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{ "cells": [ { "cell_type": "markdown", "id": "042acd49", "metadata": {}, "source": [ "# Test a minimizer" ] }, { "cell_type": "code", "execution_count": null, "id": "cb51a492", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import minimize\n", "plt.style.use(\"ggplot\")\n", "from matplotlib import colors, cm" ] }, { "cell_type": "markdown", "id": "2ac3651a", "metadata": {}, "source": [ "plt.rcParams controls the appearance of your plots globally,\n", "affecting all subsequent plots created in your session." ] }, { "cell_type": "code", "execution_count": null, "id": "97ef9933", "metadata": {}, "outputs": [], "source": [ "plt.rcParams[\"axes.grid\"] = False\n", "plt.rcParams.update({'font.size': 20})\n", "plt.rcParams.update({'figure.figsize': (12,9)})\n", "plt.rcParams['lines.markersize'] = 8" ] }, { "cell_type": "code", "execution_count": null, "id": "f15200f9", "metadata": {}, "outputs": [], "source": [ "# Generate data points with gaussian smearing\n", "data = np.random.uniform(size=100)\n", "labels = 5.*data*data*data + 1 + np.random.normal(loc=0.0, scale=0.1, size=100)" ] }, { "cell_type": "code", "execution_count": null, "id": "7237f5ed", "metadata": {}, "outputs": [], "source": [ "# show plot\n", "plt.scatter(data, labels, label=\"data\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "0d6e104c", "metadata": {}, "outputs": [], "source": [ "# define chi2 like cost function\n", "def cost(params):\n", " W, b = params\n", " return np.mean((labels - (W*data*data*data + b))**2)" ] }, { "cell_type": "markdown", "id": "8e00e16a", "metadata": {}, "source": [ "call minimizer\n", "provides a collection of optimization algorithms for finding the minimum or maximum of a given function. " ] }, { "cell_type": "code", "execution_count": null, "id": "433975c3", "metadata": {}, "outputs": [], "source": [ "res = minimize(cost, [1., 1.])\n", "# returns an OptimizeResult object\n", "# x :the solution (minimum) of the optimization problem, represented as an\n", "# array.\n", "# Results of the minimization\n", "W, b = res.x\n", "print ('function value at the minimum and fitted parameters',res.fun,' ',W,' ',b)" ] }, { "cell_type": "code", "execution_count": null, "id": "1e1f4e81", "metadata": {}, "outputs": [], "source": [ "points = np.linspace(0, 1, 100)\n", "prediction = W*points*points*points + b" ] }, { "cell_type": "code", "execution_count": null, "id": "d8de971e", "metadata": {}, "outputs": [], "source": [ "# plot fit model\n", "plt.scatter(data, labels, label=\"data\")\n", "plt.plot(points, prediction, label=\"model\", color=\"green\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "4a7d62c2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 5}
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