{
"cells": [
{
"cell_type": "markdown",
"id": "67c7cdea-6528-4921-b1fb-a4a67ca5f1cd",
"metadata": {},
"source": [
"# 2025-11-07 Quadrature\n",
"\n",
"* Polynomial interpolation for integration\n",
"\n",
"* Gauss quadrature"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "e3889dfd-9870-4d31-9dc0-b55744667149",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"fint_trapezoid (generic function with 1 method)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using LinearAlgebra\n",
"using Plots\n",
"using Polynomials\n",
"default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n",
"\n",
"# Vandermonde with Legendre polynomials\n",
"function vander_legendre(x, n=nothing)\n",
" if isnothing(n)\n",
" n = length(x) # Square by default\n",
" end\n",
" m = length(x)\n",
" Q = ones(m, n)\n",
" if n > 1\n",
" Q[:, 2] = x\n",
" end\n",
" for k in 1:n-2\n",
" Q[:, k+2] = ((2*k + 1) * x .* Q[:, k+1] - k * Q[:, k]) / (k + 1)\n",
" end\n",
" Q\n",
"end\n",
"\n",
"# And a utility for points distributed via cos\n",
"CosRange(a, b, n) = (a + b)/2 .+ (b - a)/2 * cos.(LinRange(-pi, 0, n))\n",
"\n",
"# Some test functions\n",
"F_expx(x) = exp(2x) / (1 + x^2)\n",
"f_expx(x) = 2*exp(2x) / (1 + x^2) - 2x*exp(2x)/(1 + x^2)^2\n",
"\n",
"F_dtanh(x) = tanh(x)\n",
"f_dtanh(x) = cosh(x)^-2\n",
"\n",
"integrands = [f_expx, f_dtanh]\n",
"antiderivatives = [F_expx, F_dtanh]\n",
"tests = zip(integrands, antiderivatives)\n",
"\n",
"# Plotting utils for accuracy\n",
"function plot_accuracy(fint, tests, ns; ref=[1,2])\n",
" a, b = -2, 2\n",
" p = plot(xscale=:log10, yscale=:log10, xlabel=\"n\", ylabel=\"error\")\n",
" for (f, F) in tests\n",
" Is = [fint(f, a, b, n=n) for n in ns]\n",
" Errors = abs.(Is .- (F(b) - F(a)))\n",
" scatter!(ns, Errors, label=f)\n",
" end\n",
" for k in ref\n",
" plot!(ns, ns.^(-1. * k), label=\"\\$n^{-$k}\\$\")\n",
" end\n",
" p\n",
"end\n",
"\n",
"function plot_accuracy_h(fint, tests, ns; ref=[1,2])\n",
" a, b = -2, 2\n",
" p = plot(xscale=:log10, yscale=:log10, xlabel=\"h\", ylabel=\"error\",\n",
" legend=:bottomright)\n",
" hs = (b - a) ./ ns\n",
" for (f, F) in tests\n",
" Is = [fint(f, a, b, n=n) for n in ns]\n",
" Errors = abs.(Is .- (F(b) - F(a)))\n",
" scatter!(hs, Errors, label=f)\n",
" end\n",
" for k in ref\n",
" plot!(hs, hs.^k, label=\"\\$h^{$k}\\$\")\n",
" end\n",
" p\n",
"end\n",
"\n",
"# And the Trap rule\n",
"function fint_trapezoid(f, a, b; n=20)\n",
" dx = (b - a) / (n - 1)\n",
" x = LinRange(a, b, n)\n",
" fx = f.(x)\n",
" fx[1] /= 2\n",
" fx[end] /= 2\n",
" sum(fx) * dx\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "315d2cd5-899e-40ed-a00e-8c66a7d3dcdf",
"metadata": {},
"source": [
"## Integration\n",
"\n",
"We're interested in computing definite integrals\n",
"\n",
"$$ \\int_a^b f \\left( x \\right) \\, dx $$\n",
"\n",
"and will usually consider finite domains $-\\infty < a < b < \\infty$.\n",
"\n",
"We need to consider\n",
"\n",
"* Cost: (usually) how many times we need to evaluate $f \\left( x \\right)$\n",
"\n",
"* Accuracy:\n",
"\n",
" * compare to a reference value\n",
" \n",
" * compare to the same method using more evaluations\n",
"\n",
"We also need to consider how smooth $f \\left( x \\right)$ is.\n",
"\n",
"Last time we integrated a piecewise linear fit, known as using the Trapezoid Rule."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "44aab5ee-9670-4bef-a3dc-7aaaad65cd95",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the integral using piecewise linear polynomial fit\n",
"function fint_trapezoid(f, a, b; n=20)\n",
" dx = (b - a) / (n - 1)\n",
" x = LinRange(a, b, n)\n",
" fx = f.(x)\n",
" fx[1] /= 2\n",
" fx[end] /= 2\n",
" sum(fx) * dx\n",
"end\n",
"\n",
"plot_accuracy(fint_trapezoid, tests, 2 .^ (1:10))"
]
},
{
"cell_type": "markdown",
"id": "fceed87f-d6cc-43e0-b2a8-f7772eafbd90",
"metadata": {},
"source": [
"## Extrapolation\n",
"\n",
"Let's switch our plot to use $h = \\Delta x$ instead of the number of points $x$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4ad6dd1a-f18e-4043-b0cf-b448d0148241",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_accuracy_h(fint_trapezoid, tests, 2 .^ (2:10))"
]
},
{
"cell_type": "markdown",
"id": "d94334ab-87d9-47aa-add3-b0f82c240423",
"metadata": {},
"source": [
"The trapezoid rule with $n$ points has an interval spacing of $h = 1 / \\left( n - 1 \\right)$.\n",
"Let $I_h$ be the value of the integral approximated using an interval $h$.\n",
"We have numerical evidence that the leading error term is $\\mathcal{O} \\left( h^2 \\right)$, which is to say\n",
"\n",
"$$ I_h - I_0 = c h^2 + \\mathcal{O} \\left( h^3 \\right) $$\n",
"\n",
"for some as-yet unknown constant $c$ that will depend upon the function being integrated and the domain of integration. If we can determine $c$ from two approximations, say $I_h$ and $I_{2h}$, then we can extrapolate to $h = 0$.\n",
"\n",
"For sufficiently small $h$, we can neglect $\\mathcal{O} \\left( h^3 \\right)$ and write\n",
"\n",
"$$ \\begin{align}\n",
" I_h - I_0 &= c h^2\\\\\n",
" I_{2h} - I_0 &= c \\left( 2 h \\right)^2 \n",
"\\end{align} $$\n",
"\n",
"Subtracting these two lines, we have\n",
"\n",
"$$ I_h - I_{2h} = c \\left( h^2 - 4 h^2 \\right) $$\n",
"\n",
"which can be solved for $c$ as\n",
"\n",
"$$ c = \\frac{I_h - I_{2h}}{h^2 - 4 h^2} $$\n",
"\n",
"Substituting back into the first equation, we solve for $I_0$ as\n",
"\n",
"$$ I_0 = I_h - c h^2 = I_h + \\frac{I_h - I_{2h}}{4 - 1} $$\n",
"\n",
"This is called [**Richardson extrapolation**](https://en.wikipedia.org/wiki/Richardson_extrapolation)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cf936d2d-e79c-4c12-a94f-0e34909c0b5d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function fint_richardson(f, a, b; n=20)\n",
" n = div(n, 2) * 2 + 1\n",
" h = (b - a) / (n - 1)\n",
" x = LinRange(a, b, n)\n",
" # Evaluate our function once\n",
" fx = f.(x)\n",
" fx[[1, end]] /= 2\n",
" # Itegrate with h and 2h\n",
" I_h = sum(fx) * h\n",
" I_2h = sum(fx[1:2:end]) * 2h\n",
" # Estimate I_0 per our math above\n",
" I_h + (I_h - I_2h) / 3\n",
"end\n",
"\n",
"# And how does it do?\n",
"plot_accuracy_h(fint_richardson, tests, 2 .^ (2:10), ref=1:5)"
]
},
{
"cell_type": "markdown",
"id": "1e5e3d99-ee18-448d-903a-047c4bc68818",
"metadata": {},
"source": [
"We now have a sequence of accurate approximations.\n",
"It is possible to apply this extrapolation recursively, and it works great if we have a number of points that is a power of $2$ and our function is \"nice enough\"."
]
},
{
"cell_type": "markdown",
"id": "f22371f4-2a6e-4e02-b3a5-a37d0a5183a2",
"metadata": {},
"source": [
"## Quadrature form\n",
"\n",
"At the end of the bay, we're taking a weighted sum of function values.\n",
"We call $w_i$ the *quadrature weights* and $x_i$ the *quadrature points* or *abscissa*.\n",
"\n",
"$$ \\int_a^b f \\left( x \\right) \\approx \\sum_{i = 1}^n w_i f \\left( x_i \\right) = \\mathbf{w}^T f \\left( \\mathbf{x} \\right) $$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "317599f9-6880-40c7-8361-86e7502ebf76",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"quad_trapezoid (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the weights and values for the trap rule\n",
"function quad_trapezoid(a, b; n=20)\n",
" dx = (b - a) / (n - 1)\n",
" x = LinRange(a, b, n)\n",
" w = fill(dx, n)\n",
" w[[1, end]] /= 2\n",
" x, w\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "7e833885-fdaa-4ca7-a4d3-e1f00d3918c9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.220446049250313e-16"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x, w = quad_trapezoid(-1, 1)\n",
"\n",
"w' * cos.(x) - fint_trapezoid(cos, -1, 1)"
]
},
{
"cell_type": "markdown",
"id": "7351dff5-5d9e-4ad5-95e8-2686ec72e4d6",
"metadata": {},
"source": [
"## Polynomial interpolation for integration\n",
"\n",
"Now let's use our work on polynomial interpolation to see if we can develop a different approach to quadrature (numerical integration)."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "43512cd6-ce76-4c86-bf65-b38392dd6abe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = LinRange(-1, 1, 100)\n",
"P = vander_legendre(x, 10)\n",
"plot(x, P[:,end], label=\"\\$P_9\\$\")"
]
},
{
"cell_type": "markdown",
"id": "ae7db248-b3ec-4a67-87b0-7dbfd52d0adb",
"metadata": {},
"source": [
"We want to sample our function $f \\left( x \\right)$ at some points $x \\in \\left[ -1, 1 \\right]$, fit a polynomial through these points, and return the integral of that interpolating polynomial.\n",
"\n",
"* What points do we sample on?\n",
"\n",
"* How do we integrate the interpolating polynomial?\n",
"\n",
"Recall that the Legendre polynomials $P_0 \\left( x \\right) = 1$, $P_1 \\left( x \\right) = x$, $\\dots$, are pairwise orthogonal\n",
"\n",
"$$ \\int_{-1}^1 P_m \\left( x \\right) P_n \\left( x \\right) = 0, \\forall m \\neq n $$"
]
},
{
"cell_type": "markdown",
"id": "5c3f740c-f798-49f8-88d6-65f38009ff9e",
"metadata": {},
"source": [
"### Let's see the code"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "3c68a267-38f8-4b85-9285-18288a811c2a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.0"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Weights and points for quadrature\n",
"function quad_legendre(a, b; n=20)\n",
" x = CosRange(-1, 1, n)\n",
" P = vander_legendre(x)\n",
" x_ab = (a+b)/2 .+ (b-a)/2*x\n",
" w = (b - a) * inv(P)[1,:]\n",
" x_ab, w\n",
"end\n",
"\n",
"# Function to actually do the integration\n",
"function fint_legendre(f, a, b; n=20)\n",
" x, w = quad_legendre(a, b, n=n)\n",
" w' * f.(x)\n",
"end\n",
"\n",
"# Test\n",
"fint_legendre(x -> 1 + x, -1, 1, n=4)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b1b94675-329c-4d1a-a626-7724a05734c2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = plot_accuracy(fint_legendre, tests, 4:40, ref=1:5)\n",
"plot!(p, xscale=:linear)"
]
},
{
"cell_type": "markdown",
"id": "31467bd9-4283-43a0-9b02-4fbb6cf611a5",
"metadata": {},
"source": [
"## We can do better\n",
"\n",
"Suppose a polynomial on the interval $\\left[ -1, 1 \\right]$ can be written as\n",
"\n",
"$$ p \\left( x \\right) = P_n \\left( x \\right) q \\left( x \\right) + r \\left( x \\right) $$\n",
"\n",
"where $P_n \\left( x \\right)$ is the $n$th Legendre polynomials and both $q \\left( x \\right)$ and $r \\left( x \\right)$ are polynomials of degree at most $n - 1$.\n",
"\n",
"We want to exactly integrate this function $p \\left( x \\right)$ with a sum of the form\n",
"\n",
"$$ \\int_{-1}^1 p \\left( x \\right) = \\sum_{i = 1}^n w_i p \\left( x_i \\right) $$\n",
"\n",
"I argue we can do this for a polynomial up to degree $2 n - 1$.\n",
"Why is this the case?\n",
"\n",
"* Why is $\\int_{-1}^1 P_n \\left( x \\right) q \\left( x \\right) = 0$?\n",
"\n",
"* Can every polynomial of degree $2 n - 1$ be written in the above form?\n",
"\n",
"* How many roots does $P_n \\left( x \\right)$ have on the interval?\n",
"\n",
"* Can we choose points $\\lbrace x_i \\rbrace$such that the first term is 0?\n",
"\n",
"If $P_n \\left( x_i \\right) = 0$ for each $x_i$, then we need only integrate $r \\left( x \\right)$, which is done exactly by interpolating polynomial.\n",
"How do we find these roots $x_i$?"
]
},
{
"cell_type": "markdown",
"id": "5560d97c-97d7-4d5f-b491-875f06f417fa",
"metadata": {},
"source": [
"## Gauss-Legendre in code\n",
"\n",
"1. Solve for the points, compute the weights\n",
"\n",
" * Use a Newton solver to find the roots. You can use the recurrence to write a recurrence for the derivatives.\n",
"\n",
" * Create a Vandermonde matrix and extract the first row of the inverse or (using more structure) the derivatives at the quadrature points.\n",
"\n",
"2. Use duality of polynomial roots and matrix eigenvalues.\n",
"\n",
" * A fascinating mathematical voyage; something you might see more in a graduate linear algebra class."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "5df82204-da44-4f80-b194-b48837f3eb66",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5733948071694299"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function fint_gauss(f, a, b; n=4)\n",
" \"\"\"Gauss-Legendre integration using Golub-Welsch algorithm\"\"\"\n",
" beta = @. .5 / sqrt(1 - (2 * (1:n-1))^(-2))\n",
" T = diagm(-1 => beta, 1 => beta)\n",
" D, V = eigen(T)\n",
" w = V[1,:].^2 * (b-a)\n",
" x = (a+b)/2 .+ (b-a)/2 * D\n",
" w' * f.(x)\n",
"end\n",
"fint_gauss(sin, -2, 3, n=4)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "9a0d37b0-c9b1-4547-be8c-d2b578e29597",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_accuracy(fint_gauss, tests, 3:30, ref=1:4)\n",
"plot!(xscale=:linear)"
]
},
{
"cell_type": "markdown",
"id": "167f9e3a-2f13-4cdf-bca2-ea9a0f1584e9",
"metadata": {},
"source": [
"The $n$-point Gauss quadrature exactly integrates polynomials of degree $2 n - 1$."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "3ac802e5-b25d-447a-a864-fcf61b5e2e26",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_accuracy(fint_gauss, [(x -> 12(x-.2)^11, x->(x-.2)^12)], 3:12)\n",
"plot!(xscale=:linear)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "6400e204-be80-4a7e-a09d-dc64cdc42174",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_accuracy(fint_legendre, [(x -> 11x^10, x->x^11)], 3:12)\n",
"plot!(xscale=:linear)"
]
},
{
"cell_type": "markdown",
"id": "4f2381d9-84b1-4ce6-bb28-d50f94046aef",
"metadata": {},
"source": [
"## [FastGaussQuadrature.jl](https://juliaapproximation.github.io/FastGaussQuadrature.jl/stable/)\n",
"\n",
"There are packages to help us here."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "69d1d26d-4aaf-4c41-8a0e-6cc049891f08",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General.toml`\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.11/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.11/Manifest.toml`\n"
]
},
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Pkg\n",
"pkg\"add FastGaussQuadrature\"\n",
"using FastGaussQuadrature\n",
"\n",
"n = 20\n",
"x, q = gausslegendre(n)\n",
"scatter(x, q, label=\"Gauss-Legendre\", ylabel=\"weight\", xlims=(-1, 1))\n",
"scatter!(gausslobatto(n)..., label=\"Gauss-Lobatto\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.6",
"language": "julia",
"name": "julia-1.11"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}