{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chebychev and cubic spline derivative approximation errors\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: **demapp06.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-23\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, BasisSpline, nodeunif\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Function to be approximated" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "f = lambda x: np.exp(-x)\n", "df = lambda x: -np.exp(-x)\n", "d2f = lambda x: np.exp(-x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set degree of approximation and endpoints of approximation interval" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a = -1 # left endpoint\n", "b = 1 # right endpoint\n", "n = 10 # order of interpolatioin" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct refined uniform grid for error ploting" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(a,b, 1001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct Chebychev interpolant" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "C = BasisChebyshev(n, a, b, f=f) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct cubic spline interpolant" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "S = BasisSpline(n, a, b, f=f) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot function approximation error" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = f(x)\n", "\n", "fig1, axs = plt.subplots(2,1,sharex=True)\n", "fig1.suptitle('Function Approximation Error') \n", "\n", "(pd.DataFrame({\n", " 'Chebychev': y - C(x),\n", " 'Cubic Spline': y - S(x)},\n", " index=x)\n", " .plot(subplots=True, ax=axs)\n", "); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot first derivative approximation error" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dy = df(x)\n", "\n", "fig1, axs = plt.subplots(2,1,sharex=True)\n", "fig1.suptitle('First Derivative Approximation Error') \n", "\n", "(pd.DataFrame({\n", " 'Chebychev': dy - C(x, 1),\n", " 'Cubic Spline': dy - S(x, 1)},\n", " index=x)\n", " .plot(subplots=True, ax=axs)\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot second derivative approximation error" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d2y = d2f(x)\n", "\n", "fig1, axs = plt.subplots(2,1,sharex=True)\n", "fig1.suptitle('Second Derivative Approximation Error') \n", "\n", "(pd.DataFrame({\n", " 'Chebychev': d2y - C(x, 2),\n", " 'Cubic Spline': d2y - S(x, 2)},\n", " index=x)\n", " .plot(subplots=True, ax=axs)\n", ");" ] } ], "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 }