{
"cells": [
{
"cell_type": "markdown",
"id": "c3716b6d-d1fb-4d25-914f-c681a4ac316e",
"metadata": {},
"source": [
"# 2025-11-05 Integration\n",
"\n",
"* Midpoint and trapezoid rules\n",
"\n",
"* Extrapolation\n",
"\n",
" Polynomial interpolation for integration"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "368b9a59-e20e-4b2b-8067-7edbb5ceb156",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"CosRange (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))"
]
},
{
"cell_type": "markdown",
"id": "039baf4f-0872-4c2a-87ee-3d18b54f4569",
"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."
]
},
{
"cell_type": "markdown",
"id": "c3c5bd61-c48b-483f-8a46-685858914907",
"metadata": {},
"source": [
"## Test functions\n",
"\n",
"We will use these functions to explore our integration."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "08ad9660-cb15-4057-a597-a715ee3aac98",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"zip(Function[Main.f_expx, Main.f_dtanh], Function[Main.F_expx, Main.F_dtanh])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# One with exponentials\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",
"# And one with tanh\n",
"F_dtanh(x) = tanh(x)\n",
"f_dtanh(x) = cosh(x)^-2\n",
"\n",
"# And together!\n",
"integrands = [f_expx, f_dtanh]\n",
"antiderivatives = [F_expx, F_dtanh]\n",
"tests = zip(integrands, antiderivatives)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "8ca39656-e31e-44cd-93b6-3e9c1b66a331",
"metadata": {},
"outputs": [
{
"data": {
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",
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"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(integrands, xlims=(-1, 1), labels=[\"\\$e^{2x} / (1 + x^2)\\$\" \"\\$tanh ( x )\\$\"])"
]
},
{
"cell_type": "markdown",
"id": "6fb70806-5eff-4ade-b2c2-dc4303662cfb",
"metadata": {},
"source": [
"## Fundamental Theorem of Calculus\n",
"\n",
"Let $f \\left( x \\right)$ be a continuous function and define $F \\left( x \\right)$ by\n",
"\n",
"$$ F \\left( x \\right) = \\int_a^x f \\left( s \\right) \\, ds $$\n",
"\n",
"Then $F \\left( x \\right)$ is uniformly continuous, differentiable, and\n",
"\n",
"$$ F' \\left( x \\right) = f \\left( x \\right) $$\n",
"\n",
"We say that $F$ is an antiderivative of $f$.\n",
"This implies that\n",
"\n",
"$$ \\int_a^b f \\left( x \\right) \\, dx = F \\left( b \\right) - F \\left( a \\right) $$\n",
"\n",
"We will test the accuracy of our integration schemes using the antiderivatives provided in our tests."
]
},
{
"cell_type": "markdown",
"id": "94000a5f-0b36-4807-beba-629cf4933b4f",
"metadata": {},
"source": [
"## Method of Manufactured Solutions\n",
"\n",
"We have used manufactured solutions before.\n",
"We have a few considerations in this case.\n",
"\n",
"* Analytically integrating an arbitrary function is hard\n",
"\n",
" * tends to require trickery\n",
" \n",
" * not always possible to express in closed form (see [elliptic integrals](https://en.wikipedia.org/wiki/Elliptic_integral))\n",
" \n",
" * sometimes needs special functions (see $\\text{erf} \\left( x \\right) = 2 / \\pi \\int_0^x e^{-t^2} \\, dt$)\n",
" \n",
" * don't always know when to give up on exact integral\n",
"\n",
"* Analytic differentiation\n",
"\n",
" * involves straightforward application of product and chain rules\n",
"\n",
"So, if we just choose an arbitrary function $F$ (the antiderivative), then we can compute $f = F'$ and numerically integrate $\\int_a^b f$ and compare to $F \\left( b \\right) - F \\left( a \\right)$."
]
},
{
"cell_type": "markdown",
"id": "a05bec7a-4b36-4cb0-b0b8-b118a137fe21",
"metadata": {},
"source": [
"## Newton-Cotes methods\n",
"\n",
"Approximate $f \\left( x \\right)$ using (often low order) piecewise polynomials and integrate the polynomials."
]
},
{
"cell_type": "markdown",
"id": "cd1df057-f32e-4b85-977d-eed62d5e8c0a",
"metadata": {},
"source": [
"### Midpoint method\n",
"\n",
"Consider using piecewise constant interpolating polynomial.\n",
"The area under each constant piece will be equivalent to using the midpoint of each interval and the width of the interval to compute the area of each subinterval (sketch this out!)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6a5b8c3c-6571-4140-8f58-6bd4599a3cff",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f_expx: 10.885522849146847 error=-0.03044402970425253\n",
"f_dtanh: 1.9285075531458649 error=0.0004523929942310545\n"
]
}
],
"source": [
"# Compute the integral using piecewise constant polynomial fit\n",
"function fint_midpoint(f, a, b; n=20)\n",
" dx = (b - a) / n\n",
" # Get the midpoints\n",
" x = LinRange(a + dx/2, b - dx/2, n)\n",
" # Evaluate f at the midpoints and compute areas\n",
" sum(f.(x)) * dx\n",
"end\n",
"\n",
"# Let's try it!\n",
"for (f, F) in tests\n",
" a, b = -2, 2\n",
" I_num = fint_midpoint(f, a, b, n=20)\n",
" I_analytic = F(b) - F(a)\n",
" println(\"$f: $I_num error=$(I_num - I_analytic)\")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "e6435fd9-1689-4d55-822b-babde128fd89",
"metadata": {},
"source": [
"As we saw with interpolation, we can improve accuracy by using more points."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "aa619d4f-35e9-41bc-80a9-bc500b74e341",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"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",
"plot_accuracy(fint_midpoint, tests, 2 .^ (0:10))"
]
},
{
"cell_type": "markdown",
"id": "29688b51-2dc2-4a68-9977-2e3ae45aa1fe",
"metadata": {},
"source": [
"### Trapezoid rule\n",
"\n",
"The trapezoid rule uses piecewise linear functions on each interval.\n",
"\n",
"$$ \\begin{split}\\begin{split}\n",
"\\int_a^b \\left[ f \\left( a \\right) + \\frac{f \\left( b \\right) - f \\left( a \\right)}{b - a} \\left( x - a \\right) \\right]\n",
" &= f \\left( a \\right) \\left( x - a \\right) + \\frac{f \\left( b \\right) - f \\left( a \\right)}{2 \\left( b - a \\right)} \\left( x - a \\right)^2 \\Big|_{x = a}^b \\\\\n",
" &= f \\left( a \\right) \\left( b - a \\right) + \\frac{f \\left( b \\right) - f \\left( a \\right)}{2 \\left( b - a \\right)} \\left( b - a \\right)^2 \\\\\n",
" &= \\frac{b - a}{2} \\left( f \\left( a \\right) + f \\left( b \\right) \\right)\n",
"\\end{split} \\end{split} $$\n",
"\n",
"Can you recreate this using a geometric argument (sketch it out!).\n",
"\n",
"What happens when we sum over many adjacent intervals?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8a716c8f-7c52-42b3-afb5-a6065d7f0add",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 6,
"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": "696b03d0-1ba1-4929-87bc-d4c04a9c750e",
"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": 7,
"id": "b720c8fe-70a6-409e-ba00-1e8d57262989",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"plot_accuracy_h (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"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, .1 * hs.^k, label=\"\\$h^{$k}\\$\")\n",
" end\n",
" p\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a9fd8220-02e7-44a9-b92a-92d3969f93bc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot_accuracy_h(fint_midpoint, tests, 2 .^ (2:10))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "eff46cb4-7b82-462d-9561-b9746b5a94aa",
"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": [
"plot_accuracy_h(fint_trapezoid, tests, 2 .^ (2:10))"
]
},
{
"cell_type": "markdown",
"id": "a0536fca-9ac2-488a-ad70-6ac23450e0c2",
"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": 10,
"id": "a9c979e3-2311-4ea2-9985-07f39e4008e1",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 10,
"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": "d90c08f6-a236-4042-a424-2e91305394ea",
"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": "code",
"execution_count": 11,
"id": "d49cb1c7-cbf5-4cc2-9f1f-f9226873bca1",
"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": [
"F_sin(x) = sin(30x)\n",
"f_sin(x) = 30*cos(30x)\n",
"plot_accuracy_h(fint_richardson, zip([f_sin], [F_sin]), 2 .^ (2:10), ref=1:5)"
]
},
{
"cell_type": "markdown",
"id": "5e2b01b1-b0fc-429e-9021-f5ff27eaa96e",
"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": 12,
"id": "7b29f95a-eab1-481c-92ad-3e61eb1ceb8d",
"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": [
"x = LinRange(-1, 1, 100)\n",
"P = vander_legendre(x, 10)\n",
"plot(x, P, legend=:none)"
]
},
{
"cell_type": "markdown",
"id": "5fd192a1-2b80-4756-abb4-0241f92016b1",
"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": "8ca90c28-47db-4f12-adb0-7bd12c53ff57",
"metadata": {},
"source": [
"### Let's see the code"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a58e9645-0e93-4b74-8260-eec5fae05da9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"plot_accuracy_n (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function plot_accuracy_n(fint, tests, ns; ref=[1,2])\n",
" a, b = -2, 2\n",
" p = plot(xscale=:log10, yscale=:log10, xlabel=\"n\", ylabel=\"error\",\n",
" legend=:bottomright)\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",
" p\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "483ff44e-032d-44d7-a26c-54a99c0fbf5e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.0"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function fint_legendre(f, 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",
" c = P \\ f.(x_ab)\n",
" (b - a) * c[1]\n",
"end\n",
"\n",
"fint_legendre(x -> 1 + x, -1, 1, n=2)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "fefec90e-d07b-4551-ace8-b8293d20664a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = plot_accuracy_h(fint_legendre, tests, 4:20, ref=1:5)"
]
},
{
"cell_type": "markdown",
"id": "00a027b9-6c72-4b29-b840-86e0a216fb7b",
"metadata": {},
"source": [
"This appears to be beating out approach above.\n",
"There has to be some drawbacks or potential issues though."
]
}
],
"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
}