{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Least squares of an arbitrary function\n", "\n", "Find more tutorials on my webpage: [yairmau.com](http://yairmau.com).\n", "\n", "End product:\n", "
\n", " \"least\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## import stuff" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.patches as patches\n", "import numpy as np\n", "import scipy.special\n", "from scipy.optimize import curve_fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## customize figure" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "plt.ioff()\n", "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10,10));\n", "fig.subplots_adjust(left=0.04, right=0.98, top=0.93, bottom=0.15,\n", " hspace=0.05, wspace=0.02)\n", "\n", "# configure axes and some function definitions\n", "x = np.arange(0, 12, 0.4)\n", "ax1.set_aspect('equal')\n", "ax2.set_aspect('equal')\n", "ax1.set_xlim((x.min(), x.max()))\n", "ax2.set_xlim((x.min(), x.max()))\n", "ax1.set_ylim(-1, 3.5)\n", "ax2.set_ylim(-1, 3.5)\n", "plt.rcParams.update({'text.usetex':True,\n", " 'font.size': 22, # more customizing https://matplotlib.org/users/customizing.html\n", " 'xtick.labelsize':16,\n", " 'ytick.labelsize':16,\n", " 'axes.labelsize':26,\n", " 'font.family':'serif',\n", " 'text.latex.preamble':[r'\\usepackage{amsmath}']})\n", "plt.rcParams.update()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## define some functions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def func(x, par0, par1, par2):\n", " \"\"\" Cosine function with 3 parameters \"\"\"\n", " return par0 + np.cos(par1 * x + par2)\n", "\n", "def add_rec(ax, c, v, col):\n", " \"\"\" Add rectangles to the figure \"\"\"\n", " ax.add_patch(\n", " patches.Rectangle(\n", " c, # (x,y)\n", " np.abs(v), # width\n", " v, # height\n", " alpha=0.4,\n", " color=col\n", " )\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Now let's plot\n", "\n", "[I don't know why, but running this for the first time raises an error. If I run all the cells a second time, then everything runs smoothly...]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "par = (1, 2, 1) # the parameter values\n", "# generating data with noise\n", "y = func(x, *par) + (np.random.random(len(x)) - 0.5)\n", "ax1.plot(x, y, marker='o', ls='None', markerfacecolor=\"blue\")\n", "ax2.plot(x, y, marker='o', ls='None', markerfacecolor=\"red\")\n", "\n", "# best fit\n", "popt, pcov = curve_fit(func, x, y, p0=(1.5, 1.5, 2.5)) # p0 = initial guess\n", "p0, p1, p2 = popt\n", "# The total sum of squares (proportional to the variance of the data)\n", "SStot = ((y - y.mean()) ** 2).sum()\n", "# The sum of squares of residuals\n", "SSres = ((y - func(x, p0, p1, p2)) ** 2).sum()\n", "Rsquared = 1 - SSres / SStot\n", "# plot best fit\n", "h = np.linspace(x.min(), x.max(), 1001)\n", "fit, = ax1.plot(h, func(h, p0, p1, p2), color='black', linewidth=2)\n", "ax1.legend([fit], [\"Best fit\"], loc=\"upper right\",\n", " frameon=False, handlelength=4)\n", "# plot mean\n", "mean, = ax2.plot(h, h * 0 + np.mean(y), ls='--', color='black', linewidth=2)\n", "ax2.legend([mean], [\"Mean\"], loc=\"upper right\", frameon=False, handlelength=4)\n", "\n", "# plot blue and red squares\n", "for ind in np.arange(len(x)):\n", " x0 = x[ind]\n", " y0 = y[ind]\n", " # print(x0,y0)\n", " v1 = y0 - func(x0, p0, p1, p2)\n", " v2 = y0 - y.mean()\n", " add_rec(ax1, (x0, y0), -v1, \"blue\")\n", " add_rec(ax2, (x0, y0), -v2, \"red\")\n", "\n", "ax2.text(0.5, 2.7, r\"Total sum of squares: {:.1f}\".format(SStot))\n", "ax1.text(0.5, 2.7, r\"Sum of squares of residuals: {:.1f}\".format(SSres))\n", "ax2.set_xlabel(r\"R-squared = $1 - \\frac{\\text{blue area}}{\\text{red area}}$ = \" +\n", " \"{:.2f}\".format(Rsquared), labelpad=25)\n", "ax1.set_xlabel(r\"Data: $f(x) = p_0 + \\cos(p_1 x + p_2)+ $ noise \")\n", "ax1.xaxis.set_label_position(\"top\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Save and display" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.savefig(\"figures/least-squares.png\",dpi=300)\n", "display(fig)" ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }