{ "cells": [ { "cell_type": "markdown", "id": "49a9724e", "metadata": {}, "source": [ "# Least Squares Chebyshev Approximations" ] }, { "cell_type": "markdown", "id": "22072b07", "metadata": {}, "source": [ "This notebook illustrates the least squares approximations of function using the Chebyshev polynomials." ] }, { "cell_type": "markdown", "id": "d43d9b69", "metadata": {}, "source": [ "The package FastGaussQuadrature provides nodes and weights for\n", "the Gauss-Chebyshev quadrature rules." ] }, { "cell_type": "code", "execution_count": 1, "id": "b564e39e", "metadata": {}, "outputs": [], "source": [ "using FastGaussQuadrature" ] }, { "cell_type": "code", "execution_count": 2, "id": "9d8b45fc", "metadata": {}, "outputs": [], "source": [ "using Plots" ] }, { "cell_type": "code", "execution_count": 3, "id": "8db4e350", "metadata": {}, "outputs": [], "source": [ "using Printf" ] }, { "cell_type": "markdown", "id": "9a27a999", "metadata": {}, "source": [ "### 1. The Orthogonal Basis of Chebyshev Polynomials" ] }, { "cell_type": "markdown", "id": "1866b236", "metadata": {}, "source": [ "The Chebyshev polynomials are orthogonal with respect to an inner product which requires the numerical evaluation of integrals. To evaluate the integrals, we apply Gauss-Chebyshev quadrature. The weights and the nodes ar provided by the package ``FastGaussQuadrature``." ] }, { "cell_type": "code", "execution_count": 4, "id": "99c9f1fc-b5af-4385-925a-0dfc9894ad5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([-0.9951847266721968, -0.9569403357322088, -0.8819212643483549, -0.773010453362737, -0.6343932841636454, -0.4713967368259977, -0.29028467725446216, -0.09801714032956065, 0.09801714032956077, 0.29028467725446233, 0.4713967368259978, 0.6343932841636455, 0.773010453362737, 0.881921264348355, 0.9569403357322088, 0.9951847266721969], [0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207, 0.19634954084936207])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nodes, weights = gausschebyshev(16)" ] }, { "cell_type": "code", "execution_count": 5, "id": "461e4b08-3abe-4216-b38d-04c5c2d5184c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.9951847266721968 : 0.19634954084936207\n", "-0.9569403357322088 : 0.19634954084936207\n", "-0.8819212643483549 : 0.19634954084936207\n", "-0.773010453362737 : 0.19634954084936207\n", "-0.6343932841636454 : 0.19634954084936207\n", "-0.4713967368259977 : 0.19634954084936207\n", "-0.29028467725446216 : 0.19634954084936207\n", "-0.09801714032956065 : 0.19634954084936207\n", "0.09801714032956077 : 0.19634954084936207\n", "0.29028467725446233 : 0.19634954084936207\n", "0.4713967368259978 : 0.19634954084936207\n", "0.6343932841636455 : 0.19634954084936207\n", "0.773010453362737 : 0.19634954084936207\n", "0.881921264348355 : 0.19634954084936207\n", "0.9569403357322088 : 0.19634954084936207\n", "0.9951847266721969 : 0.19634954084936207\n" ] } ], "source": [ "for i in 1:16\n", " println(nodes[i], \" : \", weights[i])\n", "end" ] }, { "cell_type": "code", "execution_count": 6, "id": "7e2988be-17cf-4058-ad7d-7c9db8c0e5b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "rule (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rule(f) = sum([weights[k]*f(nodes[k]) for k=1:length(weights)])" ] }, { "cell_type": "code", "execution_count": null, "id": "74221f04-02bb-4500-85eb-fe00f6b671fd", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "65906329", "metadata": {}, "source": [ "The ``rule`` is applied in the definition of the inner product function below." ] }, { "cell_type": "code", "execution_count": 7, "id": "26535655", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "innerproduct" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " function innerproduct(f::Function, g::Function)\n", "\n", "returns the value of the inner product of the functions f and g,\n", "by the integral of f and g over [-1,+1] with weight 1/sqrt(1-x^2).\n", "\"\"\"\n", "function innerproduct(f::Function, g::Function)\n", " fun(x) = f(x)*g(x)\n", " return (2.0/pi)*rule(fun)\n", "end" ] }, { "cell_type": "markdown", "id": "b349ea6d", "metadata": {}, "source": [ "The ``innerproduct`` will be tested on the verification of the orthogonality of the Chebyshev basis." ] }, { "cell_type": "code", "execution_count": 8, "id": "88997662", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "basis" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " function basis(n::Int64)\n", "\n", "returns an array of functions with the first n Chebyshev polynomials.\n", "\"\"\"\n", "function basis(n::Int64)\n", " t0(x) = 1 \n", " result = [t0]\n", " if(n > 1)\n", " t1(x) = x\n", " result = [result; t1]\n", " t1two(x) = 2*x\n", " for i=3:n\n", " newt(x) = t1two(x)*result[i-1](x) - result[i-2](x)\n", " result = [result; newt]\n", " end\n", " end\n", " return result\n", "end" ] }, { "cell_type": "markdown", "id": "d7ae2c24", "metadata": {}, "source": [ "As ``basis`` returns an array of functions, there is not much to see, but we can use the functions in a plot.\n", "Let us look at the first five Chebyshev functions." ] }, { "cell_type": "code", "execution_count": 9, "id": "0d9e74d8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B5 = basis(5)\n", "xr = -1:0.01:1\n", "yr1 = [B5[1](t) for t in xr]\n", "yr2 = [B5[2](t) for t in xr]\n", "yr3 = [B5[3](t) for t in xr]\n", "yr4 = [B5[4](t) for t in xr]\n", "yr5 = [B5[5](t) for t in xr]\n", "plot(xr,yr1,label=\"T0\")\n", "plot!(xr,yr2,label=\"T1\")\n", "plot!(xr,yr3,label=\"T2\")\n", "plot!(xr,yr4,label=\"T3\")\n", "plot!(xr,yr5,label=\"T5\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "0cb3b9ce", "metadata": {}, "outputs": [], "source": [ "# savefig(\"chebyshevbasis5.png\")" ] }, { "cell_type": "markdown", "id": "ad88972b", "metadata": {}, "source": [ "The verification of the orthogonality is defined by the function below." ] }, { "cell_type": "code", "execution_count": 11, "id": "d975d128", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "orthogonality" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " function orthogonality(n::Int64)\n", "\n", "Verifies the orthogonality of the Chebyshev basis\n", "for the first n Chebyshev polynomials.\n", "Prints the matrix of all inner products.\n", "\"\"\"\n", "function orthogonality(n::Int64)\n", " b = basis(n)\n", " for i=1:n\n", " for j=1:n\n", " ip = innerproduct(b[i],b[j])\n", " ipstr = @sprintf(\"%+.2e\", ip)\n", " print(\" $ipstr\")\n", " end\n", " println(\"\")\n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "id": "ebba2fc2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " +2.00e+00 +1.06e-16 -5.30e-17 +1.06e-16 -7.07e-17\n", " +1.06e-16 +1.00e+00 +1.59e-16 -8.83e-17 +2.65e-16\n", " -5.30e-17 +1.59e-16 +1.00e+00 +3.00e-16 -2.12e-16\n", " +1.06e-16 -8.83e-17 +3.00e-16 +1.00e+00 +3.71e-16\n", " -7.07e-17 +2.65e-16 -2.12e-16 +3.71e-16 +1.00e+00\n" ] } ], "source": [ "orthogonality(5)" ] }, { "cell_type": "markdown", "id": "a869bfc3", "metadata": {}, "source": [ "We observe the identity matrix (modulo roundoff of machine precision), except for the first number in the first row and column, which equals ``2``." ] }, { "cell_type": "markdown", "id": "c702547d", "metadata": {}, "source": [ "### 2. Computing the Least Squares Approximation" ] }, { "cell_type": "markdown", "id": "b2e820df", "metadata": {}, "source": [ "For any function $f$ and the first $n+1$ Chebyshev polynomials $T_i$, $i=0,1,\\ldots,n$, the polynomial approximation $p$ of degree $n$ is\n", "\n", "$$\n", " p(x) = \\frac{c_0}{2} + \\sum_{i=0}^n c_i T_i,\n", "$$\n", "\n", "where the coefficients are the inner products of $f$ with the basis functions:\n", "\n", "$$\n", " c_i = \\langle f, T_i \\rangle, \\quad i=0,1,\\ldots,n.\n", "$$" ] }, { "cell_type": "markdown", "id": "0bafe3c8", "metadata": {}, "source": [ "The coefficients of the Chebyshev approximation are computed by the function below." ] }, { "cell_type": "code", "execution_count": 13, "id": "f0fe7b32", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "coefficients" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " function coefficients(f::Function,b::Array{Function,1})\n", "\n", "returns the inner products of f with the basis functions in b.\n", "\"\"\"\n", "function coefficients(f::Function,b::Array{Function,1})\n", " dim = length(b)\n", " result = zeros(dim)\n", " for i=1:dim\n", " result[i] = innerproduct(f,b[i])\n", " end\n", " return result\n", "end" ] }, { "cell_type": "markdown", "id": "77f02777", "metadata": {}, "source": [ "With the coefficients and the array of basis functions, we can define the function for the approximant." ] }, { "cell_type": "code", "execution_count": 14, "id": "1e2be74c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "approximation" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"\"\"\n", " function approximation(c::Array{Float64,1},b::Array{Function,1})\n", "\n", "Given in c are the coefficients of the Chebyshev approximation\n", "with the basis functions in f.\n", "Returns the approximation as a function.\n", "\"\"\"\n", "function approximation(c::Array{Float64,1},b::Array{Function,1})\n", " first(x) = c[1]*b[1](x)/2\n", " rest(x) = sum([c[k]*b[k](x) for k=2:length(c)])\n", " result(x) = first(x) + rest(x)\n", " return result\n", "end" ] }, { "cell_type": "markdown", "id": "09d20571", "metadata": {}, "source": [ "Let us compute the least squares approximation of $\\exp(x)$ for $x \\in [-1,1]$ of degree 3." ] }, { "cell_type": "code", "execution_count": 15, "id": "f34ff7e5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " 2.532131755504017\n", " 1.1303182079849703\n", " 0.27149533953407656" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b3 = basis(3)\n", "c3 = coefficients(exp, b3)" ] }, { "cell_type": "markdown", "id": "05f50947", "metadata": {}, "source": [ "Observe that the coefficients are decreasing in magnitude." ] }, { "cell_type": "code", "execution_count": 16, "id": "2e4e048d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(::var\"#result#approximation##4\"{var\"#rest#approximation##1\"{Vector{Float64}, Vector{Function}}, var\"#first#approximation##0\"{Vector{Float64}, Vector{Function}}}) (generic function with 1 method)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a3 = approximation(c3,b3)" ] }, { "cell_type": "code", "execution_count": 17, "id": "39026ee0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xr = -1.0:0.01:1.0\n", "ex = [exp(t) for t in xr]\n", "px = [a3(t) for t in xr]\n", "plot(xr,ex,label=\"exp(x)\",legend=:topleft)\n", "plot!(xr,px,label=\"p3(x)\")" ] }, { "cell_type": "code", "execution_count": 18, "id": "7ceba896", "metadata": {}, "outputs": [], "source": [ "# savefig(\"chebyshevapp3exp.png\")" ] }, { "cell_type": "markdown", "id": "cd3004e1", "metadata": {}, "source": [ "Let us make a plot of the error $|\\exp(x) - p_3(x)|$ for $x \\in [-1,+1]$. " ] }, { "cell_type": "code", "execution_count": 19, "id": "b213baf6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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