{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comment mettre en oeuvre une régression linéaire avec python ?\n",
    "\n",
    "##### Germain Salvato-Vallverdu [germain.vallverdu@univ-pau.fr](mailto:germain.vallverdu@univ-pau.fr)\n",
    "\n",
    "L'objectif de ce TP est de mettre en pratique le langage python pour réaliser une regression linéaire. L'idée est, dans un premier temps, de reprendre les éléments de base du langage (condition, boucles ...) pour créer un outil qui calcule les paramètres par la méthode des moindres carrés. Dans une deuxième partie les modules spécifiques tels que [numpy](http://www.numpy.org/) ou [matplotlib](http://matplotlib.org/) seront mis à profit pour réaliser la même opération avec des méthodes existantes.\n",
    "\n",
    "*Note : Ce notebook est compatible python2 et python3. Il est recommandé d'utiliser python3.*\n",
    "\n",
    "### Sommaire\n",
    "\n",
    " 1. [Introduction](#Introduction)\n",
    "     1. [Cahier des charges](#Cahier-des-charges)\n",
    "     2. [Rappels mathématiques](#Rappels-mathématiques)\n",
    "     3. [Progression](#Progression)\n",
    " 2. [Programation](#Programmation)\n",
    "     1. [Étape 0: Lecture du fichier de données](#Étape-0:-Lecture-du-fichier-donnees.dat)\n",
    "     2. [Étape 1: À la main](#Étape-1:-À-la-main)\n",
    "     3. [Étape 2: Créer une fonction](#Étape-2:-Créer-une-fonction)\n",
    "     4. [Étape 3: Utilisation du module numpy](#Étape-3:-Utilisation-du-module-numpy)\n",
    "     5. [Étape 4: Utilisation des méthodes prédéfinies dans numpy et scipy](#Étape-4:-Utilisation-des-méthodes-prédéfinies-dans-numpy-et-scipy)\n",
    " 3. [Représentation graphique](#Représentation-graphique)\n",
    " 4. [Pour aller plus loin ; les résidus](#Pour-aller-plus-loin-:-les-résidus)\n",
    " 5. [Conlusion](#Conclusion)\n",
    "\n",
    "## Introduction\n",
    "\n",
    "### Cahier des charges\n",
    "\n",
    "Le programme que nous allons écrire devra réaliser les opérations suivantes :\n",
    "\n",
    "* Lire les valeurs des valeurs de $x$ et $y$ sur le fichier `donnees.dat`.\n",
    "* Calculer les paramètres $a$ et $b$ de la régression linéaire par la méthode des moindres carrés et les afficher.\n",
    "* (bonus) Représenter les points $(x,y)$ et tracer la droite de régression.\n",
    "\n",
    "### Rappels mathématiques\n",
    "\n",
    "La régression linéaire consiste à chercher les paramètres $a$ et $b$ définissant la droite $y=ax+b$ qui passe au plus près d'un ensemble de points $(x_k,y_k)$. Les paramètres $a$ et $b$ sont déterminés par la méthodes des moindres carrés qui consiste, dans le cas d'une régression linéaire, à minimiser la quantité :\n",
    "\n",
    "\\begin{equation}\n",
    "    Q(a, b) = \\sum_{k=1}^N (y_k - a x_k - b)^2\n",
    "\\end{equation}\n",
    "\n",
    "Le minimum de $Q(a,b)$ est obtenu lorsque ses dérivées par rapport à $a$ et $b$ sont nulles. Il faut donc résoudre le système à deux équations deux inconnues suivant :\n",
    "\n",
    "\\begin{align}\n",
    "    &\n",
    "    \\begin{cases}\n",
    "        \\displaystyle\\frac{\\partial Q(a,b)}{\\partial a} = 0 \\\\ \n",
    "        \\displaystyle\\frac{\\partial Q(a,b)}{\\partial b} = 0\n",
    "    \\end{cases}\n",
    "    &\n",
    "    \\Leftrightarrow &\n",
    "    &\n",
    "    &\n",
    "    \\begin{cases}\n",
    "        \\displaystyle -2 \\sum_{k=1}^N x_k \\left(y_k - a x_k - b\\right) = 0 \\\\ \n",
    "        \\displaystyle -2 \\sum_{k=1}^N \\left(y_k - a x_k - b\\right) = 0\n",
    "    \\end{cases}\n",
    "\\end{align}\n",
    "\n",
    "Les solutions de ce système sont :\n",
    "\n",
    "\\begin{align}\n",
    "    a & = \\frac{\\displaystyle N \\sum_{k=1}^N x_k y_k - \\sum_{k=1}^N x_k\\sum_{k=1}^N y_k}{\\displaystyle N\\sum_{k=1}^N x_k^2 - \\left(\\sum_{k=1}^N x_k\\right)^2} &\n",
    "    b & = \\frac{\\displaystyle \\sum_{k=1}^N x_k^2 \\sum_{k=1}^N y_k - \\sum_{k=1}^N x_k\\sum_{k=1}^N x_k y_k}{\\displaystyle N\\sum_{k=1}^N x_k^2 - \\left(\\sum_{k=1}^N x_k\\right)^2}\n",
    "\\end{align}\n",
    "\n",
    "### Progression\n",
    "\n",
    "Le programme sera écrit de plusieurs façon différentes.\n",
    "\n",
    "1. Tous les calculs seront réalisés à la main.\n",
    "2. Création d'une fonction qui réalise la régression linéaire\n",
    "3. Utilisation du module numpy pour simplifier les calculs\n",
    "4. Utilisation des méthodes des modules numpy/scipy pour réaliser la régression linéaire\n",
    "5. (bonus) Utilisation du module matplotlib pour représenter les points et la droite de régression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Programmation\n",
    "\n",
    "### Étape 0: Lecture du fichier `donnees.dat`\n",
    "\n",
    "Contenu du fichier `donnees.dat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 2.1\r\n",
      "2. 2.9\r\n",
      "3. 4.2\r\n",
      "4. 5.05\r\n",
      "5. 5.85\r\n",
      "6. 6.95\r\n",
      "7. 8.1\r\n",
      "8. 9.\r\n",
      "9. 10.2\r\n",
      "10. 10.9\r\n"
     ]
    }
   ],
   "source": [
    "cat data/donnees.dat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lecture du fichier ligne par ligne :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 2.1\n",
      "2. 2.9\n",
      "3. 4.2\n",
      "4. 5.05\n",
      "5. 5.85\n",
      "6. 6.95\n",
      "7. 8.1\n",
      "8. 9.\n",
      "9. 10.2\n",
      "10. 10.9\n",
      "type de xi :  <class 'str'>\n"
     ]
    }
   ],
   "source": [
    "with open(\"data/donnees.dat\", \"r\") as inp:\n",
    "    for line in inp:\n",
    "        xi, yi = line.split()\n",
    "        print(xi, yi)\n",
    "print(\"type de xi : \", type(xi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va maintenant enregistrer les valeurs xi et yi dans des listes. Par ailleurs, on peut remarquer que les valeurs sont lues comme des chaînes de caractères. Il faut les convertir en nombre flottants avec la fonction `float()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# création des listes\n",
    "x = list()\n",
    "y = list()\n",
    "\n",
    "# lecture du fichier\n",
    "with open(\"data/donnees.dat\", \"r\") as inp:\n",
    "    for line in inp:\n",
    "        xi, yi = line.split()\n",
    "        x.append(float(xi))\n",
    "        y.append(float(yi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons maintenant nos listes de valeurs de x et y :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.1, 2.9, 4.2, 5.05, 5.85, 6.95, 8.1, 9.0, 10.2, 10.9]\n"
     ]
    }
   ],
   "source": [
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous verrons par la suite comment lire ce type de fichier de façon efficace avec la méthode `loadtxt()` de `numpy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Étape 1: À la main\n",
    "\n",
    "Dans cette étape on va utiliser directement les formules présentées en introduction pour calculer la valeur des paramètres $a$ et $b$. Commençons par calculer la somme des valeurs de $x$. Le point important est de ne pas oublier d'initialiser la valeur de la somme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "somme des valeurs de x =  55.0\n"
     ]
    }
   ],
   "source": [
    "# initialisation\n",
    "x_sum = 0\n",
    "# calcul de la somme\n",
    "for xi in x:\n",
    "    x_sum += xi\n",
    "# affichage\n",
    "print(\"somme des valeurs de x = \", x_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait de même pour la somme des valeurs de $y$ et des valeurs de $x$ au carré."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "somme des valeurs de y =  65.25\n"
     ]
    }
   ],
   "source": [
    "y_sum = 0.\n",
    "for yi in y:\n",
    "    y_sum += yi\n",
    "print(\"somme des valeurs de y = \", y_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "somme des valeurs de x^2 =  385.0\n"
     ]
    }
   ],
   "source": [
    "x2_sum = 0.\n",
    "for xi in x:\n",
    "    x2_sum += xi**2\n",
    "print(\"somme des valeurs de x^2 = \", x2_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il reste à calculer la somme des produits $x\\times y$. Pour parcourir à la fois la liste des valeurs de $x$ et de $y$ on utilise la fonction `zip` qui joint les deux listes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xi =  1.0 \tyi =  2.1\n",
      "xi =  2.0 \tyi =  2.9\n",
      "xi =  3.0 \tyi =  4.2\n",
      "xi =  4.0 \tyi =  5.05\n",
      "xi =  5.0 \tyi =  5.85\n",
      "xi =  6.0 \tyi =  6.95\n",
      "xi =  7.0 \tyi =  8.1\n",
      "xi =  8.0 \tyi =  9.0\n",
      "xi =  9.0 \tyi =  10.2\n",
      "xi =  10.0 \tyi =  10.9\n"
     ]
    }
   ],
   "source": [
    "for xi, yi in zip(x, y):\n",
    "    print(\"xi = \", xi, \"\\tyi = \", yi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mettons cela à profit pour calculer la somme :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "somme des valeurs de x*y =  441.15\n"
     ]
    }
   ],
   "source": [
    "xy_sum = 0.\n",
    "for xi, yi in zip(x, y):\n",
    "    xy_sum += xi * yi\n",
    "print(\"somme des valeurs de x*y = \", xy_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant que nous disposons de toutes les valeurs nécessaires, il ne reste plus qu'à calculer $a$ et $b$. Nous avons encore besoin du nombre de points. La fonction `len` donne le nombre d'éléments d'une liste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de points =  10\n"
     ]
    }
   ],
   "source": [
    "npoints = len(x)\n",
    "print(\"Nombre de points = \", npoints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D'après les équations présentées en introduction :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.9972727272727273\n"
     ]
    }
   ],
   "source": [
    "a = (npoints * xy_sum - x_sum * y_sum) / (npoints * x2_sum - x_sum**2)\n",
    "print(\"a = \", a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b =  1.04\n"
     ]
    }
   ],
   "source": [
    "b = (x2_sum * y_sum - x_sum * xy_sum) / (npoints * x2_sum - x_sum**2)\n",
    "print(\"b = \", b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Étape 2: Créer une fonction\n",
    "\n",
    "Dans cette fonction nous allons regrouper les différentes étapes permettant de réaliser la régression linéaire. La fonction prend comme arguments les listes des valeurs de $x$ et $y$ et retourne les valeurs des paramètres $a$ et $b$. Les entrées et sorties de la fonction doivent être explicités dans la `docstring` située en dessous de la définition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regLin(x, y):\n",
    "    \"\"\" \n",
    "    Ajuste une droite d'équation a*x + b sur les points (x, y) par la méthode\n",
    "    des moindres carrés.\n",
    "    \n",
    "    Args :\n",
    "        * x (list): valeurs de x\n",
    "        * y (list): valeurs de y\n",
    "        \n",
    "    Return:\n",
    "        * a (float): pente de la droite\n",
    "        * b (float): ordonnée à l'origine\n",
    "    \"\"\"\n",
    "    # initialisation des sommes\n",
    "    x_sum = 0.\n",
    "    x2_sum = 0.\n",
    "    y_sum = 0.\n",
    "    xy_sum = 0.\n",
    "    # calcul des sommes \n",
    "    for xi, yi in zip(x, y):\n",
    "        x_sum += xi\n",
    "        x2_sum += xi**2\n",
    "        y_sum += yi\n",
    "        xy_sum += xi * yi\n",
    "    # nombre de points\n",
    "    npoints = len(x)\n",
    "    # calcul des parametres\n",
    "    a = (npoints * xy_sum - x_sum * y_sum) / (npoints * x2_sum - x_sum**2)\n",
    "    b = (x2_sum * y_sum - x_sum * xy_sum) / (npoints * x2_sum - x_sum**2)\n",
    "    # renvoie des parametres\n",
    "    return a, b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilisons maintenant cette nouvelle fonction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.9972727272727273\n",
      "b =  1.04\n"
     ]
    }
   ],
   "source": [
    "a, b = regLin(x, y)\n",
    "print(\"a = \", a)\n",
    "print(\"b = \", b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour afficher les nombres flotant, il est possible d'utiliser un format. Deux syntaxes existent suivant la version de python :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =    0.997\n",
      "b =    1.040\n"
     ]
    }
   ],
   "source": [
    "# python 2.7 et superieur\n",
    "print(\"a = {:8.3f}\".format(a))\n",
    "print(\"b = {:8.3f}\".format(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =    0.997\n",
      "b =    1.040\n"
     ]
    }
   ],
   "source": [
    "# python 2.X\n",
    "print(\"a = %8.3f\" % a)\n",
    "print(\"b = %8.3f\" % b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Étape 3: Utilisation du module numpy\n",
    "\n",
    "Nous allons maintenant utiliser le module numpy pour simplifier le calcul des sommes. Pour commencer il faut importer le module numpy. Il est courant de le donner `np` comme raccourci."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La somme des valeurs d'un tableau peut être obtenue par la méthode `sum()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "a.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La somme des carrés ou des produits peut également être obtenue aisément."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a**2).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour calculer les produits entre deux arrays numpy il suffit de les multiplier :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a :  [1 2 3]\n",
      "b :  [3 2 1]\n",
      "a * b : [3 4 3]\n"
     ]
    }
   ],
   "source": [
    "b = np.array([3, 2, 1])\n",
    "print(\"a : \", a)\n",
    "print(\"b : \", b)\n",
    "print(\"a * b :\", a * b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La somme se calcule alors de la même manière que précédemment pour le carré :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a * b).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons maintenant simplifier la fonction `regLin` en utilisant les fonctions de `numpy` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regLin_np(x, y):\n",
    "    \"\"\" \n",
    "    Ajuste une droite d'équation a*x + b sur les points (x, y) par la méthode\n",
    "    des moindres carrés.\n",
    "    \n",
    "    Args :\n",
    "        * x (list): valeurs de x\n",
    "        * y (list): valeurs de y\n",
    "        \n",
    "    Return:\n",
    "        * a (float): pente de la droite\n",
    "        * b (float): ordonnée à l'origine\n",
    "    \"\"\"\n",
    "    # conversion en array numpy\n",
    "    x = np.array(x)\n",
    "    y = np.array(y)\n",
    "    # nombre de points\n",
    "    npoints = len(x)\n",
    "    # calculs des parametres a et b\n",
    "    a = (npoints * (x*y).sum() - x.sum()*y.sum()) / (npoints*(x**2).sum() - (x.sum())**2)\n",
    "    b = ((x**2).sum()*y.sum() - x.sum() * (x*y).sum()) / (npoints * (x**2).sum() - (x.sum())**2)\n",
    "    # renvoie des parametres\n",
    "    return a, b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La nouvelle fonction renvoie évidemment les mêmes résultats :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =    0.997\n",
      "b =    1.040\n"
     ]
    }
   ],
   "source": [
    "a, b = regLin_np(x, y)\n",
    "print(\"a = {:8.3f}\\nb = {:8.3f}\".format(a, b)) # \\n est le caractere de fin de ligne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Étape 4: Utilisation des méthodes prédéfinies dans numpy et scipy\n",
    "\n",
    "Numpy et Scipy sont deux modules scientifiques de python qui regroupent de nombreuses fonctions. Nous allons utiliser la méthode [loadtxt](http://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html) pour lire le fichier texte et les méthodes [polyfit](http://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html) et [linregress](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html) pour réaliser la régression linéaire. Le module numpy est totalement inclu dans scipy. Compte tenu du grand nombre de modules et bibliothèques python existants, il est important de savoir lire une documentation pour utiliser les méthodes disponibles. De plus, l'utilisation d'une méthode déjà existante accélère le travail de développement tout en évitant de refaire la même chose. Pour obtenir la documentation à l'intérieur de ipyhon, ajouter un ? après le nom de la méthode.\n",
    "\n",
    "Commençons par lire le fichier `donnees.dat` avec la méthode `loadtxt` pour lire le fichier de données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.     2.1 ]\n",
      " [  2.     2.9 ]\n",
      " [  3.     4.2 ]\n",
      " [  4.     5.05]\n",
      " [  5.     5.85]\n",
      " [  6.     6.95]\n",
      " [  7.     8.1 ]\n",
      " [  8.     9.  ]\n",
      " [  9.    10.2 ]\n",
      " [ 10.    10.9 ]]\n"
     ]
    }
   ],
   "source": [
    "data = np.loadtxt(\"data/donnees.dat\")\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les valeurs de $x$ correspondent à la première colonne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.   2.   3.   4.   5.   6.   7.   8.   9.  10.]\n"
     ]
    }
   ],
   "source": [
    "x = data[:,0]\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les valeurs de $y$ correspondent à la deuxième colonne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.1    2.9    4.2    5.05   5.85   6.95   8.1    9.    10.2   10.9 ]\n"
     ]
    }
   ],
   "source": [
    "y = data[:,1]\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le tout peut être fait en une seul ligne :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.   2.   3.   4.   5.   6.   7.   8.   9.  10.]\n",
      "[  2.1    2.9    4.2    5.05   5.85   6.95   8.1    9.    10.2   10.9 ]\n"
     ]
    }
   ],
   "source": [
    "x, y = np.loadtxt(\"data/donnees.dat\", unpack=True)\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Utilisation de la méthode `polyfit`\n",
    "\n",
    "La méthode `polytfit` du module `numpy` prend comme argument les valeurs de $x$, de $y$ et le degré du polynome (1 ici puisqu'il s'agit d'une droite)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.99727273  1.04      ]\n"
     ]
    }
   ],
   "source": [
    "parametres = np.polyfit(x, y, 1)\n",
    "print(parametres)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les paramètres sont bien les mêmes que ceux que nous avions déterminés à la main."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =    0.997\n",
      "b =    1.040\n"
     ]
    }
   ],
   "source": [
    "a, b = parametres\n",
    "print(\"a = {:8.3f}\\nb = {:8.3f}\".format(a, b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Utilisation de la méthode `linregress`\n",
    "\n",
    "La méthode `linregress` est contenue dans le module `stats` du module `scipy`. Elle prend comme argument les valeurs de $x$, de $y$ et retourne en plus des paramètres $a$ et $b$, le coefficiant de corrélation.\n",
    "\n",
    "Commençons par importer la méthode `linregress`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import linregress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilisons maintenant la méthode `linregress`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a   =   0.997\n",
      "b   =   1.040\n",
      "r^2 = 0.99829\n"
     ]
    }
   ],
   "source": [
    "a, b, r, p_value, std_err = linregress(x, y)\n",
    "print(\"a   ={:8.3f}\\nb   ={:8.3f}\\nr^2 ={:8.5f}\".format(a, b, r**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Représentation graphique\n",
    "\n",
    "Python offre la possibilité de réaliser une réprésentation graphique en utilisant le module [matplotlib](http://matplotlib.org/). Voici un exemple d'utilisation de ce module pour représenter les points $(x, y)$ et la droite de régression précédemment déterminée.\n",
    "\n",
    "Pour une utilisation dans ipython il faut d'abord préparer l'environnement pour intégrer matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Chargeons le module ``matplotlib.``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = 8, 8 # ajuste la taille des figures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Préparons maintenant le graphique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106b24ac8>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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++OM54YQTePbZZ/noo4+YN28e/fr1Y/jw4Tz77LOLPNe2227L9OnT+fe//w1kl/psyYuz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106adbdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, \"bo\", label=\"donnees\") # les points (x, y) representes par des points\n",
    "plt.plot( # droite de regression\n",
    "    [x[0], x[-1]],                  # valeurs de x\n",
    "    [a * x[0] + b, a * x[-1] + b],  # valeurs de y\n",
    "    \"r-\",                           # couleur rouge avec un trait continu\n",
    "    label=\"regression\")             # legende\n",
    "plt.xlabel(\"x\") # nom de l'axe x\n",
    "plt.ylabel(\"y\") # nom de l'axe y\n",
    "plt.xlim(0, 11) # échelle axe x\n",
    "plt.legend() # la legende\n",
    "plt.title(\"Regression Lineaire\") # titre de graphique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pour aller plus loin : les résidus\n",
    "\n",
    "Nous allons maintenant utiliser les méthodes vues précédemment sur un échantillon plus large. De plus, nous représenterons les résidus qui correspondent à la différence entre les points issus des données et la droite obtenue par la régression linéaire.\n",
    "\n",
    "Commençons par lire les données dans le fichier ``regLinData.dat``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = np.loadtxt(\"data/regLinData.dat\", unpack=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilisons maintenant la fonction ``linregress`` pour trouver les paramètres de la régression linéaire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  2.8778150933  b =  1.06938428687  r^2 =  0.991859700018\n"
     ]
    }
   ],
   "source": [
    "a, b, r, p_vall, std_err = linregress(x, y)\n",
    "print(\"a = \", a, \" b = \", b, \" r^2 = \", r**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons maintenant visualiser les points et la droite de régression dans un premier graphique, puis, les résidus dans un second graphique. Pour ce faire, nous utiliserons la méthode ``subplot`` de ``matplotlib`` qui place des graphiques sur une grille. Les trois arguments de ``subplot`` sont le nombre de lignes, le nombre de colonnes et le numéro du graphique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10716ba90>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sOHr3nEOBt2nX7muSkhJJSTkdv38YAP37a1JebaGBXymlTpDIIXUJCTB69EeI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\n8kOBFwmfOje5ZM8ffxzrOc5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jiSevzKEz19OdecyjF5ncymBeYx8NSSafA3QnKekpNmxY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YCB6ACIaFJSf52zDjnKGTLIPLxyKHgITpvT9FK57133Xnz5si+bes1spJLhP4cxFi7+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\npQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106bc1240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# graphique 1: les données et la droite de régression\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(x, y, \"bo\", label=\"data\")\n",
    "plt.plot(x, a * x + b, \"r-\", label=\"regression\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Regression linéaire avec résidus\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "# graphique 2: les résidus\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(x, y - (a * x + b), \"g-\", label=\"residus\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Résidus\")\n",
    "plt.legend(loc=\"upper center\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les résidus sont un bon indicateur de la qualité du modèle. Ici, on dit que les résidus sont 'structurés'. Ils ne sont pas aléatoirement répartis autour de zéro, ils présentent une variation parabolique. Cette structure des résidus indique qu'une fonction affine n'est pas adaptée pour représenter les données.\n",
    "\n",
    "Utilisons la méthode ``polyfit`` pour ajuster une parabolle :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p0 =  0.075725341459  p1 =  2.04483633725  p2 =  2.8437926618\n"
     ]
    }
   ],
   "source": [
    "p0, p1, p2 = np.polyfit(x, y, 2)\n",
    "print(\"p0 = \", p0, \" p1 = \", p1, \" p2 = \", p2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reprennons les lignes précédentes pour représenter les données graphiquement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10741ce10>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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B5TzNw2TwC25uCXKui9jYDjz99BoyM4sxpj4NGsxi//7miLhISjq+uoRU4AdaAMliB+pd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L7DNbL602Iag7FB/PC5H2r+jtviPn0fv6avWKUIlOI+uzl+n0Xgz70WhBAl+LOiGS+K+4bi2Yp+\nprYKTe8bSYxg09AmANnBMm5G9ioDfEza+TJSJq+KWn1uFLL6vezjd2P174/vV5ZBZWwf244F0xYg\n1BByfCPBbH723jDLv5Diz0jGI3uBbJAwsp8ZTI2x10afSkgKSUerFlJKbSn+gD+An574U9PtaD5v\nkjPFz645h/ccjkXTFmX/nkk+OZKJYF9sn+baYhX49bnv1lArVs9bjbltcw2PpTXUqtjqrtv5dOlJ\ns3OVBX6g8Ax7NryHYXS9t9POpwR+C8WfN8DHb3NkrzCZ9mICy6iqv+xWP6W0lVLaRiltAxAGcDay\nlf5VjZXiZ2+KkZ2kJyNlNIGQDdawUvxqVaceU2uU49crfqPivrSUxg/6foBbXr8FGwY3KD93E/jZ\nCn3sGPzEn11yUpbyFb+DAT764r7ZrbOxJ6q1Go1uIJjtxl4zqxnwsUzMMO0BaPP7gNbqn0hp71kf\nee8RfPWxrwIofmQvs1v1OeS0lM670KrdoEKKX+38MMVfcFneAn38bqz+hJDIu7juGN+BBdMWuJoL\nEBcmrU1gUvG7beezgn3ORVlUFkeSqaycXxkp48hhYvUGzYHmgsXDVrhV/OrHnnfYefjFyb9Qtmdo\n9aejEGVR01nD2k/V6FcN1Z+vnz3kszhq5lGGx3LXWXfhuN7jALgL/DKVIVNZk0YwO1fVgb/QZyGS\njqAtWB7Fr7f0WY2Ukxw/O560mK/4Kz65j2Z5AMDJnu1FiTDt488FHKUS1oZiMbP6C1X1A9o3jJ0w\nagtLr/jVFqS6qEv9s95pvbjiI1fg+peuV37uVvGPJkeRkTJKLpLdZXua4zdR/Mo8gJwCYzdGfp8f\nQX/Q8kRf+/5afPf/vmv4O8PAHx/EluEtmHP9HHww9oHyu5SYwsu7X0Y8E3c9slc9acvoQ6q/cQS0\nN4UFc/xqq98XQNAfNL1htWrnc2P1x4V4XvDZPr4dC6ctdDQtjqHO7wM2c/wF2vmsYNtjA2LYktLs\n9XMa+CPpCFpDreYKskBxpRq3OX6j5ZuBAlZ/zs1QfwadWv0AcNmqy/Ct1d8yPJbpTdOVoO0m8Kvf\nG4bZtXk4MYzpYZXiN1HCdqx+/ftlFKhZipC9D0afMUPFb3Nkr/pG2CyFXJFZ/YSQs1RfnyGE/ASA\nd7cfJcJK8QP2FZD+g6Ap7rNS/GqrX1fJXijHb2b1h/whLOlaomlPczWyt7ED+2L7EGoIKR84dlx2\n2vmMqq+BrJVrK8evW95XfTNgx+6PZWKmNwfqwj4gG/gHxgdw3r3nKcU6jLSUhiiLeH7n8/l9/KKz\nZXkBGBb4GV1IXVn9/mx6xCzPb/W+e6X4t49tx8KOhe4Uv6qiH3Cg+E1y/FYwh81s+JTTwB9NZzs/\n7CjIQuSl1sxG9hZQ/PrHGt2ERdNRtIXabAV+s+I+J7gJ/IYq2uTc0ij+BnPFrx/jbBj4Jet2vv3x\n/WgJthTO8ZPiF+kBdIq/0sV9AE5XfZ0MIIpsT39VY5XjB9wHfk31pVWOX2f1q08u9YmnV/xmVn+o\nIYT2ULtiWTM10xRoQkbKriFgV/EfiB/QXETMAr/G6ic2rH7VazyjeQYmUhOa4KG2pBWrX3VTYafA\nL57JV6IMveLvae7BC7tewEGdB+GoWUdp9iUlpuAnfjy1/ami+/gBGBb4GV1I1a1/VsV9SvFj7jUz\nUwClaOczep13TGStfruOmZo8xa/L8RtVhaeltHLeOYWpLrNW1IzsMPDnpjuaBRInVr96bQy7q/Ox\nPn49ZoEyko5g+fTleYHfqKq/kOK3i1eB3+xGxm6O325xn1U73/74fsxrm+esnc/FsrzseJQcv76d\nr9zFfZTSi1RfX6KUXksp3e/ZXpSIUip+zeQ+u1X90mRVv0bxm+X4Cyj+9sZ2TKQnlJ+pe4b1Fzkz\n2N2wev/Z66EfKKKZ3GejuE/9WvmIL6+P3mg76oumncBvpEQZQ7EhjeLvndaLkxefjN+f/vu8u+e0\nmMaa+Wvw9PantSN7XeT4Aa2FzzBU/KpCQLPziAVBQRZAQBTVa6YASlHVHxfixop/2kJ3NxKqcb1A\neRS/kuPP1Qmo3aqMlHFUTOqV4re1LK/BDZ5jxZ+JYvn05Zo6G6OaEyur3y7q7chUxql3nWr5HLO8\neVE5/ow9q1+v+PXn3lB8CPPb5zsu7nOV42dWv1haq79gZCCE/BqAaYUVpfRfit0BQsgpAH6J7E3I\nrZTSvDJYQsiNAD4JIA7g85TSDfrHGGGV4weKs/pZLmZG8wzT54UbwspFhalc9clgK8cvaXP8esWv\nvhCw47ET+H3Eh7ZQm+bOkqkQfZVxqCGEseRYvmoyGISiV/zApN3fO61XOW694lerVTu9/Ea5Z8b+\nxH70tEwG/rZQGx6/4HHlWNTPS0tpHN97PG54+QZlEBLgrqofMLb69ZMfAa0zYLR6HzBZh5IUkoaO\nk55SjOxNCAnN60Upzeb4Oxa62p56XC9gP8cf8uVb4XZgnzd11bj63HVs9asUv/59dpvjN53c58+f\n3Kdu51NTqJ1vWdcyzbohplZ/geI+u6jfv5SYwt+2/c3yeqS+KWOYnVsHEge0it/kGmB7gI9fp/gN\nrP7e9l6MpkaVfbWl+P0hyFR2luNXOckd4Q7lMeW2+v8O4HUAjQCOArA193UkAHdnhYrcBMCbkE0f\nHArgfELIct1jPglgMaV0CYBLAPyX3e0b5VeMFL+dOylTq98qx6+z+ht8DfmT+9Q5fp3V3+BryLP6\ng/6gRvG7DfxAtrJfvf/MLiy4Op9FcZ++jx/Iz/OrFT/Lt6q3bdvqN1H8++P7TVu89PYgC/ar561W\nUibstSil1a/O8Rst0MNg+6F+TQtZ/ZaKv0irfyI9AZnK6GjscOcguMzxuy3uU1f1e5njN7LW9Tnj\nQhQzwMfommOUdmGth8u6llnm+M1G9jrFTyaHcrF9t7KpjSaNmp1bI4kRZWhRoRy/3uo3Gn+sT834\nfX5lwiNjf3w/5rXPc97O56KP31Txl9Pqp5TeTim9HcD/396bh8lRnefi76neZ1+0SwgNmzBilUCA\nQTACbxjb+DqJsf27xo4TOzfeEvva19jOYjtOrh0nca7BTsCJiXODd8IFY4wNQo2BgAAjQCAhBFoR\no9nX3pfz+6P71JyqOqfqVHXPdM/MeZ9Hj2Z6uqpPVVfVd973e7/vnAugn1J6E6X0JgBXoxL8a8VW\nAAcopUcopQUAP4LTO3AdqgsCUUp3AegkhKyEAkSyTdAcv6hXP3tgqLr6ReY+R47fJvW3RlqFUn97\ntB0z+RmUabmmwN8V73Iwfs8cv0I5n/2z17TZAr/d3EdLlslAa7TVO/C7MX6XwG+XB9lNenXf1WiL\ntplGx6A5flEtv7COX0HqZ+NIFVKW69bN3Oe6LK9k2VE32FMqU7kpdMW7LC1G/cB+rCp1/G4te70g\nSn9ZcvxBGL9A6i/TstkdUAVsEkYpDVzOZ9+f/btg/pUNXRusUr+gnE9mOvYLfj9s7F7kSpbjF11b\n6ULakhOvNccvmgDx94gp9ftt4KNax6+Q42+Uua8bQAf3e1v1tVqxFsAx7vdXq6+5vee44D0AgGQy\nCUKI+e/9570ft//O7ebvAFCkdcrxh7iZmZu5j3f1M3OfvXOfIWb8+XIerdFWB+OPhWMIGZU64unc\ntKWvvm/GH++Wmvv4B4Pp6lfM8dsfGms71koZv8XcxzF+r7yrW47fk/HbpP54OI6r+65GV7zLfN1X\nr36bq18lx69i7uPHwZ/ToDl+v4GaLRdsOV+cLB0kx28POqpSf11d/VyraLfA/9473ou9w3str7Fe\nD/ZzyTelUoHZnU5QPsvg1bKXhyjHz9IS/P2XLqSRKqQsQRGwTkTspjc/sAT+6ti9gpYfcx/fwMgt\nx6/cwMf2rOJZepmWMZIeqZj7/DD+0mw5X+A6/urkmBCCU3pOwZFPHbHEN9XrTARV7exrAHYTQnYC\nIACuAPClwJ/aICSTSXS81oGp3BSSE0kAwKbUJux9ci+mOqZctz0/ez6eefwZHIgeAAC0vdaG1HAK\nnVOdmCxPIjmaFG6XGkqhbaQNyWQS4aNhlOIlPJt6Fudnz0cymcQZ02fgwNMHMNk6iRNjJ9CWqrwX\nANpfa8elxUtRPFhEklZeOzd9Lp7b9RwORg9iO7YjmUwiXUjjvMx5SCaTuCh/EZ78rydx2tRpePnp\nlzHz0ozrcZ05cyZyxZz5mex8rB5ZjRPPn0Dy1crrM4MzaB9tR3G8iAiJIJlMYsXQCgwVhhzHHj0W\nRblYNvcJAC0nWjA0MYRkuPIaPUxBQgRJmsR5mfPw7OPPYmxyDN3T3Ugmkzhp7CS8+tyrSA6KzysA\ntBxvMc8jj2K5iIvyF2H3Y7uFN8eKoRUYyg0hOVbZLvFqAulUGtPT0/jW675l7m/o+BDOSZ/j2L8I\nm3Ob8fRjTyMWjqFvog+HnjlknjsA2JLbgt/+128tAW9gcgBrRtdUJqyHCZAAkkXnZ11SvATP7XoO\nFxcuNsdyVuos7HtqH1IHrJOjNSNrcHzPcctnHz582NwufiyOXCgn/BwGPjAXSgVciSuxYmiFuY/B\nmUFszm5GMplE/ngekVRE6RwxzBydQXuh3dyGUop+9OPFp17EcMswjk4excnjJ1v22Xa8DYVywdfn\nMBSOFxBNR/FC4QVsSm2y3CcH4gewbnQdQpmQcN/kMMHjxuMY6p71Mk8dnkIn7UR2LIv4dNzcLlfM\noR/9rmPkvwsA5vvZPfBS5CXL+ymluKx8GXbu3Dl7LR8GaII6vsOB8QGsHllt2f9YZgyXly7H3if3\n4uzU2djx4A4cnTyKd8XfhccfedyyfbqQxpbcFjy480Fsx3Y8/Bvrwj5ux8GjeKyIcC6MZDKJ0fQo\n+tGPXY/ssuSs7RjLjGFzbrNln+wZVj5k7VdxTvoc7Nm1BwejB7FubF3lehc8J86aOQv7ntyHw5HD\nAIDVI6sxsGcAyaGkeQynTZ6GV55+xfKc3FbehocfehiJSALpQhpvIG/AwPMDWD++vnJMA6NYNrnM\nMtbw0YqClKRJlGkZV9Ir8chvHkG2mMWF+Qul54pSigvzF+Kp/3oKISOE5UPLMZIZQcd4B6ZL00iO\ni7erGZRSpX8AVqEiu18HYJXqdh77vATAfdzvNwL4nO09/wzgeu73FwGsFOyL9vf3Ux537ruTXvfD\n6yyv/d5Pfo/++Pkfm79v+942+tDhh6gX2v+mnU5kJszfv7jji/Qrya/QN/3fN9FfHvildLs7991J\n3/HDd1BKKf3oPR+lN+26iQ6nhmnP13sopZSe/q3T6f6R/ZRSSpOHkvQD3/yAue27f/puesE/X0A/\nd//nzNc6/3cnHUuPUUop3fTtTfS5E8/RR48+Si/5l0sopZSeefOZdO/QXrrp25vonsE9nsf1of/3\nIXN8lFL6+n99PX34yMN063e30seOPWa+fsfeO+g7f/RO+vkHPk+/+tBXKaWUfuDOD9DvPf09xz5/\n9ye/S2/+8c2W13718q/oG/79Debvn77v0/Qbj36DUkrpOd85hz574ll6066b6Efv+SillNIP3/1h\n+s9P/rPr2K+9/Vra+tetjtePTByh6/5hnXS7P77nj+nNu2bH9+6fvpv+cM8PHe/79QO/pvGvxl3H\nwBD6cojmi3lKKaXX//R6x/5ifxWjmULG8tpTx5+im2/ZTCml9A/u+gN661O3Cve94R830B0Hd9AN\n/7jBfG37v22nD7zygOO92763jSYPJS2v7dy50/z5Szu/RP/iwb+QHsdYeoyu/MZK8/fh1DDFl0Cv\nuO0K87UnXn2CbrllC6WU0lufupX+4V1/KN2fCH/10F/RLzzwBctrbX/TRg+PH6aUUvr4scfpxd+9\n2PL33/nx7ziuKVX805P/RP/o539En3j1CXrhrRdSSint+8c++srYK5RSSrd+dyslXyK0XC47tj3r\n22fRe1+61/LaZ371Gfr1R75O/233v9Eb7rzBfH00PUq7vtblOhb+u6CU0u6vdUVJI+YAACAASURB\nVNPR9ChNfDVBU/mUcBv7tfPhuz9Mb3nqFsf7koeSdNv3tlle2z2wm577T+dSSild9w/r6JGJI/Qv\nd/6l5ZnCMJGZoB3/u4PO5GZo4qsJX8fB41uPf4t+/Bcfp5RS+tyJ5yi+BLpveJ/r/vYN76Mbb9po\nee0t//EWx7mntPIsnsxOUkopveHOG+htu29zvKdcLlPjy4Z5T1JK6Qf/3wct7925cyfdeNNGundo\nr2XbZX+7jA7ODFJKKX1h6AV65s1nWs7jLU/dQj9y90cs23z1oa/Szz/weUoppTO5Gdry1y2On0XI\nFrI08pWI+fvHfvEx+q3Hv0Wv+Y9r6D377zFfl30nqJjvKfUZe12lfma0I4RsBrAGFcn9GIA11ddq\nxZMATiOEnEwIiQJ4D4C7be+5G8AN1XFcAmCCUuq92gpcXP31quNXWKRH1LLXLvW75fhZbT4D7x5n\nBr96mvvqVc7nae7jvgdWWsW7+pXMfZIcv5vMz47FnuMXSadhI4xcMefZ0rlYLoKCmufbvjQvpRS5\nUs4hnfqR+lN5W46/hjp+/no6MnHEUmY5mBrEYGrQPGZWWWE3Q/JSf77sL8cvyi+v61hnllHKluWt\npXMf36vf/hn5Uh4UVHg+s8Ws4/Wp3FTF3Gc7l0EMcWwf9rUxeNjlfj9SP5/nZvfgQ0cewpUnXykc\nS6FUqMnYB4hz/EGkfllfAr5zYTwkzvGnCinEw3FrBZfhXc7HPpeNnz1LeE+Nl9TPf5de5Xz2+97M\n8YsW6SnJVyL0C6876dMAPgLg7wV/owCuquXDKaUlQsjHAfwas+V8+wghf1T5M72VUnovIeSthJCX\nUSnn+33V/derjp9Wc152c990ftrfIj2SNej5HD8/3nzJmuOnlFpyyaykj7WJ5Y/Hj7mP7wBYL3Nf\nJKHu6uc79/l19bPWtXyPb6/AbzdMiZYoBWBpv+tm4GTfCZNi7eY+Vqpkz1FbOve5XEfMZKiS41dq\n2csFh28+/k0sb1mOL17xRQAVxzRQObftsXbzOxB5IgB5W1U35Eo5Sx0/AOz96F7z/Enr+GM19Oqn\nAnMfl+MHKtetPaBmChlHYJE18PHTvIchGooilU8hbISlHgZ75ZGflr2sAgGo3IOHxg/hyeNP4rL1\nlzm2Z+e9roFf0dVfLBcdxy96NrNmZXwjK9F9YDf2yfYnMjHyefnBmcFK4Ocm2l6Bn78/vFr22tet\nkBHKsBEGAfGc2KvCNTJQSj9S/X97zZ8k/4z7AGy0vXaL7Xf52pYukHbus9Xxq5SaGMSwXJhsFp4u\npJUb+DDHtb2cz61zX1u0zdKGlx8HY/yJcCJw4F/fuR7TudmVydxa9rqV8w3ODKJQLmBdxzoh4++O\ndyNTyJgzXD5AiTr3tUa8W/aaQamYswRNFcZvZ1CidqnA7ATELfDbzxUf0AGxox+wufoldfxA5Tux\n90aoV8vebDGL4fTs4i0j6REAs/3oGXOSMv4ALXtFjJ/3YsjMffVg/GYDH1s5H1C5ntgStwzZYtYZ\nTPPTZlCxBH4Be/RCNBTFVG5Kev0Bzu/alfGXxOY+AFjbvhZ37b8LZy470xEUgVlTW10CP7We2yCu\nfpFxlKlz7HqR1fFPZieFgd9+z4gma/zkeCg1hJWtK30xfv76ZoSkVC4JJ3b2ZwuLKyIiwCYf9Qj8\nqr36f48Q0l79+c8IIf9JCLmg5k+fY9TC+B85+ogZEEU3AtvO7YEN2KT+ai96Ni5KqWUiIivnYxch\nL/MDs4yfl5b8Bv4bzrvBsnSo2cBH0qtfVhL1r7v/FX++888BiBv4EEKwpn0NBqYHKscmmED4ZvzV\niYH9xh9KDWFFiwvjDwvK+SQyq8o4+Bk+4JT6ZQ9Su9QvLeerZx2/zWWcK+UsgZ+pP2xhl1Q+hZ5E\nj+Wz+ImSzHntBlG7WB5Sxl9jOZ+jgQ9Xzier4BBJ/bLOfUFK4FjgFwVyBvt37adl73Ru2lyhbk37\nGty9/25ccfIVws8xiAGDGMgWszUFfj6Noir1s0V6eIiezbyjH5C7+qdyU5bmPbL9eZXzmVK/B+Pn\nmb1dQXRj/faeFm4p5HqW9KmW8/05pXSaEHI5gDcA+Ff4aKTTKNSS4//ig1/Eo8ceBSC+OJTL+QRS\nP7vBSrTkyfj5HL99HJ2x2nP8dsga+LBgKcvxz+RnsOvVXQCci/Qw8HI/L1nxDXzYmFWlfgLimMUr\nMX6JdG2HyjjsioFd6pcFfj9Sv6iOX1bO51rHb5P6c8WcZblWnvEDlQlJd7zbPcfvl/EL2sXyqDfj\nF/Xqt+f4uxPdjk6RtFpfP9dSv2fg98P4BTl+xvjXtK9BppgR5vcZwkbY0XLbL/g0ih+p3xH4DaeC\nISMkdqhK/V7lfIOpQUeOn19MjN9GxPjt+7MjVUgp5fiB+jbxUQ38LBpdC+BWSukvUIfOfXMNFcYv\naokJVKRXxsaEgV+yfKIdjgY+1QcDM/jZc/w848+X8hap385MO+OzjL9egd9V6i/Kpf50IY19I/sw\nkZ0QMn7AGvhFy/vaG/h4Sf2pQgqd8U4x4/fI8fMPCxWp3w2ic8VL/bJAFwvFUCgVUKblQHX8wpa9\ngocSD5HUz4I9MJvjZ2pXqiBm/PFQbTl+N2lbyvjrWMdvz/F3xbsc37PM9Mczfns77SBS/3R+2pPx\n89+Zn5a9rNkQUJH6AeDy9ZdLPytiVCaZ9Tb3BZX6He2Kbf4GUZ8DoFLDr5rjF5n7eMa/snWlrxy/\n3ajp1sQnlbeuW2FK/YK4Us9+/aqB/zgh5BYA1wO4lxAS87FtwyCaaYly/LLuUOzh7Sr1qzTwqU4g\neJYrehg5GL+tc59Q6q8z42dGInuw8jL3sYfmk8efFOb4AVvgL9vMfbRkYateAZdSWulnbWOjgELg\nt/fqr1Xqt1UF2Bv4yAICIcRUUtwmkNIcf1Cpv+wt9VsYf8J6ji0NfAK0AHY734BVhufHWUuOnzF+\nNnngVwCUBX42ORQG05izZa+fPv0MyozfLvULnjnCHH9uNse/cdlGvP2Mt5vtbkWoF+OfqwY+fhg/\n37yH7c+rZS9gvUfYsyRiRFAql8ze+6rmPvY32eTYvlKlm5LcCKn/3QB+BeDNlNIJAD0APluXEcwh\nRDMt1Rx/ppgxHwQyqT9TyKBQKrg+xOxSP/ts06nNdfpy5PjLBbRGW82LRsj45yDwz+RnEA1FLU55\ni7nPJtEDlQCxum01Hn/1cSnjX9W2CgMz1Ry/iPHbzX0ui/RkihnEwjEkIgnfjN9RzlcPqT/kLvXL\nrhE2MfTr6pe5mb1cv/bgwKR+ViY0kh5Ba6TVDPypfKoyuXLJ8QeR+t0YP39d8eMMmuNnzwE+j2yX\n+t0Cv0Pql+T4/fTpZ1DO8StI/cIcP2dEXN+5Hne/114tbUXdA38puNQva0FsrzYSTYCnclOmt4FB\n1GKZEOJQkvi4MZgaxMq2lWZ76lwx58vcB7jn+B2B34UIzLvUTylNAxgGcGn1pSIqi/U0NWrJ8fNS\nv2hltWgoisncpMVhKgKTZE0jHxfs7A9zR8veUt6S45eZ+3gzST1y/NM5p/TILkg3xn9V31V4+OjD\njgoIhmUty0wp2c747eY+L6mfmWJEN8NQyroynx32bUQuc4Z6SP1uEjBbyc+zjt+W4+9N9FokegZP\nxm97mDJ1h53r0cwo+rr7Zs19hUrgz5fy5uTAnuP3K/V7SeKyHH9NUn9JLPWzUl3XwM8FljItI1PM\noDXaKjb3+czxR4xIIMbvK8dflfqVxhOq9IxoBONXWZ3PbmyUsWCZq5/fH18WyIO/pkfSI+hNzC4I\nlCspBH6buc8rx88H/ng4jqnclLC8c14YPyHkbO7nv0Slq96fVl+KAviPuoxgDlGLq9+T8YdjmMhO\nuDr6gYpTNhKKONgyy9vaewOUaMl8wBZK1nI+h7kv3omp3JSV8RuzgT8IQ5IxEEsDH0mO/6q+q/DI\n0Uek56Q30WtKyfx+GPviz09btA0zeXm7YVb/apftKaUYSg1heYt8qWS7uc+teUpLpMVzeWC7YmBf\nltct0LFJgpvUzx7G/CRxQ9cGyzKrDJ51/Hapv/pgZga/kfQITuk+xSL1t8faETZmV4kUKUx+oCL1\nixh/PaR+k/GTkOW1tkibY6LJJm/8JHEmP4OWSAsMYjgZf0CpXzTR5mFn/L7q+LlyPhXMGeMPWs7n\nYe6T5b1VpP4yLQuPk6WvCqUCUvmUuR9GGJRy/GG1HP9Mfsbh6p/ITgjVv/nK8a8nhHyt+vN/A/B2\nAJMAQCk9DkD9amoQlOv4BSeTya+AXOqXfUF2MDnXYu7jpH6GkBECATFZf6Fsy/HbpX5Jjj9XylVW\nCQvAkGSBn128fK6VP7+pQgqn95yOnkSPNPAva1lmslRHjr9csgQtr8DPGLKdvbPJmGtdtL2cz0V6\nFq20Z4doQSNlxh9OYDo3jRItSd8jyvH3dffh0MQhx3uD1PFHjIiZ5x9Nj6Kvq2/W3JdPzZ5n7iFe\nU44/gLkvX8oHl/oFrn7mI2DfjUjZEeX4eQZtZ9hBzX1T+QA5fkk5X6FUsHR34xv4qECkRPqFiPEH\nWZZXxvhrcvVzXSZLtCQ8TjbhmMhOoCveZaY8lRm/zfPjpoqJpP6J7ITw+50XqZ9Sei+AndVf85TS\nMird+kAIaZVt10wIyvhL5RJypZwr44+GopjMTro6+hn4Gng+2Ilm1iESMsdTKFVz/LI6fomrP1PI\nmCWDfiFzGTMjGs887Yy/JdKCS9ZdYulExcMS+GWufmOW8bsxbVPqt82CvfL7gNURz1IwMgaqIq85\nGviEreY+UarIfG8kgfHsOBLhhDRlJHL1M8Zvb+GpVM5nq+Nf27EWI+kRlGkZ49lxnNx5soXxm+eZ\nk21rKufzyfiZHF9TA5+yrYFPVWVSCfz89cWb5ezHPlflfHzjGVZiKJo4hYwQCCGWdCGf41fBXLn6\n62Xus1c0yIKhiqtfJvWz62U8O25p6OTF+C3PaUWpX2TuG8+OCwnlvJn7KKW/qv74E0LIrQCWE0I+\nAuABAP9SlxHMIVRy/PZSGWD2IvUq55vOT6sx/qrBz2LuEzzMgcrNy0v7QRh/upAO/JB0exDFw3FM\n56ctAZuZEVngv3jtxYEYv8jcpyT12258lcDPl/OxTliyoCsz0fEQufr9SP1jmTHX60iU4++KdyFs\nhC3tloEArv5iDus61mE4NYzJ7CRaI63oSfRYcvx2xm9vGDXXOf5CuWAGtSAwzX32Bj7lWcbfGm1V\nC/xceZwoxz9n5r7qGArlAgxiSL9j+8SOr+NXQT2kfr5iIlfMoT3aHkzqVzD3ubr6PRr4yFQ2dg7H\nMmPWwM8xflHtv8XcF7CcLx6Oyxn/fJfzUUr/DsBPAdwH4AwAf0Ep/VZdRjCHCMr4+aYqgLjlKrtg\nVBi/SOpXYvxVV7/M3NcR68B0btrhsq4l8EdCcrNRLBTDTH5Gau5rjbbiqr6rsKFrg3Df3YluTGQn\nHH35w2Q2B2sv55MtkFML4+e38WKfqoyf34dI6ndLJYxlxly9IqK0EAD0dfXh0LhV7vdbx58rVQN/\nehijmVH0tvSiI9Yx6+rnvRQixh+kZa+Xq9+2SI/Xd+QFWY7fS+rnJ/4MPOOvV45/Kjdl9kUQgZ/c\nyox9/P74iV0Qqb+e5r58KY+OWEewBj6CSaWfHL+d8dtJXpmW5VJ/WRD4GeOn/nL8ruV8hRlrr/4q\n0Wgo4+dBKb2fUvpZSulnKKX3E0Kur8sI5hCqOX5H4OfaqALyHD8AJcbPvjCLuU/yMOcZv72O3z6O\nkBFCIpLASHqk7oxf9KCNh+OYyc+4Sv1b1mzBXe+5S7jvsBFGR6wD49lxa1kgM/eVrK+x9bBFkOX4\nVaV+ns25PUhlvcB5iKR+VcafiFQCv9sE0szx2x5Sfd19FoNfmZZBQV1TPHZGmC1msba9IvWPpEew\nrGUZ2mPtJuO3nGdBjl8kx3rBK5CzNBWb9HlNFLwgc/UrS/3c9cVSH4Ag8JcKiBpz1KufU1vcrhV7\n+sGvuY89l/weBw+71N8R6xAGrN0Du3HjAzcCUG/go+LqZwZfFalfxviL5aIj8IvalouO2a42+Crn\nq94XIiIwb+V8hJBWQsinCSHfJoR8lBBiEELeSQjZC+B9dRnBHKKejF8k9QPiL8gOJvXzjJYtterG\n+PMl6+p8ogdmR6wDg6nBugZ+WScxFvgtD09qDfxeYCV9PDNlRit7GsYtz2+R+v0yfhuDcnvo2h8s\nqXwK//DYP1jeI3L1qzTwYfv3ZPyGeJK4oXODxeDHri83SdweqHmpfzQ9it6EjfHzykq9cvwKgZyv\n5a+V8fPmPj7Hz0v9LZEWh6s/W8yiLdombZ5jN9PlS/579SuV80nOvQg8Sy6UKs50FVWSIWyEkS7W\nt4FPR6xDOHneeXgnHjn6CACXcr6yu9QvCoZ/++jforelF2cuO9O5P5vULyznU5D63QI/MwXyf1PO\n8VfvC9F3pkJCVOHF+P8dwLkAnkNlCd7HAHwKwPsopdfVZQRziKB1/CqMP6jUzwc7txx/qVwyl4U1\nG/gIlo/tjHVicMYW+Is1Bn5JeRGToexleGValrYRtYPl+flJEG/u48ftlucXBSRgtsWmG/gbyK/U\nf3jiML61y5rlUpH63Vz9njl+QTkfUHX2c1K/l8zP9mWX+k/qOAnD6eFZxh9tN139LIXjyPGH5y7H\nDwjqomtk/I4GPkTN3NcZ65SW0tnNdPZniwqUyvm4tuJe9xmfemFs3483QlRm7BeqjH/P0B5TWZLl\n+P326n/g4AP4x13/iDvefYfjflEu5/OS+r0Cf84a+P3m+AGxkixbnyMIvAL/6ZTSD1aXyb0eQB8q\n3fueqcunzzFEZRQixm+fRbEHgKu5r05Sv4zxs4cIf7GKGs10xjvrKvW7MRD2ml0uZTejShUBC/xe\n5j7AvaQvVeAa+PCMP62W4+elfj+MP1PMWII64C3150o5qXRqBn43+VbyMO7r6sPhycPm7ypNm/iH\nKXsYrWpbNZvjtzN+Zu5zyfHXW+oH3M1SfsG7+mXlfK0Rp7kvU8ygI9bhKH/k8/H8/RnU3DeTn1E2\n98nyv/z+2PfhN78PzE0dv2g9DQDYM7jHnGCqrs4n7NVf3Xcqn8J//8//jh+86wdY17HO8XlCV78o\nxx+A8fPBXcj4fbTsBcSEUrYuQRB4PanNaQqltATgVUppfaYc8wBRWZCq1N8WbbMyfqMGxs9c/aLO\nfZIcP8t3WwK/hPFTUIvLOlPI1MT4C+WC1NwHwBGwVWV+gAv8fAMfwuX4DbXAbzJRAeP3I/XbHfmi\n91oCfyHjmHXb9xEPO5fllU0uVKR+1tjJIfV3bbAwfpXA75hIhmLmdzKanjX38cvy2idY/PGyXhF8\nq2kvqDB4e/CoJRCxh7KogQ+bYMsYf1e8y7VPPn8+7f4hFURDUVBQ7zp+RamfV3T8lvIBc9OrvyPq\nNPeVyiW8MPyCK+MX+UfcGP+RySPoindhe9924bhUpX42UZQxfq/V+cYz41bG75HjtzTwCcsJ5Xya\n+84jhExV/00DOJf9TAiZqssI5hCMgTKTUImWECLWsiCZ1N+b6PVcpAfwJ/XzZSAyFscYP/tML0bB\nukrVM8fP748Hz/IAa+CX1e7bwVrNihi/vUymLerspsYgaiwDVBrQ8DerCGzmbtZE+5D6s8Ws4+Zz\ndOqqHgOb5SuZ+zykfv5/hg1dG3Bk8oh5fYvKjET7Yg9T9hBd3rocw6lZqZ+VtvGrBrrlmf2wfvYA\n9Lo+HYy/DlJ/sTy7SI+9nE8q9cdtUr9NarcE/nKwXv2A+H5j4FmtrGsfvz923fEVCKqoe8teidT/\nyvgr6Ip3mYzfl7mPu1f4SZHXpJ/vhwC4mPtCs4y/O949+1k+cvzdiW7L39j9MZOfsVQq+WL8knUJ\ngsCrjj9EKe2o/munlIa5n/1NJRsE/gsRzchFy/Jmihn0JHrMB4GIcbBFG/xK/ao5fsZEWNlRmZbF\nUn9s/gI/+2x7LbRfxj+aGXWoH6xzHz8Db4265PgL4hy//UYSwSCGmQtVkfr5my1TzJgeDAYRC+Nr\n+ZVy/B5SP/8/Q2u0tWLunBkE4N2ul+3D4hkJx9AV70KqkMLAzAB6E70wiGH6K0QmSvtkSTR5lkFV\ntnfk+GuV+ksFSx1/yHCW89mNpJlCppLjd+mTzwfaIL36lQK/H8bP5fj99ukH6lTHb1iNmSKpf8/g\nHmxdu9X0WdRSzpctZk0nv9saHaIcv1TqryXHn5Xn+N97x3vxwMEHzL/Ze/WHjBDCRlhq7pv3cr6F\nCv4LkV1cQsbf0uua42fbKrn6w06pPxKKCN2zZo6/OklhE4xCqSCV+gFr4M8Ua5P6+f3x4J3cwOy5\nZexbBa45/pLPHL/A1c9e9wIL6F5Sv4jxA9amLqKSQN7gV7OrX8L4garcX3X2B5X6DWKgJ9GD/aP7\nsaxlGQCgPdaOyeykGuP3sVCPah6cbw7llipRgaxlr4q5T5Tj5x/K9ZD6AXXGr1LOZ+b4fZbyAfWT\n+tl3xxi/Xep/bvA5nLPinErpaG46cAOfsBGGQQwUy0UMzgxiRYs741dq4BMSl/OxZ00gV3/1/hhO\nDePEzAkAMK8/+3cfC8Xkvfrnc3W+hQwL4xe4bkWBP11IWxi/7GEVC8WUc/yMTTCpUVaixRg/zx7Y\nGGXmPqB+jJ89uPyY+2rN8fPmPn7cbRGXwC9x9bPXvcCYgl+pn00G7YY/B+PnDH5eLXszRfkCPcBs\ncBCxyb6u2Vp+JXMfFxh4tWN5y3K8MvaKuVZ7R6wDI+kRhI0wwkZYWsfPxqXM+BUd+nbWWG9zX4iE\nlDr3dcW7XBfI4Y89iDKhEvh5A7JKOZ+Z48/5z/HXvWVvMYfOWKeDqe4Z2lMJ/NFKzwg+DSM6FgbR\n8bN7VEXqV2nZ62ru82D8ZVrGTH7Gct75HP9kbhLjmXEAs88qe9VFLCyOK/Mm9S8GBGL8Re8cP9tW\nVeqfzk9b2IBsZs27+tnfzMAvSDkwxl+vzn1s/6IHmGnuE+T4VQN/b0svBlMVaZrd6JYGPop1/Hxj\nGfZQKdOyp+uZgfXr9+vqt7dzZj/bb1Te4Ocl9QPu/SB4lcgOvnsfXyIpQ4iEQClFqVyyTHqWty5H\niZZmGX+0HSdmTpiTKDe52U8Tn8BSfw2MP0RCKNOypd+/aq9+FamfPT9U0kx2uE20Gfhzr1LOZ+b4\n88Fd/XVbpKckruPfM7QH56481+w+KsvxO3r1CybZTBEJIvXLGH++lHfk6lUY/2R2Em3RNkuFE++B\nmcpNYTxbCfyy60XG+LXU7wNeOX674QOo3FwdsQ5zARcp45fMzOxgK7DxF4tX5z5+rOzBmi/lnVK/\njfGz/c6l1G93Rvtl/CdmTjgmQaJyPs8cv21Z3nQhjUQkoVRWyCYMnq5+W69+Nhm0v2a/URmTByD8\n3hjc6nYZeEOoHbzUr1LHTwgxH6j8sbOAz9Ye74h14MTMCfN7tcvNdjMje6AenTyKnYd2QgbVIF7P\ncj5CCMJGGLlizmwSYy/nS4QrXSL5RY8yxQw6451OqV/i6p/Jz/iW1ust9fOTsCA5flmZsR/w352o\nZW8qn8LxqeM4vfd0s0tk0NX5gNmAOJga9Mf4ZavzGRGMZkbRGm21jMmL8bMV/fjJAv83oPKdjGXG\nKufBlt/nP6cpevUvZARl/C2RFvPhLcsxymZmdiQiCUzlpywP7jCRM/5cMWdJS7gZ0TpjnQiRkHlc\nc2rucynnU5HXAS7wG9bAX6IlB2N1zfELysz8jIPdRF7yrIzx2+V/+43KS/1ern72fhncGD9z9gNq\nUj/bn+kZ4aT+tmib+Xt7rB0DMwOmX4KxTkqpIxDzJqwHDj6Am5+8WfrZfnL89WL8bH/ZUlbawCcS\nisAghoVhshy/m9RvqZvPT/tm/G4KG0Pgcr4Arv4wCUuZsPI+7OV8Nlf/3uG92LhsI8JG2GwW5cfc\nZ79X2PnxkvrZc5RN7krlkrC/RtgIYzA16KgOUmH89vw++1zWQGomP+PJ+OPhuGb8tSJIjp89yJn8\n5yr1Ky7LO5Wbsjy4TcYvcfXz7T8tOX4B47c/iNhxB4EK4+dZk1/G3x3vdigvNZn7uBx/Kq9m7GPH\noprjt5dzAbA08RExfovUX65N6nfL8XfFu8xmOyrlfGx/9utpectyk+0DcsbPfBh8PpbPc6cLaUxk\nJ6SfHUjqr5Hxs/1li7OB317OB8Dh7GdSPx8s6i31B2H8yuV8Aev4+XEFgZfUz/L7AEzGH9TcB1hz\n/G5dO0NGCAYxzE6LUsYfimBwRhD4FXL8osDPPCasZwFj/K5SvyzHr819auCNFaIvTLQsL3uQs/p7\nN6lf1dU/nZu2PLi96vgLJXGOX8T46xn42RhlgT9shE0ziunqL6i7+kNGCD2JHsv4LFK/PccvqeMX\nLR7DSvxUwG4irxpxFcafLqSdjF+xnM+X1C94SPGTI5VyPrafQtnG+FuXm8Y+QJ7jFz14edabLqRN\n85IIgaT+Gsv5gMp1zQd+ezkfAIfBL1vMojXaipARsvQ+4L9rnmHP5Gd8S+uq5Xxmy16POn5Hy94A\nUj8/riBgJchMHbIz/gOjB7CxdyOAynU2lZsK3MAHUJf62T7Z+SnTstTc58X47du5Mv5qDGITdHZ/\nzORnhEQlFnZx9WupXw18fkWW4xe5+hnjZ1K/6Eboind5NosBKg91mblPmuPngiDP0Ozj6G3ptcwa\n55Lxx8Ixh0Tvl/GzMfP7sXTu43P8Pnv1+ykrNMv5FFbn88zxFzKOz+XL+bxc/YCi1C94SPGB36/U\nzz9El7csN/P8gJzxix68fDnfnDH+ekj9xaylgQ8v9QNwGPxYkOWfEW4NfKZzwaV+T8bPSf2qLXsn\nshOmB0gV9WD8hBAz+PPlfEw1mcxNmsHRy9ynwvhj4RjGs+Omn8AN/Pfl7bJEOgAAIABJREFU1sBn\nKDUUiPGPZ8fFjL9UwFRuCiESms3x58U5fhZ77Kin1B8sOiwg1Jrjd5P6737P3a43LAOT+kXmPhnj\n56V+9mAVmcTWd67Hox961HI87LiDwEvqtzP1EvXXwAeo5Pn5C1hazuezjl+1hh8IXs4ndPWLzH3h\nhMXVLwtcSq5+F8bPGyBVA79I6n/r6W/F65a/znwPC/ybVmwCMMs6RasZ2gOjW+BXzfGzwAHU3rIX\ncEr99nI+wBn4WZBhakdbtK0xUn9IXernGf9EdsLSeU4F9Qj8wGzVRK6YQ0ukxfw9EopY+gvw5Xyq\nPVZEjP/Y5DGsbF3puSCRJfC7mPvypTx64uo5fqYgjWfGHeec5finclM4qfMkzxz/zW+9Gaf3nO54\nXUv9PhA4xx+pMn4XqT8RSSitfCWS+mVlM7yrX0XqB4C1HWstx8P2HwRe5j5Rbt6PqQ6oBH77uSiU\nCyjTsmVpTlngL5VLyBVzSIQTzhy/4jjMcj4PNslqqBlbkTH+oOY+FanfLcfPlzyqlPMBYqm/PdaO\nc1eea77HIfWHZ1MjDsbPlSsxxs+3JeXRCFc/UDlme47fi/Gbgd9lkZxaXf1uqTUGvrLEq5yPz/Hb\ne8b7GU89Jlr5Uh5lWjb7QLBj4BcP4hv42Jflla3OZ79XYqEYjk4e9ZT5AZvUX5aX8wEQMv5sMSsM\n/AYxYBADo5lRaY5/MjuJDV0bMJ4ZB6W0EvgjzsB/9oqzhfeINvf5gBfjZzW+fAtW1lCFlfioshQZ\nEpGE09wnucHsq/Ox98jMfXbUnOOvjlF24Yly874Zf2KZYwKRLWYda8nLcvyMYRNCgjN+Vs7nIfUb\nxLA8LLLFLKKhqHkDsn7/QnOfQuc+tl3QOv5YKGamSVTK+dj+CqWC6/XEFuoxpf6QXOrnz0+6kAYF\nNXuw29GIOn62P37xKlGOvyXSYrneWD7fUkcvcvWXCqCU+vKY8NsD7oF/TfsajKZHMZGdQLak7uof\nz447Ssu8UC/GHzbCSOVTiIVjlfuUmzyJGH+t5XxHJ4+61vAz8J4u2SI97DU/rn623Uh6xDXHv7xl\neWU9hEJKmuN3G7vO8SvCq46ftcTlLzAL4y9mapYa4+E4UoWUg+UCThYnq+N3Y/w85jPHz+Q7P+Y+\nwMn4Q0YImULG8d3I6vh5Zh+U8fM5a69AxM+0M4UMuuPds/n7Us4sBeORiCR8NfDxasMKiBk/IQSt\n0VakCinfUr/bsbMHs+U8q+T4ixXGLJP7gzB+tz4IqjBz/FVWaS/nA+BYmpexa/vETyT1pwtpxEIx\nR/c5L6gE/ng4jsvXX44dB3d4t+zl1BeR7OyFugb+Qsr83vjqGAfjl0j9LJXI1CNKqfBaiIVjODZ1\nzD/jl5QtsnHIcvwyE23YCAsDP5/j74h1oDvejfHMuLSOXwZ7hZG94ZQfLKnAL3sw2gM/M/d55fhV\nwW5Ue46ffTYPS46fM3Wxhite45hrV79M6vdt7rPtJ1PMOAKbXer/X/f/LxyZOGJh9kFd/fFQ3GT8\nXoGID/zZYhbdiW7zd5Gj376N28RRydXvwviBWblf2dzHSf2ygMNMUhbGXxRPlOyMH4CZx7RDNYjX\n29wXMSLIlXKe5XxKUj/v6q/mg4PI/EDl3BnE8Pze3nLaW3Dfy/cpt+xlAcrPfQnUx9UPWBk/YF3e\nmmf8buY+QohjUaloKOpIrzLG79ann8Fu7pOV8wHOwM8MwbL7LGyEMZweltbxm4E/0Y2xzJhvT4h9\nifCh1JDytnYsqcAvyvEDzpI+1XI+VbCHukjqd1udz57jV3lo1hr42c2mau4LJPULcvzZYtZxLuyB\n/ycv/AT3vXyfO+P3Ye4zc/x+GH+xwvh5BUB07GxhJqB2qd8txw/Mnic/dfym1C8JqIyRmRMsruGR\nW46fqRxSxq8weQXqX86nKvW7mfv41xjYvRmkeQ/bPh6Oe3qF3nLaW3DfK/d5t+ytqi/M2KfiQeIx\nV4zfIvXzjN+lnI+Nw76MtB0sx68i9TvMfX6lfomrnx3zSHrEobKwHP9UbgqdsU70JHownh33H/ht\nXUTZqpxBsKQCvyrjZw9zrwY+qjDb6Qqkfrc6fkeOX4Gdmn30SfCCDfYwsiMWqk8537IWZ46ffygz\nJMIJ5EuVJXAppRiYGcAjxx6xfB6bhQM+Gb9iOR97r53x8418RGzdXscvC1xho7IIjpLULwnqrOxR\nuY6f7wTpkuMHxIxfJPXzjL830esu9Tcgx+/X3Me8G6rlfEEc/Wx7lcqg03tOR8SI4JkTzyiV8wXJ\n7wP1NfelC2nze+PvIUuO30XqB6zXlmzSw/w0qlI/m8S5rc4HwHH+2OTFK/DLcvyTuUlT6g/K+KOh\nKCazkwBgrnkSBEsq8MuWzXQEfs7c51bHrwr2ULd37gMkOf6yeuc+OxhjD8r4gUo3QFEAdWP8fkwq\nW9duxYfO/5BlPyKpnxBiGq7GMmPIl/J49OijTqk/COMPceV8HkGFl9hYjp//XSb1q+T4AeCTWz/p\nWm/tVscPzJogfUv9bozfR44/akQtdfxr2tdIm/ioyvZMije3qXPnPlYuKAv8+VJlQZ+QEbI88AHr\nfcwCbZDmPQCwonUFvtL/Fc/3EULw5lPfjNHMqFI5X5BSPqD+5j62H77lMx/w3Fr2snHw/gphY5vq\ntREkxy8r5wOCMf7RtNPVz9IVTOrvSfSYOX4/ZlBCCPq6+8y1OTTjdwHLrwD+GD8z9zHGX8uDh12s\n9qDJPpuHbHU+e291N0RD0ZoC//N//LyQLazvXI8rTr7CcgxBGP+qtlX4/Qt+3/w9RMTmPmBWxh6Y\nGcCZy87ERHYCL4+9bAlIrKWq7179PqR+PsfbFe+ySP9Cxq8o9QPA37/5712/Ly/Gz0v9KkoPb+7z\nyvHbJ1iiiZKd8a9pX1Mz47csy1snV3+hXHBt4NMaaTVLI/lz49W1MF/KB2reA1TO3ce2fkzpvW85\n7S0AvJfwLZQKgUr5ALnp2C9CJGQaHoHZe4i9xj6HZ/wiYySf45ddr+w1t3a9DKoNfAA4Jk5Mai/T\nsnAhsLARBgWVlvNZzH0BpH4AOKX7FBwcPwhA5/hdoZLjlzL+SH1y/BEjAgLiaNkLuOT4S4JFehTz\no7UGfplEuLZjLW5+6+wCLIyV+emYJwJfzmcHM669Nv0a1ravxetPej3uP3i/GZAMYpgtVf2U8zHp\n0a/Uz3L8LKjLGL9qy14VeOX4WfWDao7fskiPJAi3RlpBQMSd+0LuLXvdAr/quah7HT+3lDRQzfG7\nmPssgb967CKpmTf3BQn8fnBV31UIG2Glcr7AUn89zX0FztxXDZq8zA/MmvtKZWc5HxuHrKKCgX2G\nX8bvluNnz3/L54RiSBVSCBthoXcibIRhEMNxHfDlfJ3xSo4/iNQPAKd0zQZ+LfW7gM22AHfGzxhd\nqVwym+fUK8dPCEEikhBK/a51/Nx72AIp8xH4VRGU8Yv2IzL3AbP564HpAaxuX43LTroMOw7usHwe\nY2R+ygr5unQ/rv5MIWNx9csYv2rLXhV45V3Z5Ei5jl/QwMcOQgjaY+2OXv2yBj52xi9z9StL/aT+\ndfz8/6JyPnvgZ98rr5DYv2s+xx/E1e8H7bF23Hn9ndjQtUH6HjPHH6CUD5iDOn5m7qteP7yxD5hN\nU7HUih3sWgW8GT/fcloGFcYfNsLCVuyxcAypfEp6j4WNMLriXY5JgdnAh+X4E5VyvloZvw78LnDk\n+D0YP2vXSwipW44fqEi/fur4+XK+aCiKmfwMIoazXlyE+Qr8LE/qt47fDlmOH5iVsV+bfg2r21bj\nsvWXYTw7bpH0GSPz27kvW8z6dvVni1lLjl9WzqfauU8FnlJ/hJP6fdTxex17R6xDqVc/3y0uU8zU\nReq3M/56BCL7/8Icf7UPAd+oR0nqz08Lu7DVG287423uaSEux1+L1F9vxs+kfjvjN4iBRDiBydxk\ncMYfiqE30aukdqnk+E/pPgV/96a/E36O25LnYSMsnGw5yvni3RjLjvnyJDHoHL8i/Lr6WX4fQN0Y\nP+A0xnl27rO17J3JzyiznvkK/IQQGMSQBj9VsO9INGY+x7+mfQ0uWnMRIkbEGvg5xu+rnK/q6ldl\n/GVaRq6UQ1e8yyL1yxbUUOnVrwIvc59F6ldp2ctJ/W6ycW+i1wweXjn+QrnSvS5T8Aj8Psx9dV2d\nr/qANxv4GN6M3xL4Sznhynhs0jMfUr8KLK7+AIyfkQu/jYjscDB+JvXnnCsGtsfaMZ4Zl5fzcZNK\nmZFWReZn++OlftFzPRaO4T1nv0f4OgX1ZPyi10XmPp3jn0M4cvyStqc84ze7qUXqyPhtUr/J+F3q\n+HmmN52bVn74zVfgB2DmHGt5ULBtZea+VCGFgZkBrG5bjUQkgc2rN1sCfFDGL5Ou7WAPLcaQWyIt\nVqlfkuPPFDMolUuONQj8ImSEHM2TeLBzpFrOx4KDV5rj/vffj7OWnwXAm/GbnQDDMbNOWYR8OWCO\nv85Sv6iBT2tUYu4Lz0567N/1fEr9KjBz/JlgOf6wEa75Wcf2Y8nxM6nfxviBirN/PCsO/HwayS3H\nrxz4DVsDHx8mRi+vjSzwW3L8sc7ADXwAYEPXBhyZOIJSuaSlfjfUyvjrYe4DnFK/n8590VAU0/lp\n5THMd+CvReZn+wDENxRjs69Nv4Y17WsAAO888504tftU8z2BGH9IbXU+oNLlL1ecZXz2nL/M1Z8t\nZk1fht9GKnbs+9g+1xy/H6mfN4u6Hfvy1uXmuM0cv6yBT6lgKj9d8S53xq8o9bPV+erVspf/X1TO\nxy8DzQcZtyqIaCiKfDm4q7/eYN/FRC641F+3wJ9POVz9IsbfEeuQSugqUv+Grg24eO3FSuNSkfpl\nMIjhWirtxvizxaxZ9tyT6DGDtt9z3RJpQU+iB0cmj2AqN+VrW8uYAm+5QOA3x8/L1olwAtP5ymIj\ntUpf8XBc7Op36dXf7FI/UOfAL2L81fw1M/cBwI2X32h5TxDGH0TqZ+YuXsZ3kx/rNWkE4GroYoG/\nI9ahbu7zUR4KqDF+ZvLsjnfX3Ku/3uV8dle/qJxveetyDKeHAVirNUypX+TqrzLsmULzSP1MgQgk\n9YcidWX8/Dk0Xf0CqR+AUBVTMfddcfIVljJjN6hI/W6IhWO+A3/EiGA8O462aBsMYqA73o3Xpl8z\nS2b9oq+7D08cfwLLWpbhBE4E2kfDGD8hpJsQ8mtCyH5CyK8IIcIOJoSQw4SQZwkhuwkhT/j9HN+M\nv2hl/BPZibrcCDKpX9XVP5OfaVqpfy4ZP5/jX922Wrh9EMbPm/tUy/lYMOBL9aSMvyr118OY5gXG\nVP207FVtCMUQMSIolUtIF9LiRXrKBTPwd8W73Bv4BOnVX2/GLyjnW9W2CidmKg9SqdTv5uoP0MCn\n3mDfRdByvrmS+llqbTonlvrZNnaoMH4/sLv6/fYr4HsQ2BEJRYSTLdbYhwX6rngXyrQceKJ4Svcp\neOzYY0p9C2RopNR/I4AHKKUbATwI4POS95UB9FNKL6CUbvX7IfYcv4rUzwJZIpKoX+APJ6zmPolT\n25Lj51SB6fz0omX8bKYvy/G/OvUqoqGoNKgHYvzcsrxe3y/P+B1SvwvjzxazNRv7VGDm+P0sy1vN\n8as+SNkqllO5KekiPawipi3aVklz2NZSBwLW8dexnM+tgU9Pogcz+RmHg99L6i+UCk0j9dfawCdi\n1IfxhwxrAx9LHb+E8cty/F4NfPygIYw/FMFYZswM/CEjhM5YZ/DA33UKHnv1MWVfgwiNDPzXAfh+\n9efvA3in5H0ENYzTzvhlLXv59bbZg7wl0oLJ7GRdbgS71O/F+O0te6dz/nL8taYmVBE2wr7XIBft\ng/+fR2u0FQfGDkjZPlAJ4tO56UoOTjFnFw/HMZ2bViqRNBl/VQ3ia/TThbS8c18dpX43+M7xB5D6\ngcpDbzI3KV2khzF+Qgi64l2YzE069hFkWd45aeDD5fjZ3wxiYEXrCgymBn25+uergY8K6tGyt16M\nn+/Vz85hLYxf1izLD2rJ8QPujN8tx58pZtAZmxW1uxPdNTH+Z048o7QokQyNzPGvoJQOAgCl9AQh\nRDZ9oQDuJ4SUANxKKf2ubIfJZFJqovosPosb779ROGOUmfsS4QRShZRrH3VVOBr4+MzxT+enlWfw\nC43xe0n9L42+5JrjjoVjGMuM+aqJZUFMJQjFwjGMZ8fNYMDX6LuV86kqCrWCL+dTdfWn8infATUW\nimEyKwj81Tw338iJyf32pip+pP5sMTu7Bnu9G/gIyvkAYHXbagxMD1gIgKqrvxkCfzQUNZl1kOdW\nvc19bF9M6s8UMzgjeoblvV6B3yvH7wcsbcr25zfPHjTHD8DyWT2JHuXrRRbT/gP/obS9CHMaHQgh\n9wPgpyUElUD+Z4K3U8luLqOUDhBClqMyAdhHKX0kyHiMIwZohCJZSlpe7xzoxNTYFJLpJI6fOI41\n42uQTCaRLWbRj3505buQTCaF+1TFquFVCE2HzP2cmDmBfvRj9+O7sT+y33zfwLEBbM5uxrKhZRjZ\nO4LkUBKTQ5PYlNqEVWSV0jjWja1D5kAGyVRtY1bB5uxmrJxc6RjX4cOHlc9ZKp9CP/qxcti5n9xg\nDn0TfTg7erZ0f+vH1uP4nuPYVt6m/JnjmXFsSm1CxIhIt2HHUD5ehpE2sH9mPzZOb8TTjz2NzdnN\nSCaTSBxPIJPOIDnt3Md2bMfTjz2N8zPn13z9uGE4NYwN4xsQp3HkxnNIZqyfZf8uysfKMHIGzsuc\nh+d2PYdXoq8ofc6lxUsRHYtieO8wkidm9zcxPIHuoW688vQrOHXyVCSTSWwtbMUTjz6B4x3HLfvo\nm+jD4WcOI/dKzvWz6FEKUiB4cOeD2I7t+M1Dv/F1TdnR9lob+tGPJx99ErFwDAPTAzht8jR057vx\n1H89ZU4sLshegN2P78ZkZhJducp9n38tj+h0FBNjE+jKWp8FxyaOYd3YOnTlu3DomUOY3O9UOXjU\ncgwqGJwZxPrx9VhlrMJvHvqN7+2HUkO4IHuB5xi9jmPNyBoYMwbCR8NIJpMovFZAZDqCcqmMfDqP\n5Mzstuy72f34bhyIHrDsZ8XwCgwVhpAcTaJ8qAwjYtR0/uirFEbWwL3334s1pTV44YkXsJfsVd7+\nvMx5ICDCMbzReCMSxxNIjln/NpIeQT/6zXuD7SecC8/pteCGOQ38lNI3yv5GCBkkhKyklA4SQlYB\nEHYjoJQOVP8fJoTcCWArAGHg7+/vx86dOy2vfTn5ZZRpGV/e/mX86X1/imWdy9B/ab/lPb8s/BJG\nwkD/5f148akXkR3Ior+/H/lSHtc8eg02tm1Ef791G7/4SeoniHZE0b+tsp+9w3uR/G0Sd11xl2Um\nmC/l8dCJh3Bl95V4x3nvQP/p/RjfN44dL+3A1cuuVhrHraO3ovuUbvRfUNuYVfCRPR9BYnXCMa5k\nMql8zsYz40g+lkTfmj7HNlP7p7DzxZ3YfOpm6f5uGb0FK3pWYP/EfuXPPD51HO964l1Y27pWug07\nhpeffhkvvfoSVmxcgaHsEK7afhWu/a9r8av+X+GmoZtwxdlXoP8s5z6ue/w6fGHTF/DywMs1Xz9u\nODp5FP/zpf+JzlWdOGPtGejfYv0s+3exZ9ceDIwO4OHhh/HDK3+ozHr+8Lk/RKaYwcc2fwz9G2b3\nN/niJO7bfR+uOPMKTGAC/f39+Otjf40Vm1ag/1TrWD6292P4s4v/DJtWbHL9rKcfexqjU6PYetlW\n7Hp8F/r7+31dU3bcW7gXyeNJ3HPFPWiNtuLZE8/ia8e/hn2Zffh5/8/NwP+D6R8AqwGaoUCu8kw5\ntPsQnj/yPJb1LjNfY9j16i58e/jbODJ5BN/Z9h2salvlOo5ajkEFL468iPfvfj/Wdsivay+87U1v\n81TxvI7jltFb8Njhx3Dp6Zei//Wz53AkPYI3nf8m9G+c3faZx59B8kgSP7v8Z+ht6bXs5/ap29Gy\ntgX9W/pxR/oOrOpdhf6Lgx0XAOx9ci+ODR1D15ldyO7JYvv27b62/9zLnwOlVHjs/RCP6+Wxl5F8\nMolTTzrV3O47w9+BQQyl74hSKycu0zISf53ArW+7FR+84IO+xs/QyBz/3QA+WP35AwDusr+BENJC\nCGmr/twK4E0AnvfzIao5fpHUz/K/9ZC++rr6sLZjrfm7n859TEpVlTu3b9iOs1ecXfOYVVAXcx9r\n4COq46/6B7xy/OPZcV/j4BcP8YI9x8+uoWK56Jp3jIfjmMzVxyPiBt7Vr5rjNxvu+JH6w2Kpn8mx\nDqlf0MRHtcqBNdipV6pE1MCnUCo4mnqtbluNEzMnhIv0LASpn/ktguT3GWq9nwHO1W+v45c08AHE\nJdPMjwLU19y3f2Q/ehO93hvYYO/AqgL2XLPk+OPBc/wGMbCha8OCzfF/HcBPCCEfAnAEwLsBgBCy\nGsB3KaVvQyVNcCchhKIy1tsppb/28yH2On6Vcj524bP14Ovx4PnsZZ91jAtwBjuDGCjRygPPPjlQ\nHceHt3y41uEqY87r+Ks3B2veI0IsVM3x+zAZsgeIyoPE7urnX5Mt0gNUPCKT2cmajWleYK5+Pw18\n/Cz6xMBWJxOW85UKFb9DuBr4Y+ImPqrmvq54F54+8bTFIFYLRDn+bDGLsBG2mDtXta3Cs4PPoj3a\njuWtywFY2xXbF29hOfVsMVuXgFkr2PcZxNFfT5gNfGyr84nKHt1c/bJS66CIhioLnu0f3e9QF1QQ\nC8UcDNwL7LjsOX5mEA6Cv33D3+LSdZcG3r5hgZ9SOgbgDYLXBwC8rfrzIQDn1/I5DsYvaeDDDB92\nBpcIJ+aEsUVC4p7YrGwqlU85uvvNdQAJgrl29bPAz5r3iBALx3Bs6pg/cx+3apgX7HX87LVMIeO6\nTkEiksBUbmrOGX80FEWZlpEupJXr+FOFlO+OgnxNtn1/dnNfd0LcxEfV3Pe+c96H2/fcjk/+8pN1\nue555z4w6zq3fzer21fjvlfuQ6Qj4ijnk7n6mdqksoDWXMNcSz5ADX89ESaVzosWxh+gjp8pGECd\nGf/ofryxRZqJliIWjpnxRBXsO+ED/+tPer25LkQQXHfmdYG3BZZYy163On62LK99Vlkvxi8al6x5\nBJuI2Bl/swb+uXb1A/Vn/IzpKbn6Q86udayJj8zVD8yf1E8IQWukVbrCmR1s7Qe/D1HZZMlezgdA\n2sTHTznfj3/3x3hx5MW6Mf4QCZkTnRAJIVPMOL4b1sRHKvULGviMZcaaQuYHZu+hWqT+eoARGr6c\nT1bHzwLifDbwCSr1u5XzySBi/G/f+HZcf/b1vj+/XlhSgV8lx29ncInIHDF+IyJlZzwjY+8F1PLR\n8416BH6DGCAgwvPBWLxrjj9AOR8hBLFQzJfUz5d4+ZH65zrwA5UJ0kR2Qlnqn86rL/rEoML42bmQ\n9ev309egK96Fe953D/7Hlv/ha5wihI2w5dywBjOiwM/K+VSW5WULsDRD1z5gliQ0OvCzc8038JHW\n8bu07GUNiYD6Bf50IY2D4wcdaRsVuJXzyWDm+OtQFl4vLKnAL2P8sXBMmkeaK8bfk+jB7e+6Xfi3\nhSb11yO3GTJCQsbfGevE9Zuud135LAjjByrfux+p357jzxQzrua+RCQxL4wfmA38Ki1I/a79wMDL\ntjxYjt8i9ce7MZGzBn5Kqe/eAaf1nIZPXfopX+MUIRKyLq7CnguiwD+YGnTW8bs08AHQPIy/+sxo\nhhw/YJ0sZgoZZIoZx33aHm23qDE8mBEVqF/gPzB2AKvaVvlu3gNU7gG/24kYf6OxpAK/W45f1LIX\nmLscPyEE79j4DuHfZFL/fAQQvwgZobq5gEU3VCQUwY9+90eu27IGO34Dfzwc9+fqtzV38mL8TOqf\nD6XGF+MPRXyt/cDgJ8cvkvqL5WJd1noPAgfjr7JL+z0VD8fREmnBwPSAsGWvyNUPNFHgN5okx29n\n/KEYRjOjaI20OgJ8e6xdet3OhdR/cPwgNi7bGGj7IFK/KMffaCz6wB8JRVCk/lz9/M09V4zfDdFQ\n1NJH2mT8i1TqZ/vxu2AGQywUQ5mWfUn9bDtf5j6O8YkMf3aYUr8x99dPa7RVOfCzFtBBGb99O5bj\n5ytiRFJ/PXruB4V9OVVZy2ygklY6NHFISepn27spUvOJkBEyV4BrJOyMPxaOYSQ9Ipwgdce78Ymt\nnxDuhzf3ydbF8AP2fW3sDRj4A0j9bJKpA/88opY6fmDucvxu4Ov3+f+bUervTfTWVE/KIGP8KmAP\nlyCM3285H5/jTxfSQsMXv918uPqBCuMs07KvHH8Qc59obQOZq99exz8f6xbIEDbCFqWB/SwaDzP4\nicx9onUKgOZh/EDlmJpF6udb9qYLaeEEKWSE8I03fUO4n7lg/EANgT8A4yeEIGyELXX8jUYj6/jn\nBX5X57Ob+xrF+AFnk59mZPxeMrwq7FKsH7AJkW/Gr5jjZ73aecbPVm5kZZkiJMLzm+MHxL0Q7IiE\nIr6b9wCV8yB68Ipy/Gvb1+LVqVctvQXqsdhOUNivL1fGXy0dZRM6toiXaAlmxrDbIs0T+CNGpCml\nfgC+TZBz0cAHAM7oPQMIUE0XhPEDFU9XoydjPJYE42cXjlKO35azTYQT8/6wsjP+Zjb31QshIjb3\nqaAWxu8nx8+z+3g4jvGMe7fARGT+XP3s2FWlfsD/RFJWBcFWhOMDf3usHes712Pv8Gwf9IZK/TZz\nnyzHDwCrWittd3mpX7YsL9tHs0j9QGU8zSj1A/5TItFQFPnyHDD+WnL8xH/gP/CJA76JyVxiSQR+\nlc59Zh1/oTly/G7/L0bUJPVXJ0R+vQa+y/kK1hz/eHbcNec4X3X8wCzjV5X6Af8TSRnj51v28udj\ny+ot+O1rvzV/XyiMn/XbV5H62T6aSeq/9oxrXftezAfsjJ+dN7/CHSs/AAAPVUlEQVSMfy7K+RLh\nBNZ1rAu0fVDG30z5fWCJBX5Zjr830YuXx17GVG7KYlAC5s7V74aFJPXXCzWZ+8JzK/VHjEqtdqqQ\nMgNbIpzAWGbMtYVoIpyoW8tZL/gK/NV7IEiOX3QsrOTKfu9sWb0Fvx2YDfz1WF43KFgDHwa3HD+T\n+u3mPpm5rNkC//ff+f2GKxDsXLPvO6gJMmJUKlAopXUJ/Os71+O2624L3GWxJ9HTdEE8CHSOH8A5\nK8/Btadfi4/f+3FHHq891o4yLc/beIHZm8Te0W4xS/31YPxzJfUTQirsPTvpkPq9GD8wP0oNO3bV\nOn4ggNQvy/Ebzhw/AGxZswU/fuHH5u/1WnAnCOyufvbgd2P87Ls1W/YWnHX87O/N0sCnWWBn/Gyx\nM7/n6eJ1F+Mz938GNz5wI0IkVHMpaNgI19Qx74Pnf3De48FcYEkFflmOHwC++eZvYsutWzCYGrQ8\nzP/k4j8Bhb9FGWpFNBRFxIiY9a7MFbqYGb+sgY8KAjN+xXI+oBLEJ7ITFqn/yOQRd8bPmcPmGvMi\n9UtSIyGj0nxlOjdtCfwXrLoAe4b2mAa/ZpL62Wuycj5gduLGDHwz+ZkFIfU3A+w5fqBy/fgN/Os6\n1uGJP3wC7/rJu2pm+/WAQYymWJOhViz8I/CASo4fqASNH/7OD7GydaXl4dUZ75x3N6aoO1Q0FF30\njL9mV/8clfMBs02CeKnfi/HzjHGu4SfwBzWLyhg/2+dkbtJy79gNfo0094murxAJuTJ+S9AKx1Ao\nF6SKhw78VtgZP1A5h0FSEMtbl2PHDTvw8/f+vG7jW+pYUoFfluNnuGD1BTj+6eOBJed6gTF++2va\n3CdGUMbfGmlVNgQyqZ9n/GOZMdft51Xqj6q7+s2+EAFc/bLJQsSIoEzLDgVky+oteOq1pwBUc/wN\nmrxGQhGHTCxj/D2JHnzjjd+wnEvWw0AkNTebq78ZEDbCICCWcxgPxwOnRKKhKK7ccGW9hrfksegD\nPzNmAfIcP49GtBO1IxqKOoJgxIgsaqm/1s59gH/G/5XtX8F7z3mv0nvj4TgoqCXH72nuq/5tPoKd\nrzp+I6C5z4Pxx0IxhwzKO/tzxcbl+GOhmOOzQ0ZI2FWREILPvP4zlteioajrsWvGbwVLTfLteWOh\nYIxfo/5Y9IF/Xcc6HBw/iGOTx1xz/M0EEbtfClL/fDP+lW0rlR/YPNMHKkFdpZwPWDxSf0esQ+po\njoQiQvXjwjUXms7+Rkr9W9duxb+/898tr8kYvwixcEw6yfuna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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1071ac358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# graphique 1: les données et la droite de régression\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(x, y, \"bo\", label=\"data\")\n",
    "plt.plot(x, p0*x**2 + p1*x + p2, \"r-\", label=\"parabolle\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"Regression linéaire avec résidus\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "# graphique 2: les résidus\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(x, y - (p0*x**2 + p1*x + p2), \"g-\", label=\"residus\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Résidus\")\n",
    "plt.legend(loc=\"upper center\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cette fois, les résidus sont bien répartis aléatoirement autour de l'origine. Calculons le coefficient de détermination selon\n",
    "\\begin{equation}\n",
    "    R^2 = \\frac{\\sum_k (y^{calc}_k - \\overline{y})^2}{\\sum_k (y_k - \\overline{y})^2}\n",
    "\\end{equation}\n",
    "où les $y_k$ sont les données, les $y^{calc}$ sont ceux calculés avec le polynômes et $\\overline{y}$ est la moyenne des valeurs $y_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.995605211387\n"
     ]
    }
   ],
   "source": [
    "R2 = ((p0*x**2 + p1*x + p2 - y.mean())**2).sum() / ((y - y.mean())**2).sum()\n",
    "print(R2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme attendu le coefficient de détermination est meilleur que celui obtenu pour la droite (0.9916). Pour information, la fonction utilisée pour produire les données du fichier ``regLinData.dat`` est :\n",
    "\\begin{equation}\n",
    "    f(x) = 0.08 x^2 + 2x + 3 + \\hat{g}(X)\n",
    "\\end{equation}\n",
    "où $\\hat{g}(X)$ est un bruit gaussien obtenu par le tirage de nombres aléatoires dans une distribution gaussienne centrée en zéro et de largeur 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Ce TP est terminé. D'un point de vue théorique il permet de découvrir ou réviser la regression linéaire. D'un point de vue pratique, il vous a permis de mettre en pratique la syntaxe du langage python et d'utiliser des modules tels que ``numpy``, ``scipy`` ou ``matplotlib``."
   ]
  }
 ],
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