{ "cells": [ { "cell_type": "markdown", "id": "029e46ba", "metadata": {}, "source": [ "# Corrélation\n", "On simule une jeu de données à l'aide du code suivant : " ] }, { "cell_type": "code", "execution_count": 1, "id": "b433007b", "metadata": { "tags": [ "keep" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(0) # pour que le générateur \"aléatoire\" soit \n", " # le même pour tout le monde\n", "N = 100\n", "x = np.linspace(2000, 2018, N)\n", "y = np.arange(N)*0.2 + 45 + np.random.normal(size=N)\n", "\n", "plt.plot(x, y, 'o');" ] }, { "cell_type": "markdown", "id": "aa58f021", "metadata": {}, "source": [ "1. Tracez et ajustez les données par une une droite $y=ax+b$.\n", "\n", "2. Quel est l’incertitude sur $b$? Qu’en pensez-vous ?\n", "\n", "3. Calculez la valeur et l’incertitude de votre fit en $x= 2010$.\n", "\n", "4. Réalisez $M$ simulations ($M$ = 1000 par exemples); tracez sur un graph les coefficients a et b; Calculez la matrice de covariance.\n", "\n", "5. Trouvez une fonction de fit plus pertinente pour ce problème." ] }, { "cell_type": "markdown", "id": "f6f461ff", "metadata": { "tags": [ "sol" ] }, "source": [ "-------------------------------\n", "\n", "## Solution" ] }, { "cell_type": "code", "execution_count": 2, "id": "542aa1d7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.08348182e+00 -2.12175517e+03]\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Question 1\n", "from scipy.optimize import curve_fit\n", "\n", "def fit_function(x, a, b):\n", " return a*x + b\n", "\n", "p_opt, cov_mat = curve_fit(fit_function, x, y)\n", "a, b = p_opt\n", "print(p_opt)\n", "plt.plot(x,fit_function(x,*p_opt))\n", "plt.plot(x,y,\"o\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "b06fe309", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Incertitude sur b : 38.8\n" ] } ], "source": [ "# Question 2\n", "\n", "sigma = np.sqrt(np.diag(cov_mat))\n", "\n", "sigma_a = sigma[0]\n", "sigma_b = sigma[1]\n", "\n", "print(f'Incertitude sur b : {sigma_b:.1f}')\n", "# L'incertitude sur b est beaucoup plus importante que l'incertitude\n", "# sur chaque point" ] }, { "cell_type": "code", "execution_count": 4, "id": "08ead99b", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Valeur en 2010 56.04328983428377\n", "Incertitude sans correlations 54.92410215981484\n" ] } ], "source": [ "# Question 3\n", "x_test = 2010\n", "\n", "print('Valeur en 2010 ', a*x_test + b)\n", "\n", "sigma_y = np.sqrt(x_test**2 * sigma_a**2 + sigma_b**2)\n", "print('Incertitude sans correlations', sigma_y)" ] }, { "cell_type": "markdown", "id": "cb8f72f3", "metadata": { "tags": [ "sol" ] }, "source": [ "Les variables $a$ et $b$ ne sont pas indépendante. La variance de $ax + b$ est donnée par $x^2\\mathrm{Var}(a) + \\mathrm{Var}(b) + 2x\\mathrm{Covar}(a, b)$" ] }, { "cell_type": "code", "execution_count": 5, "id": "a174eb17", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Incertitude avec correlations 0.103\n" ] } ], "source": [ "sigma_y = np.sqrt(x_test**2 * sigma_a**2 + sigma_b**2 + 2*x_test*cov_mat[1, 0])\n", "print(f'Incertitude avec correlations {sigma_y:.3f}')" ] }, { "cell_type": "markdown", "id": "5e71aed3", "metadata": { "tags": [ "sol" ] }, "source": [ "Il est donc important de tenir compte des correlations obtenu par le fit pour calculer exactement l'incertitude sur une valeur du fit." ] }, { "cell_type": "code", "execution_count": 6, "id": "c1f966fc", "metadata": {}, "outputs": [], "source": [ "# Question 4\n", "def one_simulation():\n", " N = 100\n", " x = np.linspace(2000, 2018, N)\n", " y = np.arange(N)*0.2 + 45 + np.random.normal(size=N)\n", " p_opt, cor_mat = curve_fit(fit_function, x, y)\n", " return p_opt\n", "\n", "M = 1000\n", "many_results = np.array([one_simulation() for _ in range(M)])\n", "Ta, Tb = many_results.T" ] }, { "cell_type": "code", "execution_count": 7, "id": "1f62bb99", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'b')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.scatter(Ta, Tb, s=1)\n", "ax.set_xlabel('a')\n", "ax.set_ylabel('b')" ] }, { "cell_type": "code", "execution_count": 8, "id": "3b1d5b0e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 3.47366872e-04 -6.97875508e-01]\n", " [-6.97875508e-01 1.40207350e+03]]\n" ] } ], "source": [ "cov_numerique = np.cov(many_results.T)\n", "print(cov_numerique)" ] }, { "cell_type": "code", "execution_count": 9, "id": "b8b088e6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 3.73523915e-04, -7.50409536e-01],\n", " [-7.50409536e-01, 1.50758303e+03]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov_mat" ] }, { "cell_type": "code", "execution_count": 10, "id": "51adbf46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Valeur en 2010 56.04328985689939\n", "Incertitude sans correlations 0.2790998350851877\n", "Incertitude avec correlations 0.10325894775854749\n" ] } ], "source": [ "# Fonction de fit plus pretinente\n", "# Le parametre $b$ correspond au fit en l'an 2000\n", "def fit_function(x, a, b):\n", " return a*(x-2000) + b\n", "\n", "p_opt, cor_mat = curve_fit(fit_function, x, y)\n", "a, b = p_opt\n", "\n", "sigma = np.sqrt(np.diag(cor_mat))\n", "sigma_a = sigma[0]\n", "sigma_b = sigma[1]\n", "\n", "x_test = 10\n", "\n", "print('Valeur en 2010 ', a*x_test + b)\n", "\n", "sigma_y = np.sqrt(x_test**2 * sigma_a**2 + sigma_b**2)\n", "print('Incertitude sans correlations', sigma_y)\n", "\n", "sigma_y = np.sqrt(x_test**2 * sigma_a**2 + sigma_b**2 + 2*x_test*cor_mat[1, 0])\n", "print('Incertitude avec correlations', sigma_y)" ] }, { "cell_type": "code", "execution_count": null, "id": "ef50918e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "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": "3.8.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }