIsEAi\n/bz6NUk5EKgUCpLCA0kKD+QHM8ZisdpIP1PJlqwCtp88zYb0XJLCAlgzdyKzRgy7JEHRqFX8ct40\nHli3ic3ZBVyf3Lc01WllFYwNCer1vEKb0cia1A2o5QreXLaiV4Xg06rLeXB3Ku1mE49Pms2Pk8b1\nOPq12u2sLznFv3LSKOloJtLNiz+On8+Nw0ai6UPSsgpdC/tqCzlYf4YjjaXozy6KitB4Mz0ghlFe\nISR5BRPvHoDqCqUquRz4qYO5J+aPvWp7L09fZmsGliH9V6nSt9Js0uGt7rv7ZU3iJD44fYy1Bek8\nNX5+r487VF2GXQimBvfOv9+g03F36nq8nJx5bXHPYXHtRiO/37yDbQVFzIqO4oWlC/DqIaKm3WDk\nP4eO8eHh47QbTVyXMIw1MyYwOqx3C7B0RjMHC0rZm1vMgfwymrV6JAmGh/jzo1njmBATRnJkEC5X\nQey8UiFnSnwEU+Ij+N2KWXx9LI93v8nkwXc3MiYymMduvI744L5HnFyXEE1cgC/vHszsk9A3aHXk\n1zfw0IwpvWpvtdt5YEtqrwvB2+x2Xs5K45WsNCLdvfhg8U09RtRY7Da+KjnFv04dokzbSqJXAK9N\nX8mC0LheDQisdjuZTWXsrilgX10RpdrOYnDhGi+WhY5kkn8U430i8HW6dkNyrzWGtNC3mg0s3vEa\nz4y9njnBfUsY5e/syszgYeysLOLJcfN6PdJLLS7Ax8mlV4meTFYr9369gVajkU9XrcbP5eIPpFM1\ndTzwVSq1HVp+M3s6P5148VGZwWzhg7Qs/n0gg3ajibnDY7hn1gRGBPe8ElhvMrP71Bm2nTjNoYIy\nzFYb7s5qpiZEMj0hkqkJkXhfBatdL4bGScXNU0Zzw8SRbEjP4R9fH+CWv3/EvfMn87M5KX0Ka5XJ\nJFaMSeSFrfuobm0n2LN3aSW2FRQCMD+udymnnz2wt9eF4BsNOu7ftYnDNRXcEJPIn6bNu+hIXAhB\nalkeL57YS5m2lZHegbw540bmhcb2eP1b7XaONJSwpSqHndX5tFkMqGRyJvpFcduwFKYHxBDpOvC1\nExxcGYa00Me4+RGq8eT+I5+wJm4aDyVe16dX89khMeyoLORMexMxHj1PlBmsFvaUF7MiJrHHiSkh\nBI9/s5NjtTW8umgZI/wvLr5fnMzhyW278HZxYd0dN5Mc0v1o3Ga381VWLq/uTqOuXcus+CgenDOF\n4UEXD72zWG0cLCjl62P57M0txmC2EuDhys2TR3HdyBjGRAb32f987vfVGkzUtmhpbNPR1K6jRWug\nTWdEZzSjN5oxWqxYrDbs9s7ksnKZhFIhR61S4Oqkxt1FjbebC74eGoJ83Anx9cDNuf8J6hRyGTdO\nGsmckTH85as9vLr1EFklVbz0o2W4qHsfTjozLooXtu5jf2Ept6SM6tUxW/MLifbx7lVK6E9zsnn3\n+DHuTB7LLSNGXrTtsbpq7t+1kSajgb/NXMSquKSLtk+rLeO543s42VRDvKcfb81cxdyQmB4nw7Nb\nqtlUcZKtVTk0mnRoFCquC4pnbtBwpgZEo1Fc+lue0WamztBGg6mdJpOWVrOONoserdWEzmrEZLNg\nFlZsdjuCzmgrhSTHSa48G0bpjJdSg7falUBnT4KdvfBWuToWal0CQ1ro1XIFH8/4Cc+c3MJbpw9g\nFXYeGdGzD/xbkn06kzfltzb0Sui3lJxGb7WwLLrnt4e1x4/xeW4OD0yYxOLYuG7bmW02ntnxDR9n\nnWRSRBj/WL4YH033I+lDZ8p4dvNeiuqbGBUayF9vWkRK5MVHfmdqm/jiyClSM/No0RnwdHFi2bhE\nloxNIDkyuE9+dovNRklNM2eqmyiuaaKsvoXy+laqG9vQGi/MJy+XSWicVLioVTipFCgUnWmHhRCd\nYXEWG0aLBZ3B3OXxvh4aYoJ9GR7uz6hhQYyJDsFdc2mTvZ4aZ56/fREp0aH8+Yvd3P/v9bz2sxW9\nXjsQ5euFm5Oawrre1a2vaG3jSHklD07vOWIms6aKx/ecLQQ/beZF267LP8ETB3cSqHHji+tvI8m3\n+0HEmfYmnsncxZ7qMwS7uPPXSUtYGZV00beZRqOW9eUn+LIsixJtEyqZnJmBcSwNHcnMwNg+pQS3\nCzs1hlYKO2op0dZTqmugQtdItaGZZrOuy2M0CjUauRq1XIlKpkAudYbe2s+GURptFvQ2E1qLEfv3\nMtK7KpyIdg0g3j2YJM8wkr0iCXR2VMHqiYEqDr4WWArUCyEuGHpIncr8T2AxoKez0O2x3vStkit4\nKnkpCpmctYWH0ChU/Dzh4jfKt4S5dkYUVGpbe9X+v/kniXT3ZFLQxUPs9peV8uyBvcyPjuEXE7v3\nzTbp9Tz41dccLa/kZxPH8cisad3egJUtbbywdR87cosI8/Lgn6uXMi+x+xGZ2Wpl58kiPk07SWZx\nFQq5jNkjhrE8ZQRT4iN6NTFos9sprmnmVEkNOWV15JXXUVTdhOVsXLxcJhHi60G4vxdjYkII9nEn\nwMsVPw9XfNxd8HJzwdVJ1esHr9Vmp0Wrp6FVS01TBxUNrZTUNnO6soEPdmRitduRJBgREcjMUdEs\nGB9HqF/fbmJJkrhp8iicVUp+v24rD727iX/dtaJXbhxJkgjxdKeypa3HtgCfnTiFTJJYNeriK7Gr\nO9q59+uNBLu58+qiZd2+LVrsNv6ctof/5GYxPSSSV+csw0Pd9UNPazHx6qlDrM0/ipNcyW+TZ/Pj\nhPHdirQQgvSmMj4pyWRHVS4WYWecTzg/iZ3CgpBE3JQ9P1yFENQaWznVWkFOWyX5bVUUtFejs/0v\nLt7fyYMwFx+m+w8n2NmbQGcPfNXu+Krd8FJpcFM693rFuV3YabcYaDR1UGNopVrfTKmugSJtLZuq\nMvm0PA2AcJcrV2CnL0iStJBO3ZMD7wghnuum3Y3A50CKECJDkiQl8A4wlk6Nfl8I8Wx/bBmoEf17\ndBb/fr+b/YuA2LP/TQReP/v/XiFJEo+NWkSHxcRreXuZ6h/NaO+eswS6KtWoZHLazMYe22Y31HK0\ntpLfT5x5UeEqbmnm/i2pxPn48uK87qv+5NU1cO8XG2nQ6vjbsoUsT+p6gs9ksfLWvqO8cyADuSTx\n0Nyp3DllbLcx4o0dOj45eIJP07Jp1uoJ8XbnoSXTWDlhRI8+d5vdTn55PemnK8g8XcmJM9XfjbLd\nnNUkhPtz6+xk4kP9iQ3xJSLAC+UAVm5SyGX4eXQ+KBIjzl8rYDRbySmtJf10BQdPlfDaxoO8tvEg\nY2JCuGXWaGYnx/RptezSccPRmy386fNdfLT/OD+c2buV0p4uTrQbe75eDBYL/806yeyYKILcuw9x\nNFgs3J26AaPVykcrb8ajm3z1zUY99+3cRFpNOT8bOZ7fTZjZ5QNBCMGG0hz+cmw3DUYdNw0bxa+T\nZ3W7XsRgtbCp4iQfnDlCUUcD7konVg9LYXXUeIa5XVwghRBU6ptJbyriWHMJx1tKqTe1A6CWKYhx\nC2RRSDJxbsHEuAUS5eqPRjFwtSJkkgxPlQZPlYYYt/OvF5uwc6ajlmPNJaQ1Fg7YOQcKSZLkwGvA\nPKASSJckaaMQIvd77dyAXwBHztl8E6AWQoyUJMkFyJUkaZ0QovRS7RkQoRdC7JMkKfIiTZbT+VQS\nwGFJkjwlSQoSQtT09hwySeKJ0YvJaCzlsWMb+HL23QMayrX2VCauShWrE0Z326bdZGJN6nqUMhlv\nL12BRtW1//KbohIe2vA1rmo16+64mVHdLIA6WlLJkxt2UtrUwpKR8TyyYDqBHl2LRkl9M//Zm8nG\n9Dysdhszhkdx69RkJsdFXNQ109yu51BuKQdOlXAkv5w2XaeIRQV6syAlntHRwYyKCiLMb3DTyjqp\nFIyLC2VcXCj3LJ1MTXM729IL+PJANr97ZzOhfh6sWTyJxROG99oVddOkkezLLeblzQeYmRhFhF/P\nYba9/Q02nMqjxWDkJxPGddtGCMFvd24jt6Ged65fSaxP15OZpW0t3Ln1c6p1Hbw4cxE3duOPL+9o\n4Q/p29hfU8IonyDemrmKZN+uc8u3mPSsK0nnwzNHaTHrGe4RyDNjr2dRSBLOFyl8Y7SZSW8qJq2x\ngEMNp6k2tADgp3ZnjFcko70iGOkZToxbIIpBrNUql2TEuQcT5x7M6sipvMyP+91nrbGWZ/NeGADr\nAJgAFAkhigEkSfovnTqY+712fwKeB359zjYBaCRJUgDOgBlo748xV8pHHwJUnPO58uy2C4RekqQ1\nwBqA8PDzM1G6KtU8mbyUe9I+5qvy49wSdfG6qza7Hauw9zixWtnRxqYz+dyRmIx7N9n+bHY7v9ia\nSnlbGx+sWEWIe9dRGe9nZPHMzr3E+/vy9k0rCHC7MAStVW/kr9v28eWxHEK93HnnRzcwNabrcM6c\nilre3pXO7lNFKOVyVkxI5Eczx11UtCoaWtmdVcSeE0Vkl9QgBPi4uzBj5DAmJ0aQEh+Gj/vQTlAV\n5O3OnQtS+MG8cew7Wczbm4/wxH+2seFQDo/fMY9w/55dOpIk8cSquSx7/j1e336Y527vueC72Wrt\nUcBsdjtrjx5jeIAfKWHdR2e9ln6E1MICfjNlOrMjh3XZ5nBNBXfvWI8MiXVLbuky2stqt/NO3hH+\nmX0AuSTjqfHzuCN2bJfuqFpDO2sLD/F56TEMNgszA2L5SdwUUny6rwfbataxrz6Pb+pySW8qwmS3\n4ixXkeITzR1R00nxiSHcxccxCXo+vpIkZZzz+S0hxFvnfO5K887zYkiSNBYIE0J8LUnSuUL/OZ0P\nhRrABXhYCNHcH2OH3GTs2R/rLYDx48dfUBt4RkAMwz0CWVecwc2R4y568TUaddiFIMD54qsH3zhx\nFEmCNaNSum3zwqH97C0r5S/XzWNi6IU+fLsQvLB7P/8+msm8uGj+tmwRLl1MAn5TUMwTG3bSrNPz\ns+nj+fmsSV1OFuZV1vPatkPszS3BzVnNXXMmctu0ZHzcunbPNLRq2ZpRwNb0fPLKO3OGJ4T5s2bx\nJKaPHEZCmH+fJmVtdjuNLTrqmjtoaNHS0q6ntcNAu86I1mDGZLJgttqw2uxIdIYnqpQKnNRK3FzU\neLo54+Phgr+3G8F+HgT7eVxSxI9cJmN2cgwzR0WzMS2Hl77Yx+o/f8Bjt89lycSe4939PVxZOWEE\nnxw6yW+Wz+zRvdXQoWNkyMVTUGzJL6SkuYWXVy7p9vrbcaaIlw4fZEX8cO4e1/V1telMPr/6ZjPh\n7p6sXXAD4e4XPryK2hr5VVoqJ5tqmB8ax1Mp8whyuXCQUW/s4M2C/XxWegwhBEvDRvKT2CnEuncd\nqaWzmthbl8u2mhMcbSrCJuwEOXmyIiyFaX4JjPGOQiXrvTwIIWizaGkwtdJkbqXZ3EGbRYvWokNn\nM2K0mTHbLdiEDQFISChlCpxkKlwUTrgqXPBWueGr9iRA7U2Qsx9O8iu7riPQKZBHh/+mV21/z28b\nhRAXH2leBEmSZMBLwJ1d7J4A2IBgwAvYL0nSzm/fDi6FKyX0VcC56hh6dlufkSSJmyLH8vSJzRR2\nNBDXzYUMUKnrnFQLcule6Cs62vi0IJtVcUkEu3Y9Sv8iL4e3j2Xwg1HJrE66MOzOZLXy29RtfJ13\nmh+MS+axuTMvGG21G4w8u2Uv67NyiQvw5Y07VpAYfKHthTWNvLYtjV3ZRbg7q3lg0RRum5bcZWoD\ng8nCrqxCUg/nkn66AiEgMSKAh2+cwZwxsQT79BwLbjRbKK5soqiigZKqZkprmimvbaGmsR2b7cKE\nYxpnFRpnFc5qJUqFHMVZv7ndbsdssaE3mdHqTeiNlvOOUyrkRAZ7kxgVQFJMMCkjwgny7X0JRJlM\nYsXUJKaMiOSxtVt4/L2t1Ld28OMFPSciWzVpJB/tP86Ok4XcMqV715zVZqe2Xcu8xO6vF6vdzisH\nDhPj682C+K6TkOU3NvDw9s2MCgjkL3MuXMMhhODt7HT+cmQvEwJDeWveCjydzl80Z7PbeTvvKH8/\nuQ+NUsWr01awJOLCB1uzScebBfv5pCQTm7CzMiKZu+OmE6K58KFhE3bSm86QWpXJ3ro8THYLQc5e\n3B45jTmBI0lwD+5x1G4TNir1DZToqijX11Kur6PKUE+NoQmT/cKoKrVMhUbhhLNcjVKmQCHJkZCw\n0xlhY7KZ0dmM6KwGxDkRNhISgU4+xLqFkeAWwSjPWKI0wd8VBb8K6Enz3IAk4Juzv3kgsFGSpOuB\n24CtQggLUC9J0kFgPDDkhX4jcP9ZP9VEoK0v/vnvMy0gBoCMxrKLCn1uSx0Awy9SW/blY4dAggfH\ndB09k1VTzWO7djA5NJw/TJ91wf4Oo4m7P99AekUVv5k9nZ9NvPAt42hJJb/9fAsNWh13z5zAz2dN\nRPW9nDb1bVpe2XKIjRm5uKiV/Hz+JG6fMQb3LjJPFlY18vm+E2w5mo/WaCbU14O7Fk9i4fh4IgO7\nr5okhKC8toUTp6vILqoht7iW4som7KLzBlMr5YQHeRMf4c91KbEE+XoQ4OOKn5cbPh4ueLg693pU\nbjJbaWrTUdfUQVVDGyVVnQ+TPRlFbNh7CoDIIG9mjY9h/uQEokN7Fznh7+nKv35xA0+9v51X1h9E\n46Tm5pndizdAdIAP/h6uZJ6puqjQFzc0Y7baiA/s3pb1p/IobmrmtRuWdTkR32zQsyZ1PW4qNW92\nUQjeLgRPp+3mvZxjLImK58VZi78rdPMtldpWHj60iYyGShaGxfN0yoILJlsNVgvvFh3i34WHMFot\nLA8fzb0JMwjTXOjSazR1sKEinQ2VGdQaW3FXOrMkZAwLg5MZ7dm9Sweg2dRGTnsJee0lFHSUcUZb\nicne+RCXISPI2ZcQZz+SPeMIcPLGX+2Nj9oDb5UHHkrXXr8V2ISNNnPnG0GtsYlKQx0luhry20vZ\n15AFgKfSlck+o5jul8xoz9ihLvrpQKwkSVF0CvxqOgUcACFEG/DdhSZJ0jfAI2ejbuYA1wEfSJKk\nASYB/+iPMQMVXrkOmEWn36oSeBJQAggh3gA20xlaWURneGW/Zk5CXTzxc3LleHMltw3r3t1ysqkG\nb7VztyP6wpZGvijM4ccjxhLkemGbmo4O7vl6I4Gurry6aOkFUR91HVru+mw9RQ1NvHT9IpaNOD/+\n3mKz8cquNP59IIMwbw8+vms1o0LPdwvoTWbW7sng/b2ZWG2CH8wYy8/mpOCpcb6gr91ZRXzyzXGO\nn6lGrZQzd2wcK6YmMTYmpNubtbKulaM5ZWTkVnAsv5KW9s6sgu4aJ0ZEBzJ9TDTxEf7EhPsS7Odx\nySXnvo9apfjOZTMm4X8RUkIISqqbSc8pY/+xYj74Op33Nh1lVGwwP1yawrTknvPVKOVy/vjDBeiN\nZp7/ZDcR/p5MHN59ygpJkhgTGcyJsouPLbKragG6XZhmtFh5ZX8aIwMDmNfFSlizzcZ9mzdRr9Px\nyarVFxSCN9ts/HrvFjacyeOnSeN4bNLsCx4W60tO8UT6dgD+PmUZyyNHnPd72IVgQ/kJ/pm7mzpj\nB/OCh/NQ4nUXRNAIITjeUsqn5Wl8U5eLTdiZ6BPDgwmLmOE/vFsBbjVrOd56mhOtpznZWki1sREA\nlUxJjGsoC4OmEOsaxjBNMCEuAX1y71wMuSTHW+2Bt9qDePfz/5aNplZOtBZytDmHbxoy2VJ7iEAn\nH1aGzGJh0GRUsqFXQEcIYZUk6X5gG53hlWuFEDmSJD0NZAghNl7k8NeAdyVJygEk4F0hxMn+2DNQ\nUTe39rBfAPcNxLmg88YN13hTZ+h+IloIwaHaMib4h3crHH8+/A0apYr7ukhgZrRauPvrDegtZj5Y\nuQqv7xUhKW9p5UfrvqBZb+DNm5YzfVjkefsrmlt55LMtnKys5cZxSTy6aOZ5dViFEKQey+cfqfup\nb9exKDmeBxZPIczn/FfuDoOJL/dns25PFvWtWkL9PHjohulcP3kEnq4X5sixWm1kFVSxL+sMh44X\nU1nf6b4K8HZj0sgIkuNCSI4PJSLIa1Am1yRJYliID8NCfLhl/lha2vVsOZjHZzuP88jfN5AQGcDD\nt88iOf7iKSgUchl/+elibn/2Y57+cCefP/nDiy6MCvP1YGd2YWclqG7mKg4XV+CjcWGYb9dvRe+m\nH6O6vYPnly7o8rd7+rtC8IsZHXD+A91gtbBm+3r2V5Xy65Tp/Hz0xPP60FnMPJG+jS9LTjHeL5QX\nJy+9IBnf8eZK/nxiMzmtNYzyCuFvKTcy3vd8UbTabeyqPcVHpfvJb6/GTeHELRFTuCFsAuGaC99U\nhBAU66o43JTN0eZcCjsqEAhcFc4keUSzOHgqSe7RDHMNQTlAot5XfNWezAlIYU5ACiabmUNNJ0mt\nPsDrZ77g04qd/Chy6aDY1RNCiM10DnLP3fZEN21nnfNvLZ0hlgPGkJuM7S3eag3FHQ3d7i9ub6Za\n3859SV27ZPZXlrK3soTHJs7C+3tVdDrD4raTU1/HW0tXEOdz/g1S2NDIj//7JSarjQ9vX8XIoPNv\n6u05hfxh/Q4k4B+3LGFB0vkrZ0/XNPLsV3vIOFPJiLAAXvzRUpIjzw+Ta2zTsW5PFp/tPYHWaGZC\nfBiP3TaHqSOiLhAqs8XK0VPl7E4/zf6sYtp1RtRKOeMSw1m9cBwTkyIIC+hb+KQQAoPRQofOiE5v\nxmS2YLHaEXaBJJNQyGU4qZVoXFR4ujmj7kOqgXPxcnfhtkXjuHleMlvT8nnri0Pc/cwnrJw9il/e\nMQvVRXLOO6uUPHbrHO76+2d8uDOTuxZ3n3HUx9UFm13Qpjfi1cUD0m4XpJ0pZ3J0eJcPgiadnjfT\n0pkbG82kLqp+fXjy+DmF4M/3pbeZjNy1/Ssy6qp4YcZCbo4/P/1Bfks9DxxYT3FHMw+OnMoDSdPO\nixRrNul4KWcXX5RlEeDkxgvjV7IkdOR5bwNGm4VNlRl8VHqAakMLERpffpe4nEXBY3D+XhoDIQT5\nHWUcaMjiUFM2tcYmJCTi3SK4I2IR47wSiHEL63MpTbPdgs6qxWAzYrKbsNqt3/nd5ZIcpUyJs9wZ\nV4UGJ5nTJQ001HIVs/3HM8tvHCfbinivJJWXTn/U537+v3HVCr1Ckn3nW+6KrRUFAMwOufAV22K3\n8ce03YS7efCDxAtzx7+ecZRNp/N5ZPI05gw7//ic2jruXPclKoWcD2+/6bxiExabjb9t28/7aVkk\nhQTw91uWEOr1v3zfepOFN7an8f6+Y7g5qXl81RxunHj+cvWGVi1rt6Wz/mA2FqudOWNiuHNBCsPD\nz59nEEJwvKCKLQdz2Z1eSIfehJuLmmljhjFrXAwTR0bi3IP4anUmSiubKK9qprK2leq6Vuoa2mlo\n1tLcpsds7n2xa42LikA/D0ICPYkM9SE2yo8RccH4+/SuKpRCIWfp9BHMmRDH218e4qMtmZypbOS5\nB5fh49F9KOi4uFCmJUXx2b6T3LkgpdtFVd/+xt1dM8fKq2jS6ZkVH9Xl/hf3HsRktfLr2RcWer9Y\nIfhmo547Nn9GYUsjL89eytLvpdf4ovgkjx3dhrtSzQfXrWZKYOR3++xC8EVZFi+e2oHOaubHMZO5\nL2EmGuX/JuaNNjOflx/hw5L9NJu1jPQM5+GEJUz3T7jAh12pr2NnXTrf1GdSZ2pGIclJ9oxjddg8\nJvok4am6+N/KYrdQY6ylxlBLrbGWBlMDjaYmWiwt/B975xkYxZVt6686KrRyzhEkEEiIILLIUeSM\nccQY58CYGSfG2TMO4+wxYxwwGZOjyDkLhJBAAeWcU0vdUud6PxpLyJJsj6/vu77vzf7Xp05Vl1pV\n++yz99prNRrU6Cy/3Gj2oykkClwVLngoPfC18SHAzp9QVSg+Nt6/KvcuCAIxzj34sN+zHKtK4jCf\n/erv/v/R/tc6eoPF9LOcHAeLMxng7tclFG3drevkNtbxzcTZnQphJ/Lz+PDSeab3jOTxgR0RHSml\n5Ty8bQ+ONkrWL55LoEt7mqW6WcOffkgkuaiM+4b0Y+WkeBR3dZVeyi7izR0nKK1TM3dwH55LGNEh\nD9/Q3MLaI1fZfjYVs1kkYUgvHpoU1wkvXl3fzMHzGRw4e4vSajV2NnJGDQhnwpAI4qKCuu1k1Wj1\nZOZWkJFTye38KrLzq6isaU99SSUCXh6OeHs4EtPLHzcXe5wcbXGwt8HeToFSIUchlyIIAqIoYjSZ\n0emNaFsMNDa1UNegpaJaTWFJHReu5mK+Q2zm4+lEXL9gxgztSWxUANJfKObaKuU8s3gUUWE+vLnm\nMMve3MqaVQvxcOmeEnfuiL6s+Nc+zt8sYEy/8C7nGO7QOijlXf8+h2/loJRJGR3RGe+eWl7JjtRb\nLB08gFC3jmmdYnUjT94Rgv/kJ0Lw1S0a7k3cTlFTI19PnMPogPZFRG828XbycTbmpDDMK4hPhs/s\nUDcXWPsAACAASURBVHAt1NTxesoBrtQWMtAtiFf7Te0AlTRYTOwuSeL7/DPU6ZuJcwtnadgY+rt2\nXKhazXrOVl/naNUVMpoKkCAh1qUn9wZPYYhbH1SyruGmRouRopZi8jX5FGiLKGopoqK1EgvtSCxn\nuTPuSjcC7QKJdnLCUe6IvcweW6ktSokCuSBHIkgQETGLZgwWA63mVjQmLWqjmjp9HdX6GrKabmMU\nrQVee6k9UU69GeASS6xzP5TSn++0lQgSJnn/eu2In7PS1mr+kvr573KtP5r9oR299me0Jev1LTjK\nu+ZxT6+vJLOhmtcHTuh0rELTzEfJFxgTEMq4wI7RenZdLc8dOUiUpxfvjZ/YYWt5paiE5dv34qGy\nZ/3iufg6tS8gKcXlPLv1ABqdng/mTWFaTHvU1tSq4x/7zrI7KZ0gd2e+e2I+g8Lai5NanYH1x66x\n6cR1dAYTU+MiWZ4wpAPHiyiKJKUXs/PEDc6n5GO2iPTv5c/Ds4cyZmCPLiN3jVbP9VvFXL9VzI2M\nUvKKavgxmPX3cSGqpw8zJ8YQEuBOkJ8rPl6/DefelRmMJvKKarh1u4LrN4s5ejaDvUdTcXdVMWti\nDDMnxuDi9PN49nFxPfF2c+DJd3fwwmf7WP3SApSKrh/X4X1CUNkquZBe2K2jr9e0IJNKuszjG0wm\nDqRlMSYitEMdBaxwylcPn8BTZc+TwzuydmgMBpbv34NFhK+mz8LhLiH4ck0TSw5uo6pFw9pJcxjm\n155Lr2xp5olzu0ipLWd5r8H8ud/otlSNWbSwLvcyn2WcQiGV8ka/acwP7t/2LJpFC4fKUvgq9zhV\nOjX9XUL4e7/F9HMJ7nBvRdoK9pef42T1NVrNegJsvXg4ZAZjvQbhqugc/JgsJnI0uWQ2ZZHZnEWB\npgCjaN3ROcudCbILpL9LLP62fvja+uKl9PxFJ/xrzSJaqNRVkqvJ53ZzNrfUt0iqv4pSomSY2xAm\neI/Hz7brDuD/2K+zP7Sj15i63wqWtjQw0qvrl3prbioKiZRZwZ3Jpt68fBKzKPLmsHEdHHlDayvL\n9+/BTq7oBIu7WFjMo9v34u/syLrFc/G8C02xM/kWb+w/gY+TA9/cP4eed0HzLmUXsWrrUeqatTw8\ndhCPTxzSxmFjtljYdzGdL/dfpK6phQn9e/DY9GGE3AWP1BmMHLqQydYj1yksr8fFwZYlUwYyY3Qf\nArw6FupEUaSgpJYL1/K5mJxPRnY5ZouIUiGjb6QfSxcMo0+EH73CvVHZ/358JF2ZQi6jV7gPvcJ9\nmJ/QH73eyIXkfA6evMk3Wy+wYdcV5if05/65Q7Cz7b4pJirMh9cfncwLn+3n081n+MuD47qcJ5NK\niAryIqOoqttrldU34evi2CWq6HhmHupWHfMGdqYO3pScSkZVNZ/NTujgyC2iyPNHE8lrqOf7WXMJ\ncW7/f5Rpmlh0YCuNulY2TJ3fods1pbaMR8/spMVk5MuRs5kS2B4UFGnqeSl5Dyn1JYzzieDVfgl4\n2rSnU67W5fFJViI5zRX0dvLnr33nEufW/g5YRAvX6jPZU3aalMZs5IKMeI9YpvoMp5djcKeceL2h\ngdTGNG40ppLZlIXeokdAINg+iHFeY+mhCidUFYqr4r8mFv5LJhEk+Nr64mvrS7zHCCyihezmHM7X\nXuB87QVO1ZxhsOsg5gfMxUP574vK/Frzt/Xk/Zinf9XcD3jmv+0+/jvsD+3o9WZjl+ONhlZqdBqC\n7TtzhzQb9ewpuMXUwEiclB0j/qOFORwqyGblwBEE3NWFaDSbeerQfio1GjbPXYCPQ/vLdS6/kMd3\n7iPIxZn198zDzc4aiZrMFt49dIZNV24wNCyQjxcm4HQH895qMPLh/nP8cDGVYA8XPn16EX0C2wu2\nV2+X8MH20+SW1RIT6sNHj82gb0g7P726uZXtx2+w7VgKao2OiGBPXnt0MuPjenYoToqiSGZuJacu\n3ubMlRzKq6wIm56hXiyZPZi4mCCievoi7yZd0Z2Jd+iFTSYzoggSqbXr9ZfSLt2ZUiln7LAIxg6L\noKi0jnU7L7NxdxLHz2fx2nMJ9I3sHmEzemAPFk3qzw9HrzNvQj9C/brmi+nh5872s6ndXievqo5A\n965pEzZfScXfxZGhoR0pN8rUTXx89gIjQ4KY/JPmqI8vX+BYfh6vxo9heEB7tF7S1Mjig9tQG3Rs\nTFhAjEf7/3VHXhqvJB3Gy86BjeMW09PZ6rREUWRLwTU+uHUUuUTKBwPnkODfp80xl2jr+CTrIOdq\nsvCxcebtmIVM8I5uO260mDhZdZUdpScpba3GTeHEQ8HTmOwzDEd5x/pGjb6GpPprXKtPJl9bAIC7\nwp0R7sPo49SHSIee2HWTzunORFHEghmTxYiIiICATCJHKvw29yIRJEQ6RhDpGMGCgPkcrTzGkapj\npDSmcm/QPcS7j/gPHcO/aX9oR28RO3dmAtxssDaY9XXt7CC256WiMRlYGtkRX68xGHj14nF6uXrw\naEzH3Pvb505zqbSEf0yYTH+f9i3iufwiHt2xj3B3V75fNBfXO5J/Gp2eP21L5FxOIQ8O68/zE0e2\npT2yyqr5y8ZDFFTXc198f56ZOhybO865ulHDhzvOcCw5Gz83R95/JIFxse3qP/VNLWxKvMbOE6m0\n6o2MjA1lyZSB9IvoiJMvrWjg8Ol0jp7LpLxKjUwmYUDfQJbMimP4wDDcXbvPZ5vNFiqr1BSX1FNW\n3kBlZSPVNc3U1WtobGyhqbmVlhZDm3jI3aZQyHB0sMHFxR5PD0f8/VwICnSjR7g3IcHuv2ohCPJ3\n49VnE5g9qR9vfprIU3/dymP3xbN4Rvf9EA/NGMze0zdZu/cybz2R0OUcZ5UteqMZncGEzU9SPFqd\ngbyqOiZEd+5kTS+rIrmojBemjOqAthFFkdePnEQU4a0pHTUQDmbf5p9Xr7Awqi8PxLQX80ua1Sw6\n+AMao4HNUxfQ18O6uFtEkX/cOMPqjEsM9w7m8xEzcVFanWm9Xssr1/dxujKbEZ5hvN1/Bl621tSK\nzmzk+/zTbMg/i1wi5cmek1gUNAyl1Lrb1JsNHKm8zPaSE9QaGgm19+Mvkfcx0j22A1+Pxqjhcn0S\nF2svkae1NleG2Icwz38Osc798LPtviNWFEWaTA3U6MqoNVRSr6+i0ViL2liPxqSmxdSMztKCWTR3\nOlcqSLGVqlDJHHGSu+Gq8MJT6YevbTD+dqHIJb+8s3SUOzAvYA5jPEfzdf63fFfwPZlNmSwNeegP\niZ//o9of2tGb6RohkVxXjASBPs4d83YGs5lvM68yyCOAvm4dFZzeTTpDlVbD6vEzkd/1Emy5lcaG\ntBssix3AnF7tqZ5z+UU8vnMvYW6urF88D+c70XpZg5rHNu6lsLaBN2aOZ8Gd7b4oimw8l8LHB87j\nbG/DmkfnMLSnNdIzmS1sPZXCvw5cwmyx8Ni0odw/YWCbQ6pvamHjwavsOJGK0Whm4tAIHpgWR+hd\n3aKtOgOnLmZz4ORN0jLLkEgE+vcJ5IF5QxgZ1wNHVecOWotFpKi4lozMcrKyK8jNraagqAa9vh1N\nY2urwNPDATdXFb0ifXF0sMHOTomNjRy5zCoIYbaIGAwmWlsNqJtaqa/XUFpWT9K1fIxG6wtub6eg\nf2wwQweHMXJExC+mh/pG+rH2H/fz7peH+ee6M1gsIktmdU1n4Oxgy9xxMWw6dI3n7hmNm3NnFI69\njTUFpNXpOzn61CIrsVt0UGdVr2/PX8NeqWBe/45pvoOZ2ZzOK+ClcfH43VWPuVldxcpjhxng48sb\no9vTfyVNjSw6+APNBj2bExa2iYW0moz86eJ+DpfcZnF4P94YNLHt+btQlceLyXtoMrbySvRkloTG\ntV3vXHUW/8jcT0VrA5N9+vFMxGTcbaz3YbCYOFxxkR9KjlFvaKKPYxjP9VxEf5fItvMtooVb6nTO\n1JwlpTEVs2gmwNafBQHziHMdhIeya0x9o7GWIm02Ja25lLUUUKErpNXcLiAiFWQ4yd1wkrviYxOE\nnUyFrdQehcQGqSBDQIKIBbNowmDR0WLSoDGp71z3NjpL653rSAmyiyDSsT8xzsNwUfx8SsZN6cpf\nIp9nf/lBdpXtQWfW83SPJ5AK/3MMmv+b7A/t6CV0HWWcq8ol1i0AlbyjM9lTeIvylibeiZvcYfxi\nWREbM2+wrO9AYj3bF4ekslJeO32CUUHBvDA8vm38UmExj+/cS6ibNZL/0cnfLK3k8Y17MZjNrLl/\nNkPDrFt9dYuOVVuOcDojn9G9Q3lj4YQ28qyskmre3HCMrJJqRvQJ4S8LRrcVWrWtBjYfusamQ8no\nDSYmDYtk6YwhBPq050SLy+vZdegGh07fQttiINDXlcfuHcmk+N54/AS6KIoi+QU1JKcUciO1mLRb\npWi11oK2SqWkR7g30xP6ERLsQVCAG/5+Ljg62v7mbbDZbKGispHMrApSb5aQdDWfcxey+eSLY8SP\n6Mn8OYPo2aN7gjCVvZI3n5/BG58cZPWGs3i6OTBhZNdEZZOG9WJj4jUuphUwPb4zja/eaF28bLoo\ntp7LKkAhkzIgtOMOsKCmnsPp2SwbMagDl1CtVsubR08S4+vNAwPbI/YarZbHDuzBzc6W1Qkz24Tg\nyzVNLD64DY3RwKapC9qcfK1Oy7LT20mrq+CV/uN4OHKQdeEULXyeeZqvbp8jzMGDr4cvIdLJ+jvV\n6Zv5MPMAxytvEqLyZPWgZQxwsyKBzKKFU9XX2FCYSLW+gT5OYfwl8n6indoFajRGDWdqznKy+gy1\nhlocZCrGe45lhMdwAu064/8bDbXkNKeRp71FniYDtdGqriUT5PjYBhHtNBRvm0A8bfxxV3rjJHdF\n8hud64+7g9KWPAq1WWQ3p5JYsZHEio2Eq/owwj2BSMf+3cIrJYKEmX7TsZfZs6FoExuKNvNg8H2/\n6V7+f7M/tqPvwgFVtzaT0VjBc73Hdhg3Wsx8eesifVy9GeXbDpFrMRp46fxRgh2dWTmwHeNc2qTm\niYP7CHRy4tPJCW1FuivFpTy6Yy9BLs6sWzQXlzvpmlO381m5LREXO1vWLZ1HmKc1V3yruJLn1x+k\nuknDCzNHsWRkLIIgWAVFDl5m/bFruKhsO6RpTCYze8/c4uvdl2hoamHsoB48Onc4wb7WQqwoilxL\nK2bbgWtcul6ATCZhzNAIZk2MIbpXxzSOTmfk2vVCLl3J5UpSPnX1GgAC/F0ZHR9J3yh/onr74uf7\n+3fCSqUS/P1c8fdzZcK4KGsjzu0Kjh5P58jxWxw/mcGokRE89fg43LvB00skAquenkJtvYb3Vh8h\nprd/l9j7HgHuuDrZcT2ztEtHr9UZEAQ6RfOiKHI2o4BBYf6dEDerz1xBKZPxwLCOoiRvHTuNxmDk\n3YSJbc/F3ULw2+cvxv1OraZS28w9B39ArW9lc8LCtnRNflMdS09to6pVw7/i5zIxwNo0V6PTsPLq\nTpJqC5kbFMsr0VOwlckRRZHE8hQ+zjpIq8nAYz0mcF/IyLZu1Gv1mXxbsJdCbQU9VAE813Mx/Zx7\ntv1Py1vLOVx5lIu1lzGKRiIdIlgQMI8BLrHI7upotYhmirTZZDRdI6vpOlX6UgBUMidC7XsToupF\nkF0EPraBvznH3p0JgoCT3BUnJ1einAaRwH3U6atIaTxHUt0Jvi98D1/bEOb6LyfArmugBcB4r7HU\n6etIrDxMtFNf+rv0+13v8/9F+0M7+q5arhPLrIRYE307Rn7bclMp0jTy7ej5HRzae0lnKW5qZMu0\nRW1IGq3BwPIDezFaLKyZNgvHO3JtN8oqeHT7HnwdreiaH5389ms3eX3fCSJ9PFh970w8HVSIosj2\nS2m8u+cM7o52rHtyQVtqIKOokr9+f4SCynqmD+3Nn+aOwumODurltEI+3nyawvJ6YiP8+HDFTKLC\nrOeZzRZOX85m4+4kcgqqcXW2Y+nCYcyaGIPrXekKnc7I5aQ8Tp/N4kpSPjq9EXt7JQP7BxM3KJRB\n/YPx8Pj1zJC/lwmCQK9IX3pF+vLwQ/Hs3H2NzT9c5mpyAc89PZEJY7uW3JPLpax6Zgr3PP0d32w5\nz8tPdeaNFwSBYF9XSqu7loUsq1Xj5eLQCVWTUVpNcW0jS8d0ZJTNrqzlQFoWD48YiNtd1MWJmbdJ\nzMxmRfwwwt2ti7koiqw61S4E39vDimevbdWyJHEbNa1a1k+Z3+bkU2rLePj0diQIbB5/D7Hu1p3E\ntdoiViTtQGPS8ff+M5kVZHVQtbom/pa+h/M1WUQ7B/JKnzmEqKzfUdJSxZq83VxryMTbxo0XIx8g\n3iO27RnPbc5lf0UiNxpTkQtyhrkPZaLXOPzt2iG8FtFCgTaT1MYL3FInoTGpkQpSQux7M9B1LBEO\nMXjZBPyPFDjdlF6M95rHGM9Z3Gi4QGLFJr7IeZlRHjOY5LOo28Vmrv9sUhpT2VaynWinnxdO/4/9\nwR19V4RJB0puEuXsQ8hdJE46k5Evbl1kgLsfY3zbsfEXy4pYl5HCw30GtOnAWkSRlccOk11Xy3cz\n5hDqYo2i0yureXjbbtzs7Fi3eC7u9vaIoshXZ5L49MRFRoQH8cmiadgrFeiMJv626yS7k9IZERnM\n3++ZjLO9LSazhe8OJ/FN4hVcHe34/KnZDI8KBqCsupFPNp/h7PU8/L2c+eC5mYyMtRJ4mcwWjp3L\nZP3Oy5SUNxDk58qLT0xiYnyvNpSNxSKSdrOEI8ducvZCNi0tBlxc7Jk4oQ/xw3sSEx2ArJtmKbPZ\nQkV5IyVFtZSV1FNVoaamuomGei2NjVpatAZ0OgMmoxVlI5VKUNrIUamUuLiq8PByxM/fhaAQDyJ7\n++Lj98u7A5W9kgfuHc74sb15/8NE/vbeAXJzq3jskTFdnuvj6cTcqbH8sP8a984eTKBfZ74ZHzdH\nktKLu/y+oqoGArvQlz1wPROZVML4nxRiPzt5EXuFgodHtBeBa7VaXj9ykmgfL5YPbR//7sZ1dmam\n80zc0DYh+EZdK/clbqesuYl1U+a1QSjPlOfxxLnduNvYs37sIoIcXBBFkc35V3n35hH87Jz5dvi9\n9HSypndOVN7k3fS96MwGVkQmsCBoKFJBgtakY0vxEfaUncZGouSR0FlM922P8DObsthbtp/M5iwc\nZCpm+c1gvOdYHOTtu6EqXSnJ9adJaTyP2liHXKKkl0N/+jgNJtIxFhtp1+gaURTRmuqoMxShNpTR\nZKyk2ViN1lRPq7kRvUWLwdKCRTRhEc1IBClSQYFCYoedzAWVzA0nuR+uykC8bHripgz5xXSPVJAx\nwHUUUU6DOFi+gdM1eylpzeWB4BewkXbul5FJZCwMmMcnOZ9zse7yz17711qRtpbHrnz9u1zrj2Z/\naEf/U8Hi9MYK0hsreCW6Yw7+u6yrVLY28/HwGW1ORK3XsfLMIUKdXFg5aGTb3M+uXOJIXg6vjBxN\nfFAwALm1dTy0dRcqhYJ1i+fi5aDCYhF599BpNly+wfToSN6ePRGFTEqVWsOza/eRXlLF8vGDeXLS\nUCQSgeLqRlatPcStwkqmDIrkhYVjcLS3wWgyszHxGmv3XkYikfDE/BEsntwfhVyGxSJy7Hwm3229\nQGllI+HBHry1cjqjBvdsQ4A0NGo5fOQmBw6lUl7RiJ2dgvgREUwYF0VM386dpqIoUlJUR8atUrIy\nysm9XUlBXnUHOgM7OwUeXo64uqnoGeGDvUqJja3CCsMUwGIWaW01oNXoqK/TkptdybnTmVjM1uK4\nm7sDg4aEMmJ0LwbGhSKVdY+28fN14aP3F/P56uNs23kVlcqG++7pmn9o0fSBbN13jdOXs7l/budu\nRxulvE24/G7TG01kl9WyaHS/TuP7r2UyJioMJ7v2Zym5qIwTmXk8PXYoznfGRVHk5cRjtBiNvDdt\nUlsD09k7QvCTwnrwzOChgBXB9cDhneQ11vPNpNkMvhNE7CtM5/mLB4hw9mDtmAV42KrQm028fuMA\ne4pTGePdk/cGzsZBboPGpOODjP0cKk+hl6Mfb0TPJ1jliSiKnKtJ4V95u2gwNDPRezAPBk/HWWFF\nUuU057KjdBdZzbdxkjuxOHAhYzxGtTUvGS16UhsvcaXuOEUtt5EgoadDP6b63EuU40AU0s5Fe42x\nlorWDCp1mVTrcqjR5aG3NLcdlwpyVDIPVDJ3XJVBKCUq5BJbpIIciSDFIpoxiXoM5hZazA2ojRUU\naZMxi1Z+eoXEjgC7WEJVwwh3GImimwUGwEZqx9yARwmyj2BHyWo2FX3EgyEvdll07eccg5fSk6T6\nq91e7z9mtT+0o1f+BD61reAaNlIZMwLaOcVrdVpWp19ivH8Phni146Bfv3iCqhYNO2csadPITMzJ\n5rOkS8zrHcXSfta8bEmjmge37kIqEVi3eC7+zk6YzBZW7TnK3huZ3D80lhcmW6F3N4sreXbtPrR6\nA58+NIOxfay7h8SkTP6+5SQSQeDdZVOZOCACgLSccv723TEKyuoYF9eTZ+8ZhZerA6IocjmlgH9t\nPEtuYQ1hQR787S8zGRnXXlS7nV3Bzj3JnD6bhdFoJiY6gAfvG8HI4T2xsen4u1RXqrl2JY/kqwWk\nXS+isdFKRWyvUtIjwofpcwYQHOpBYLA7/gGuOP5CV2pXZjSaKSqoITO9jBvJhZw7ncXhA6m4uqmY\nMXcgcxbEYWvXdfOTVCrh2Scn0NJi4Lt159rqBz81d1cVvXp4c+5qbpeOXhTFLsvzmcVVGE1mYsM7\nFluPpuWgbtExf2h7I5TFIvL+4bN4Otjz4PB2vddtqbc4lVvAK+NHtaVs8hvqefqOEPw/JkxGIgjo\nTEaWHd3FrdpK/jVhFvH+VsqBjdnXefXqEeI8A/l69Dwc5EpqdBqevvwDqQ2lPBk5iiciRyERBDLU\npaxK3Up5SwPLwsayNGwMMomUal09/8zdTlJ9BmEqf17tvayNsre0pYwdpbtIabyBk9yRJYGLGe0Z\nj0Ji/c0bDbVcrD1MUv0JWswaPJS+JPjcR3+XeBzkHXc6erOGYu11irXXKGlJRW20wpWlghx3ZRg9\nHEfhrgzBVRGIs8IflcwN4d8kOBNFC2pjJVW6LEpbUinUJJGnucCpqs+IdBxHnPu9OMi715IY6Doa\ns2hiZ+lXHChfx0y/pZ3mCIJArEs/jlWd+LfurTsLsnfnX4Mf+VVzv7Kqnf6vsT+0o7/b6vVa9han\nMS2gL46K9qjkgxun0VtMvBg7pm1sX14mu3MzeLb/MPp5WvPf6dVVrDx2iP7ePrw12oqLrmrW8MCW\nneiMRjYtWUCwqwt6o4nntye2RXyPj7bSyR68nsWrPxzFw9Ger5YvooePO616I+9uPcn+yxn0C/Pl\nnaVT8HF1pEVn4Mtt59lx4gaeLg589PwshsdYC8S5hTV8se4019KK8PVy4vUV0xg7LAKJRLAyKF7J\nZeu2K9xML8XOTsG0KTHMmt6fwMD2RiFRFMm5XcmFM1lcOp9DQZ5VOtDN3YGBQ8Lo2y+QPtEB+Ae6\n/VvygT9ncrmU8J7ehPf0ZvrsARiNZq5eyuXg3hS+X3OavTuu8uSfJjFqbO8uzxcEgZXPTaaktJ5P\nvzhG3MAQ7Ow6QzD7RwXyw4FrmM2WTruV5hY99l100l7KKEIiCPQLa0dUiaLIhrPXCfZwYXB4ewCw\n90YGaaWV/H3OpDapx4K6Bt45fpphwQHcfwdl06TX8ch+qxD8mmkzsVcoMJjNPHF8H1cqSvhkTAIT\ngsIRRZHV6Zf4IPUM4/zC+WLELGxkcjIaK3jq8lYaDa18GjefiX69rSmcwvN8cfsIbkoVq+OWEesa\ngkW0sL/8HN/l70MElofOYoZfPFJBitqoZlfpXs7UnMVGasM8/zlM9BrfFsGXtRRwumYvNxsvISIS\n5RTHMPfJhNl35LFvMlSSqzlPfvNFyltvIWJBIbHD3y6GaJfp+NpG4WETjlT4fbDpgiDBWeGLs8KX\nCMexiKJIpS6TjMbDZDYdI7PpGIPcljDQrfs8/GC38VTqirlQe4hYl5EE2nXug+jlGMnhyqO/yz3/\nv2z/axz9lvyr6C0mHgof2jaWVlfB9rw0lvUaTJij1RGWa5pYdf4YsZ4+PB1rnVvb0sLyA3txsbFh\n9bSZKGUyGlt1PLh1J/UtLaxbPI8IT3daDUae2ryPi3nFrEoYw5Ih/awv8pFLfHn0MgNC/fj4gem4\nqGwpqKznz2v2U1BZzyNTB/PI1CHIpBKuZ5Xw1tdHqahVM39CLI/PG46djYLGpha+2XKBfcfTUNkp\neXbpWGZNjEEul2I2Wzh+MpNNWy9RWFSLl5cjTz46limTorG/C49emF/DiaM3OXM8g4ryRiRSgT7R\nASx/ajxxQ8MIDHb/v1ZQk8ulDIuPYFh8BBm3SvnioyO8vWoX58dnsfKV6V3SFisUMp59cgKPP7Oe\nHbuvcf+S4Z3m+Ps4YzJZqK5rxsfTqcOxqrrmLhE5Z9PyiQ716cDPfzWvlMzSal6bP75tsdPo9Hx0\n7DwxAT7MiLEW841mMyv3H0YhlfLeNGvUbrJYePbwQUqa1GycPR9/RydrbefMIU6W5PO3EROZGW51\n3P9IPcOX6ZeYGRzFB0MTkEuknKrI5vmrO3BS2LIx/iF6O/vQbGzlzZs7OVOdwSjP3vy171wc5bZU\nttbxSfYWUtU5DHCJ5OkeC/CyccNkMXGo8gh7yvZhFI1M8BrHTN/pqOTWFE6hNovjVTvIbk7FRmLL\nCI8EhrtP6YBH15rqud10kuym01TpsgBwU4Yw0G0RwfZxeNv2+s1QyX/XBEHAx7Y3Pra9GeS+hAvV\nX3O59nvyms8zze91HBVdw3AneS/mRsN5DldsYXlYZyp3L2X36nH/sXb7X+HoNUY9G/KSGO3dkzBH\n64NstlhYlXQYNxt7nrrDOW+2WHju1EHMooVPxiQgk0gwmM08fnAvDbpWts1bhIedPVqDgWXbxjvQ\nNAAAIABJREFUdlPUoOa7hbOJ8fVGo9Pz2Ma9XC8u42+zJzK7fxRGk5nXth1jf3ImMwb24vX5E5DL\npBxNvs2bG46hkMv48uk5DO4VhN5g4outZ9ly5Dr+nk6sfnkBsRH+WCwie46m8tWmc7S06JkzOZal\nC4fhqLLBbLZw4lQG6zZeoKS0nuAgd15+YRpj4iPbCqtajY6TR9M5dOAGOVkVSKQC/QeGcM+DIxg2\nsufPpmHUDVpKC2spL66juqKRuppmGuu1tDTraG0xYDZbEEURhVKGrZ0CpzuFV58AN0J7ehMS4Y2i\nGyKxu613H38+X/MQWzdeZN3Xp9Fq9Lz+7vwuz42M8GFwXCj7E29w3z3DOi1M7ndYKusbWzo4+h9l\nEEfGdmSXLKpq4HZpDc/NGdlhfM3xK7g52DF9QDs667OTl6jTtvDPJTPbnP+n5y6RVlHJZ7MS8Haw\nfvd7F85ypqiQd8ZOIM7PH1EUefXCcfblZfLCoHju6RVjlQRMPsa628ksDu/H23HWRWJD3hXeTTtC\nL2dvvhy6GE8bB7KbynkhZTOVukZWRCawKMj6vB6uuMSa/N0APNdjERO9hyAIAhlNmawv3ESFroIY\np77cE7gIb1urIyzU3uZo5Q/kam5iL3Nksvc9DHWfiK3UisoyiyYKNJdJbzxEkfYqIhY8lOEM91hG\nuEM8zoruycFMlhaajUVojcW0GCtoMVWiNzdgtKgx3Sm+iliQCHJkgi0KqTM2Mg9Ucn8c5KG4KHsj\nl/4yLbWj3Ispfqvo0TyK4xUfsbNkJfMCP+oylWMjtSXeYzqHKjdTp6/ETdlxQXBRdE1r8R/raP8r\nHP2m/CTUxlaeiGxvatqcm8LN+ko+Gz6zLZXzr9QkkipL+XDUFIIcrWiH106fILminM8nT6OPp5d1\n+71zP7cqqvhiznSGBAXQrNPzyPrdpJdV8Y/5U5naN4LmVj0r1u3nSk4JT04eyqPjB2O2iHy88ywb\njicTE+rDu8sS8HJxILekhldXJ5JXWsfccTE8tXAkdjYK8opqeG/1UTJyKoiNCmDFsnGEBrojiiKX\nruTxzdoz5BfUEBLszuurZjJyeESbA8rLqWLvjqucOpaOTmckNNyTx5+dwJgJUbh0QXHQ3NRK+vUi\nsm6WkJNeTv7tChrqNB3mOLnY4eSqwsHRFpWjLbI7RVSDwUSLRk95cT3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t4SQcbJXMGWHN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\nu/VErmQ3/QK9ycTJ8kr2FRSxK7+QvLp6AOJ8vHl4bCr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x,y): return exp(-y**2)*sin(x-y)\n", "\n", "xx =linspace(-3,3,150) # 150 points entre -3 et 3\n", "yy =linspace(-2,2,100) # 100 points entre -2 et 2\n", "\n", "Z = [[f(x,y) for x in xx] for y in yy] # Une liste de liste contenant les valeurs de f.\n", "\n", "contour(xx,yy,Z,30) # Afficher 30 lignes de niveau\n", "colorbar() # Si on veut une échelle des couleurs" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Note : ce Notebook a fortement été inspiré de celui d'Amic Frouvelle et de David Gontier (U. Paris-Dauphine)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.0" } }, "nbformat": 4, "nbformat_minor": 1 }