{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TP1: Evaluation De Perfermance\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Réalisé Par : Intissar Sidaoui Et Rania BenSalah" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Groupe 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On Commence par:\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import random\n", "import matplotlib.pyplot as plt " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comment calculer la moyenne\n", "=> Voila " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def Xn(t,n):\n", " x=0\n", " for j in t :\n", " x=x+j\n", " return x/n " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comment calculer la convergence\n", "=> Voila" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def On(t,n,xn):\n", " tita = 0\n", " for i in t :\n", " tita=tita+(i-xn)**2\n", " return tita/n " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comment Crée un table de n variable uniforme\n", "=> Voila" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def creat_alea_table(n):\n", " t=[]\n", " for i in range(n+1):\n", " t.append(random.uniform(0, 1))\n", " return t " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# On passe maintenant à resoudre et exécuter les exemples:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exemple n°1:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "les valeur aleatoire 1000 leur moyenne0.5020069986063366 et leur variance 0.08636524097756378\n", "les valeur aleatoire 10000 leur moyenne0.5011334872206992 et leur variance 0.08363417782574396\n", "les valeur aleatoire 100000 leur moyenne0.49958061880102583 et leur variance 0.08380244584709111\n", "les valeur aleatoire 1000000 leur moyenne0.499996466232293 et leur variance 0.08332147014692759\n" ] } ], "source": [ "n=[1000,10000,100000,1000000]\n", "titatable=[]\n", "xn=[]\n", "for i in n :\n", " t=creat_alea_table(i)\n", " xn.append(Xn(t,i))\n", " titatable.append(On(t,i,Xn(t,i)))\n", " \n", "plt.plot(n,titatable, 'r*')\n", "plt.plot(n,xn, 'b*')\n", "plt.show()\n", "for i in range(len(n)):\n", " print ('les valeur aleatoire {} leur moyenne{} et leur variance {}'.format(n[i],xn[i],titatable[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Remarque:\n", " le nombre de variable ne sont pas inclus dans la moyenne ou dans la variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exemple n°2:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def creat_alea_table(n,lamda):\n", " t=np.random.exponential(1/lamda,n)\n", " return t " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "49.999646623229296\n" ] } ], "source": [ "print(Xn(t,10000))\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":13: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n", " plt.subplot(2,2,1)\n", ":15: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n", " plt.subplot(2,2,2)\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xn=[[]]*4 \n", "titatable=[[]]*4 \n", "from ipykernel import kernelapp as app\n", "lamda=[10,100,1000,10000]\n", "\n", "\n", "for i in range(4):\n", " for j in range(4):\n", " t=creat_alea_table(n[i],lamda[j])\n", " x=Xn(t,n[i])\n", " xn[i].append([x])\n", " titatable[i].append([On(t,n[i],x)])\n", " plt.subplot(2,2,1)\n", " plt.plot(lamda[j],titatable[i][j],'ro')\n", " plt.subplot(2,2,2)\n", " plt.plot(lamda[j],x,'bo')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Remarque" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans la distribution discrete on observe que la valeur de lamda inclu dans la calcule de moyenne et de variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exemple n°3:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5 3 3 4 3]\n" ] } ], "source": [ "def creat_alea_table(n):\n", " return np.random.randint(0,n+1,n)\n", "print(creat_alea_table(5))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":4: RuntimeWarning: overflow encountered in long_scalars\n", " x=x+j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "les valeur 1000 leur moyenne 492.613 leur variance 86556.01523099998\n", "les valeur 10000 leur moyenne 5002.6861 leur variance 8168267.898366751\n", "les valeur 100000 leur moyenne 6982.87175 leur variance 2678233164.182701\n", "les valeur 1000000 leur moyenne -2142.779629 leur variance 335902710489.4809\n" ] }, { "data": { "image/png": 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l+gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.style.use('seaborn-deep')\n", "xn=[]\n", "tita=[]\n", "for i in n:\n", " t=creat_alea_table(i)\n", " x=Xn(t,i)\n", " xn.append(x)\n", " tita.append(On(t,i,x))\n", "plt.subplot(2,2,1)\n", "plt.plot(n,tita,'r*')\n", "plt.subplot(2,2,2)\n", "plt.plot(n,xn,'b*')\n", "for i in range(len(n)):\n", " print('les valeur {} leur moyenne {} leur variance {}'.format(n[i],xn[i],tita[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Remarque" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans la distribution discrete uniforme on observe que la plupart de moyenne implique plus dans les deux valeur moyenne et variance\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exemple n°4:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def creat_tabe(n):\n", " x=[]\n", " t=np.random.uniform(0, 1,n)\n", " for i in t:\n", " if i<0.3:\n", " x.append(0)\n", " elif i<0.5:\n", " x.append(2)\n", " else:\n", " x.append(6)\n", " return x" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "valeur aleatoire1000 leur moyenne 3.284 leur variance 7.351344000000038\n", "valeur aleatoire10000 leur moyenne 3.4 leur variance 7.225599999999773\n", "valeur aleatoire100000 leur moyenne 3.40084 leur variance 7.241007294405245\n", "valeur aleatoire1000000 leur moyenne 3.402022 leur variance 7.236650311469096\n" ] } ], "source": [ "xn=[] \n", "tita=[]\n", "for i in n:\n", " t=creat_tabe(i)\n", " x=Xn(t,i)\n", " xn.append(x)\n", " tita.append(On(t,i,x))\n", "for i in range (len(n)):\n", " print ('valeur aleatoire{} leur moyenne {} leur variance {}'.format ( n[i],xn[i],tita[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Remarque" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On observe que si on augmente la valeur aleatoire (de 1000 à 1000000) à chaque fois la moyenne presque le meme ( petit augmentation apres le vergule) et aussi la variance aussi pas de grand changement presque le meme( petit diminution apres le vergule)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }