{
"cells": [
{
"cell_type": "markdown",
"id": "88a9df50-9c8e-4c52-97dd-12c3465d8383",
"metadata": {},
"source": [
"# 2025-10-29 Nonlinear Regression\n",
"\n",
"* Nonlinear models\n",
"\n",
"* Computing derivatives\n",
"\n",
" * analytically (by hand)\n",
"\n",
" * numerically\n",
" \n",
" * algorithmically (automatic differentiation)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "4e1141cc-9d4c-4e64-b250-7c5d91f9f1ef",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"vcond (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",
"# Here's our Vandermonde matrix again\n",
"function vander(x, k=nothing)\n",
" if isnothing(k)\n",
" k = length(x)\n",
" end\n",
" m = length(x)\n",
" V = ones(m, k)\n",
" for j in 2:k\n",
" V[:, j] = V[:, j-1] .* x\n",
" end\n",
" V\n",
"end\n",
"\n",
"# With Chebyshev polynomials\n",
"function vander_chebyshev(x, n=nothing)\n",
" if isnothing(n)\n",
" n = length(x) # Square by default\n",
" end\n",
" m = length(x)\n",
" T = ones(m, n)\n",
" if n > 1\n",
" T[:, 2] = x\n",
" end\n",
" for k in 3:n\n",
" #T[:, k] = x .* T[:, k-1]\n",
" T[:, k] = 2 * x .* T[:,k-1] - T[:, k-2]\n",
" end\n",
" T\n",
"end\n",
"\n",
"# A utility for evaluating our regression\n",
"function chebyshev_regress_eval(x, xx, n)\n",
" V = vander_chebyshev(x, n)\n",
" vander_chebyshev(xx, n) / V\n",
"end\n",
"\n",
"# And our \"bad\" function\n",
"runge(x) = 1 / (1 + 10*x^2)\n",
"runge_noisy(x, sigma) = runge.(x) + randn(size(x)) * sigma\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",
"# And a helper for looking at conditioning\n",
"vcond(mat, points, nmax) = [cond(mat(points(-1, 1, n))) for n in 2:nmax]"
]
},
{
"cell_type": "markdown",
"id": "ada22d23-b485-467c-a0cc-37736d30c4dd",
"metadata": {},
"source": [
"## Gradient descent\n",
"\n",
"Instead of solving the least squares problem using linear algebra (QR factorization), we could solve it using gradient descent.\n",
"That is, on each iteration, we'll take a step in the direction of the negative gradient."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f0df26ab-9701-4270-9a3c-c613cb213d64",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"grad_descent (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function grad_descent(loss, grad, c0; gamma=1e-3, tol=1e-5)\n",
" \"\"\"Minimize loss(c) via gradient descent with initial guess c0\n",
" using learning rate gamma. Declares convergence when gradient\n",
" is less than tol or after 500 steps.\n",
" \"\"\"\n",
" c = copy(c0)\n",
" chist = [copy(c)]\n",
" lhist = [loss(c)]\n",
" for it in 1:500\n",
" g = grad(c)\n",
" c -= gamma * g\n",
" push!(chist, copy(c))\n",
" push!(lhist, loss(c))\n",
" if norm(g) < tol\n",
" break\n",
" end\n",
" end\n",
" (c, hcat(chist...), lhist)\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "bef80d3b-6a32-4cf4-946c-04cf94b4d45a",
"metadata": {},
"source": [
"Gradient descent shows quadratic convergence."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "79f0afaa-d96c-42f0-9e75-e4c951688bc0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cond(A) = 9.465784928823188\n"
]
},
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = [1 1; 1 8]\n",
"@show cond(A)\n",
"loss(c) = .5 * c' * A * c\n",
"grad(c) = A * c\n",
"\n",
"c, chist, lhist = grad_descent(loss, grad, [.9, .9], gamma=.22)\n",
"plot(lhist, yscale=:log10, xlims=(0, 80), label=\"loss\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "bc4c69cb-0d49-4b7f-9621-f4a243331e34",
"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": [
"plot(chist[1, :], chist[2, :], marker=:circle, label=\"search path\")\n",
"x = LinRange(-1, 1, 30)\n",
"contour!(x, x, (x,y) -> loss([x, y]))"
]
},
{
"cell_type": "markdown",
"id": "c15b19a9-26a5-4cb8-8234-cffde8e364d9",
"metadata": {},
"source": [
"## Chebyshev regression via optimization\n",
"\n",
"Let's try to fit our function that shows the Runge phenomenon with noise."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "65d128d3-6b90-4ddb-b325-e9b78f7b2f0b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c = [0.7237557249716973, -0.14061045581056947, -1.889447788301095, 0.33246539780616563, 0.6624478190092153, 0.14423918299995464, 0.6713664710235767, -0.515548367571375]\n"
]
}
],
"source": [
"# Set up the problem to solve\n",
"x = LinRange(-1, 1, 200)\n",
"sigma = 0.5\n",
"y = runge_noisy(x, sigma)\n",
"n = 8\n",
"V = vander(x, n)\n",
"\n",
"# Here's our loss function\n",
"function loss(c)\n",
" r = V * c - y\n",
" .5 * r' * r\n",
"end\n",
"# and our gradient\n",
"function grad(c)\n",
" r = V * c - y\n",
" V' * r\n",
"end\n",
"\n",
"# Solve\n",
"c, _, lhist = grad_descent(loss, grad, ones(n), gamma=0.008)\n",
"# and our final coefficients are....\n",
"@show c;"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1cfc136d-b122-4db1-b0e7-5618782d3fb1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cond(V) = 230.0054998201452\n",
"cond(V' * V) = 52902.529947850875\n"
]
},
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c0 = V \\ y # Solve exactly\n",
"l0 = 0.5 * norm(V * c0 - y)^2\n",
"\n",
"@show cond(V)\n",
"@show cond(V' * V)\n",
"\n",
"plot(lhist, yscale=:log10, ylim=(15, 50), label=\"loss\")\n",
"plot!(i -> l0, color=:black, label=\"exact\")"
]
},
{
"cell_type": "markdown",
"id": "11101d99-d5dd-418d-9ca5-e2db80718df2",
"metadata": {},
"source": [
"## But why\n",
"\n",
"Why would we use gradient-based optimization vs QR or other direct solves?"
]
},
{
"cell_type": "markdown",
"id": "2fe20d4f-0c6f-49db-98f8-80c242e57fb1",
"metadata": {},
"source": [
"## Nonlinear models\n",
"\n",
"Instead of the linear model\n",
"\n",
"$$ f \\left( x, c \\right) = V \\left( x \\right) c = c_0 + c_1 T_1 \\left( x \\right) + c_2 T_2 \\left( x \\right) + \\cdots $$\n",
"\n",
"let's consider a rational model with only three parameters\n",
"\n",
"$$ f \\left( x, c \\right) = \\frac{1}{c_1 + c_2 x + c_3 x^2} = \\left( c_1 + c_2 x + c_3 x^2 \\right)^{-1} $$\n",
"\n",
"We'll use the same loss function\n",
"\n",
"$$ L \\left( c; x, y \\right) = \\frac{1}{2} \\left\\lvert \\left\\lvert f \\left( x, c \\right) - y \\right\\rvert \\right\\rvert^2 $$\n",
"\n",
"We will also need the gradient\n",
"\n",
"$$ \\nabla_c L \\left( c; x, y \\right) = \\left( f \\left( x, c \\right) - y \\right)^T \\nabla_c f \\left( x, c \\right) $$\n",
"\n",
"where\n",
"\n",
"$$ \\frac{\\partial f \\left( x, c \\right)}{\\partial c_1} = - \\left( c_1 + c_2 x + c_3 x^2 \\right)^{-2} = - f \\left( x, c \\right)^2 $$\n",
"$$ \\frac{\\partial f \\left( x, c \\right)}{\\partial c_2} = - \\left( c_1 + c_2 x + c_3 x^2 \\right)^{-2} x = - f \\left( x, c \\right)^2 x $$\n",
"$$ \\frac{\\partial f \\left( x, c \\right)}{\\partial c_3} = - \\left( c_1 + c_2 x + c_3 x^2 \\right)^{-2} x^2 = - f \\left( x, c \\right)^2 x^2 $$"
]
},
{
"cell_type": "markdown",
"id": "28e2bd34-e1ac-482f-8aa0-32e088cf9ab5",
"metadata": {},
"source": [
"## Fitting a rational function\n",
"\n",
"Now let's fit our rational function with gradient descent, as above."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c7ad05e8-9c1f-4ba3-8203-9d2b92d8ce23",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"gradient (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(x, c) = 1 ./ (c[1] .+ c[2].*x + c[3].*x.^2)\n",
"\n",
"function gradf(x, c)\n",
" f2 = f(x, c).^2\n",
" [-f2 -f2.*x -f2.*x.^2]\n",
"end\n",
"\n",
"function loss(c)\n",
" r = f(x, c) - y\n",
" 0.5 * r' * r\n",
"end\n",
"\n",
"function gradient(c)\n",
" r = f(x, c) - y\n",
" vec(r' * gradf(x, c))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "99faedf6-37e3-4664-91a5-517d8e05a666",
"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": [
"c, _, lhist = grad_descent(loss, gradient, ones(3), gamma=8e-2)\n",
"plot(lhist, yscale=:log10, label=\"loss\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "0f38c7d2-aea3-406d-9471-3d8eb3fac3bd",
"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": [
"scatter(x, y, label=\"data\")\n",
"V = vander_chebyshev(x, 7)\n",
"plot!(x -> runge(x), color=:black, label=\"True\")\n",
"plot!(x, V * (V \\ y), label=\"Chebyshev fit\")\n",
"plot!(x -> f(x, c), label=\"Rational fit\")"
]
},
{
"cell_type": "markdown",
"id": "130c5e29-b665-4d96-8393-e3c93c5f1b40",
"metadata": {},
"source": [
"## A \"bad\" fit\n",
"\n",
"Let's fit the [logistic function](https://en.wikipedia.org/wiki/Logistic_regression) to this data, just to see what happens!\n",
"\n",
"$$ p \\left( x \\right) = \\frac{1}{1 + e^{- \\left( c_1 + c_2 x \\right)}} $$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "df3aae65-7b46-47ec-903a-54b4aad51e9d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"gradient (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p(x, c) = 1 ./ (1 .+ exp.(-(c[1] .+ c[2].*x)))\n",
"\n",
"function gradp(x, c)\n",
" p2 = p(x, c).^2 .* exp.(-(c[1] .+ c[2].*x))\n",
" [p2 p2.*c[2]]\n",
"end\n",
"\n",
"function loss(c)\n",
" r = p(x, c) - y\n",
" 0.5 * r' * r\n",
"end\n",
"\n",
"function gradient(c)\n",
" r = p(x, c) - y\n",
" vec(r' * gradp(x, c))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "763121d7-4a8a-4fc9-bda3-1adc1ec01272",
"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": [
"c, _, lhist = grad_descent(loss, gradient, ones(2), gamma=5e-2)\n",
"plot(lhist, yscale=:log10, label=\"loss\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d47fb626-4481-4a45-82d0-baeaf3f3d97f",
"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": [
"scatter(x, y, label=\"data\")\n",
"V = vander_chebyshev(x, 7)\n",
"plot!(x -> runge(x), color=:black, label=\"True\")\n",
"plot!(x, V * (V \\ y), label=\"Chebyshev fit\")\n",
"plot!(x -> p(x, c), label=\"Logistic fit\")"
]
},
{
"cell_type": "markdown",
"id": "a74b4d60-a354-4b55-8bc6-9312a7fa2d29",
"metadata": {},
"source": [
"This is a terrible fit!\n",
"*But*, gradient descent found the best fit we could have with a poor model choice.\n",
"Model choice is very important!"
]
},
{
"cell_type": "markdown",
"id": "07aa29af-5b4b-45c8-b355-07ebcecbd843",
"metadata": {},
"source": [
"## Computing derivatives\n",
"\n",
"How should we compute these derivatives as the model gets complicated?\n",
"\n",
"Recall the definition of the derivative:\n",
"\n",
"$$ \\lim_{h \\rightarrow 0} \\frac{f \\left( x + h \\right) - f \\left( x \\right)}{h} $$"
]
},
{
"cell_type": "markdown",
"id": "e6d9443b-9360-479f-9925-263bedf3e214",
"metadata": {},
"source": [
"### Taylor series\n",
"\n",
"Classical accuracy analysis assumes that functions are sufficiently smooth, meaning that derivatives exist and Taylor expansions are valid within a neighborhood.\n",
"In particular,\n",
"\n",
"$$ f \\left( x + h \\right) = f \\left( x \\right) + f' \\left( x \\right) h + f'' \\left( x \\right) \\frac{h^2}{2!} + \\underbrace{f''' \\left( x \\right) \\frac{h^3}{3!} + \\dotsb}_{\\mathcal{O} \\left( h^3 \\right)} $$\n",
"\n",
"The big-$\\mathcal{O}$ notation is meant in the limit $h \\rightarrow 0$.\n",
"Specifically, a function $g \\left( h \\right) \\in \\mathcal{O} \\left( h^p \\right)$ (sometimes written as $g \\left( h \\right) = \\mathcal{O} \\left( h^p \\right)$) when there exists a constant $C$ such that\n",
"\n",
"$$ g \\left( h \\right) \\leq C h^p $$\n",
"\n",
"for all sufficiently *small* $h$."
]
},
{
"cell_type": "markdown",
"id": "eeb5d701-fd53-4d87-a5da-36ac34ed0cb6",
"metadata": {},
"source": [
"### Rounding error\n",
"\n",
"We have an additional source of error, *rounding error*, which comes from not being able to compute $f \\left( x \\right)$ or $f \\left( x + h \\right)$ exactly, nor subtract them exactly.\n",
"Suppose that we can, however, compute these functions with a relative error on the order of $\\epsilon_\\text{machine}$.\n",
"This leads to\n",
"\n",
"$$ \\begin{split} \\begin{split}\n",
"\\tilde f \\left( x \\right) \n",
" &= f \\left( x \\right) \\left( 1 + \\epsilon_1 \\right) \\\\\n",
"\\tilde f \\left( x \\oplus h \\right)\n",
" &= \\tilde f \\left( \\left( x + h \\right) \\left( 1 + \\epsilon_2 \\right) \\right) \\\\\n",
" &= f \\left( \\left( x + h \\right) \\left( 1 + \\epsilon_2 \\right) \\right) \\left( 1 + \\epsilon_3 \\right) \\\\\n",
" &= \\left[ f \\left( x + h \\right) + f' \\left( x + h \\right) \\left( x + h \\right) \\epsilon_2 + \\mathcal{O} \\left( \\epsilon_2^2 \\right) \\right] \\left( 1 + \\epsilon_3 \\right) \\\\\n",
" &= f \\left( x + h \\right) \\left( 1 + \\epsilon_3 \\right) + f' \\left( x + h \\right) x \\epsilon_2 + \\mathcal{O} \\left( \\epsilon_{\\text{machine}}^2 + \\epsilon_{\\text{machine}} h \\right)\n",
"\\end{split} \\end{split} $$"
]
},
{
"cell_type": "markdown",
"id": "7e854f0f-fef8-488f-bf15-cd4a9af5c2dd",
"metadata": {},
"source": [
"### Some tedious arithmetic\n",
"\n",
"Propagating this error calculation gives\n",
"\n",
"$$ \\begin{split} \\begin{split}\n",
"\\left\\lvert \\frac{\\tilde f \\left( x + h \\right) \\ominus \\tilde f \\left( x \\right)}{h} - \\frac{f \\left( x + h \\right) - f \\left( x \\right)}{h} \\right\\rvert\n",
" &= \\left\\lvert \\frac{f \\left( x + h \\right) \\left( 1 + \\epsilon_3 \\right) + f' \\left( x + h \\right) x \\epsilon_2 + \\mathcal{O} \\left( \\epsilon_{\\text{machine}}^2 + \\epsilon_{\\text{machine}} h \\right) - f \\left( x \\right) \\left( 1 + \\epsilon_1 \\right) - f \\left( x + h \\right) + f \\left( x \\right)}{h} \\right\\rvert \\\\\n",
" &\\le \\frac{\\left\\lvert f \\left( x + h \\right) \\epsilon_3 \\right\\rvert + \\left\\lvert f' \\left( x + h \\right) x \\epsilon_2 \\right\\rvert + \\left\\lvert f \\left( x \\right) \\epsilon_1 \\right\\rvert + \\mathcal{O} \\left( \\epsilon_{\\text{machine}}^2 + \\epsilon_{\\text{machine}}h \\right)}{h} \\\\\n",
" &\\le \\frac{ \\left( 2 \\max_{\\left[ x, x + h \\right]} \\left\\lvert f \\right\\rvert + \\max_{\\left[ x, x + h \\right]} \\left\\lvert f' x \\right\\rvert \\right) \\epsilon_{\\text{machine}} + \\mathcal{O} \\left( \\epsilon_{\\text{machine}}^2 + \\epsilon_{\\text{machine}} h \\right)}{h} \\\\\n",
" &= \\left( 2 \\max \\left\\lvert f \\right\\rvert + \\max \\left\\lvert f'x \\right\\rvert \\right) \\frac{\\epsilon_{\\text{machine}}}{h} + \\mathcal{O} \\left( \\epsilon_{\\text{machine}} \\right) \\\\\n",
"\\end{split} \\end{split} $$\n",
"\n",
"where we have assumed that $h \\geq \\epsilon_\\text{machine}$.\n",
"This error becomes large (relative to $f'$ - we are concerned with relative error after all) when\n",
"\n",
"* $f$ is large compared to $f'$\n",
"\n",
"* $x$ is large\n",
"\n",
"* $h$ is too small"
]
},
{
"cell_type": "markdown",
"id": "38043b8b-7e09-416c-944c-0115346743ad",
"metadata": {},
"source": [
"### Automatic step size selection\n",
"\n",
"Walker and Pernice, Dennis and Schnabel developed ways to automatically choose the step size when computing the derivative numerically."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "367d7ed7-de32-4c30-bf8e-9faee70e9cad",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"diff_wp(sin, x) - cos(x) = -4.139506408429305e-6\n"
]
}
],
"source": [
"# Derivative via differancing\n",
"diff(f, x; h=1e-8) = (f(x+h) - f(x)) / h\n",
"\n",
"# And automatic selection of h\n",
"function diff_wp(f, x; h=1e-8)\n",
" \"\"\"Diff using Walker and Pernice (1998) choice of step\"\"\"\n",
" h *= (1 + abs(x))\n",
" (f(x+h) - f(x)) / h\n",
"end\n",
"\n",
"# Let's try it!\n",
"x = 1000\n",
"@show diff_wp(sin, x) - cos(x);"
]
},
{
"cell_type": "markdown",
"id": "a125c026-1b42-48d0-810b-dcc4d87d73d7",
"metadata": {},
"source": [
"## Symbolic differentiation\n",
"\n",
"We can also use a package to symbolically differentiate like we would by hand."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6019496d-cb53-4f32-b8b0-24d5b73e75e4",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\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": {
"text/latex": [
"$$ \\begin{equation}\n",
"\\frac{\\mathrm{d} \\sin\\left( x \\right)}{\\mathrm{d}x}\n",
"\\end{equation}\n",
" $$"
],
"text/plain": [
"Differential(x)(sin(x))"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Pkg\n",
"pkg\"add Symbolics\"\n",
"using Symbolics\n",
"\n",
"# Some setup\n",
"@variables x\n",
"Dx = Differential(x)\n",
"\n",
"# And an example\n",
"y = sin(x)\n",
"Dx(y)"
]
},
{
"cell_type": "markdown",
"id": "9a378a83-2e8b-4faf-a7eb-cf2c7772b08d",
"metadata": {},
"source": [
"### Product rule\n",
"\n",
"This package can follow the product rule!"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "0adbd2a8-5e0a-47a2-8ee7-035c2fdeed4e",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$$ \\begin{equation}\n",
"\\frac{\\left( \\frac{\\cos\\left( x^{\\pi} \\right)}{x} - 3.1416 x^{2.1416} \\log\\left( x \\right) \\sin\\left( x^{\\pi} \\right) \\right) \\cos\\left( \\cos^{3.1416}\\left( x^{\\pi} \\right) \\left( \\log\\left( x \\right) \\right)^{3.1416} \\right)}{\\log\\left( x \\right) \\cos\\left( x^{\\pi} \\right)} - \\left( \\frac{3.1416 \\cos^{3.1416}\\left( x^{\\pi} \\right) \\left( \\log\\left( x \\right) \\right)^{2.1416}}{x} - 9.8696 \\cos^{2.1416}\\left( x^{\\pi} \\right) \\left( \\log\\left( x \\right) \\right)^{3.1416} x^{2.1416} \\sin\\left( x^{\\pi} \\right) \\right) \\log\\left( \\log\\left( x \\right) \\cos\\left( x^{\\pi} \\right) \\right) \\sin\\left( \\cos^{3.1416}\\left( x^{\\pi} \\right) \\left( \\log\\left( x \\right) \\right)^{3.1416} \\right)\n",
"\\end{equation}\n",
" $$"
],
"text/plain": [
"((cos(x^π) / x - 3.141592653589793(x^2.141592653589793)*log(x)*sin(x^π))*cos((log(x)^3.141592653589793)*(cos(x^π)^3.141592653589793))) / (log(x)*cos(x^π)) - ((3.141592653589793(log(x)^2.141592653589793)*(cos(x^π)^3.141592653589793)) / x - 9.869604401089358(x^2.141592653589793)*(log(x)^3.141592653589793)*sin(x^π)*(cos(x^π)^2.141592653589793))*log(log(x)*cos(x^π))*sin((log(x)^3.141592653589793)*(cos(x^π)^3.141592653589793))"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = x\n",
"for _ in 1:2\n",
" y = cos(y^π) * log(y)\n",
"end\n",
"\n",
"# This will be... a lot\n",
"expand_derivatives(Dx(y))"
]
},
{
"cell_type": "markdown",
"id": "c1ab4e63-97d3-4b70-9369-7fc5dd038332",
"metadata": {},
"source": [
"The size of these expressions can grow **exponentially**!"
]
},
{
"cell_type": "markdown",
"id": "3975d4db-31ca-4503-82dd-85f560b2e84e",
"metadata": {},
"source": [
"## Hand-coded derivatives\n",
"\n",
"With (mild) algebra abuse, the expression\n",
"\n",
"$$ \\frac{df}{dx} = f' \\left( x \\right) $$\n",
"\n",
"is equivalent to\n",
"\n",
"$$ df = f' \\left( x \\right) dx $$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "7262419c-76dd-436c-872a-8774b53bf7b8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-1.5346823414986814, -34.032439961925064)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function f(x)\n",
" y = x\n",
" for _ in 1:2\n",
" a = y^π\n",
" b = cos(a)\n",
" c = log(y)\n",
" y = b * c\n",
" end\n",
" y\n",
"end\n",
"\n",
"f(1.9), diff_wp(f, 1.9)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "2223383a-163f-4526-a7ef-c14ac366c524",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-1.5346823414986814, -34.032419599140475)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function df(x, dx)\n",
" y = x\n",
" dy = dx\n",
" for _ in 1:2\n",
" a = y^π\n",
" da = π * y^(π - 1) * dy\n",
" b = cos(a)\n",
" db = -sin(a) * da\n",
" c = log(y)\n",
" dc = dy / y\n",
" y = b * c\n",
" dy = db * c + b * dc\n",
" end\n",
" y, dy\n",
"end\n",
"\n",
"df(1.9, 1)"
]
},
{
"cell_type": "markdown",
"id": "3395b35a-8015-4ed8-8f06-fe0211369f8d",
"metadata": {},
"source": [
"### Forward vs reverse mode\n",
"\n",
"We can differentiate a composition $h \\left( g \\left( f \\left( x \\right) \\right) \\right)$ as\n",
"\n",
"$$ \\begin{align}\n",
" \\operatorname{d} h &= h' \\operatorname{d} g \\\\\n",
" \\operatorname{d} g &= g' \\operatorname{d} f \\\\\n",
" \\operatorname{d} f &= f' \\operatorname{d} x\n",
"\\end{align}$$\n",
"\n",
"What we've done above is called \"forward mode\", and amounts to placing the parentheses in the chain rule like\n",
"\n",
"$$ \\operatorname{d} h = \\frac{dh}{dg} \\left( \\frac{dg}{df} \\left( \\frac{df}{dx} \\operatorname{d} x \\right) \\right) $$\n",
"\n",
"This expression means the same thing if we rearrange the parenthesis,\n",
"\n",
"$$ \\operatorname{d} h = \\left( \\left( \\left( \\frac{dh}{dg} \\right) \\frac{dg}{df} \\right) \\frac{df}{dx} \\right) \\operatorname{d} x $$"
]
},
{
"cell_type": "markdown",
"id": "58cb56d1-8c3a-487b-83aa-15e036107040",
"metadata": {},
"source": [
"## Automatic differentiation\n",
"\n",
"There are packages to do this differentiation 'automatically' on the code itself."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "cf6eb221-f27c-4a29-ab64-6406e981ea3c",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\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"
]
}
],
"source": [
"using Pkg\n",
"pkg\"add Zygote\"\n",
"import Zygote"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "b6162a72-181a-46fe-a43f-df7ea3288b54",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-34.03241959914049,)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Zygote.gradient(f, 1.9)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "aa603359-6055-4e00-91ab-efb63c20254d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[90m; Function Signature: gradient(typeof(Main.g), Float64)\u001b[39m\n",
"\u001b[90m; @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:152 within `gradient`\u001b[39m\n",
"\u001b[95mdefine\u001b[39m \u001b[33m[\u001b[39m\u001b[33m1\u001b[39m \u001b[0mx \u001b[36mdouble\u001b[39m\u001b[33m]\u001b[39m \u001b[93m@julia_gradient_40009\u001b[39m\u001b[33m(\u001b[39m\u001b[36mdouble\u001b[39m \u001b[0m%\"args\u001b[33m[\u001b[39m\u001b[33m1\u001b[39m\u001b[33m]\u001b[39m\u001b[0m::Float64\"\u001b[33m)\u001b[39m \u001b[0m#0 \u001b[33m{\u001b[39m\n",
"\u001b[91mtop:\u001b[39m\n",
"\u001b[90m; @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:153 within `gradient`\u001b[39m\n",
"\u001b[90m; ┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:94 within `pullback` @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:96\u001b[39m\n",
"\u001b[90m; │┌ @ In[20]:1 within `g`\u001b[39m\n",
"\u001b[90m; ││┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface2.jl:81 within `_pullback`\u001b[39m\n",
"\u001b[90m; │││┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface2.jl within `macro expansion`\u001b[39m\n",
"\u001b[90m; ││││┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/chainrules.jl:234 within `chain_rrule`\u001b[39m\n",
"\u001b[90m; │││││┌ @ /home/jeremy/.julia/packages/ChainRulesCore/Vsbj9/src/rules.jl:138 within `rrule` @ /home/jeremy/.julia/packages/ChainRules/14CDN/src/rulesets/Base/fastmath_able.jl:56\u001b[39m\n",
" \u001b[0m%0 \u001b[0m= \u001b[96m\u001b[1mcall\u001b[22m\u001b[39m \u001b[36mdouble\u001b[39m \u001b[93m@j_exp_40014\u001b[39m\u001b[33m(\u001b[39m\u001b[36mdouble\u001b[39m \u001b[0m%\"args\u001b[33m[\u001b[39m\u001b[33m1\u001b[39m\u001b[33m]\u001b[39m\u001b[0m::Float64\"\u001b[33m)\u001b[39m\n",
"\u001b[90m; └└└└└└\u001b[39m\n",
"\u001b[90m; @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:154 within `gradient`\u001b[39m\n",
"\u001b[90m; ┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:97 within `#88`\u001b[39m\n",
"\u001b[90m; │┌ @ In[20]:1 within `g`\u001b[39m\n",
"\u001b[90m; ││┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/chainrules.jl:222 within `ZBack`\u001b[39m\n",
"\u001b[90m; │││┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/lib/number.jl:12 within `literal_pow_pullback`\u001b[39m\n",
"\u001b[90m; ││││┌ @ promotion.jl:430 within `*` @ float.jl:493\u001b[39m\n",
" \u001b[0m%1 \u001b[0m= \u001b[96m\u001b[1mfmul\u001b[22m\u001b[39m \u001b[36mdouble\u001b[39m \u001b[0m%\"args\u001b[33m[\u001b[39m\u001b[33m1\u001b[39m\u001b[33m]\u001b[39m\u001b[0m::Float64\"\u001b[0m, \u001b[33m2.000000e+00\u001b[39m\n",
"\u001b[90m; │└└└└\u001b[39m\n",
"\u001b[90m; │┌ @ /home/jeremy/.julia/packages/Zygote/55SqB/src/lib/lib.jl:9 within `accum`\u001b[39m\n",
"\u001b[90m; ││┌ @ float.jl:491 within `+`\u001b[39m\n",
" \u001b[0m%2 \u001b[0m= \u001b[96m\u001b[1mfadd\u001b[22m\u001b[39m \u001b[36mdouble\u001b[39m \u001b[0m%1\u001b[0m, \u001b[0m%0\n",
"\u001b[90m; └└└\u001b[39m\n",
"\u001b[90m; @ /home/jeremy/.julia/packages/Zygote/55SqB/src/compiler/interface.jl:155 within `gradient`\u001b[39m\n",
" \u001b[91m%\"new:\u001b[39m\u001b[0m:Tuple4.unbox.fca.0.insert\" \u001b[0m= \u001b[95minsertvalue\u001b[39m \u001b[33m[\u001b[39m\u001b[33m1\u001b[39m \u001b[0mx \u001b[36mdouble\u001b[39m\u001b[33m]\u001b[39m \u001b[95mzeroinitializer\u001b[39m\u001b[0m, \u001b[36mdouble\u001b[39m \u001b[0m%2\u001b[0m, \u001b[33m0\u001b[39m\n",
" \u001b[96m\u001b[1mret\u001b[22m\u001b[39m \u001b[33m[\u001b[39m\u001b[33m1\u001b[39m \u001b[0mx \u001b[36mdouble\u001b[39m\u001b[33m]\u001b[39m \u001b[0m%\"new::Tuple4.unbox.fca.0.insert\"\n",
"\u001b[33m}\u001b[39m\n"
]
}
],
"source": [
"g(x) = exp(x) + x^2\n",
"@code_llvm Zygote.gradient(g, 1.9)"
]
}
],
"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"
}
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"nbformat": 4,
"nbformat_minor": 5
}