{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Spline Approximation\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demapp09.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisSpline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return 50 - np.cos(x**2 / 8) * (x - np.pi + .5)**2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "xmin, xmax = 0.0, 1.5*np.pi\n", "off = 0.05\n", "xlims = [xmin - off, xmax + off]\n", "n = 401\n", "x = np.linspace(xmin, xmax, n)\n", "y = f(x)\n", "ymin, ymax = y.min(), y.max()\n", "ywid = ymax - ymin\n", "ylims = [ymin - 0.5*ywid, ymax + 0.1*ywid]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figs = []\n", "for nnode in 3, 5, 9:\n", " F = BasisSpline(nnode, xmin, xmax, k=1, f=f)\n", " xnodes = F.nodes[0]\n", "\n", " xx = np.r_[x, xnodes]\n", " xx.sort()\n", "\n", " fig, ax= plt.subplots(figsize=[10,5])\n", " ax.set(title = f'Linear Spline with {nnode} nodes',\n", " #xlabel='', ylabel='', \n", " xlim=xlims, ylim=ylims)\n", " \n", " ax.plot(xx, f(xx), lw=3) # true function\n", " ax.plot(xx, F(xx), 'r', lw=1) # approximation\n", " ax.set(yticks=ylims, yticklabels=['', ''])\n", " xe = ['$x_{%d}$' % k for k in range(nnode)]\n", " xe[0], xe[-1] = '$x_0=a$', '$x_{%d}=b$' % (nnode-1)\n", " ax.set_xticks(xnodes)\n", " ax.set_xticklabels(xe, fontsize=18)\n", " for i, xi in enumerate(xnodes):\n", " ax.vlines(xi, ylims[0], F(xi), 'gray','--')\n", " \n", " figs.append(fig) " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "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": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }