{ "cells": [ { "cell_type": "markdown", "id": "70e958f2-da01-4b28-8c9e-0b5d24b1b0bb", "metadata": {}, "source": [ "# 2025-09-03 Rootfinding\n", "\n", "* Review condition numbers\n", "\n", "* Forward and backward error\n", "\n", "* Volume of a polygon\n", "\n", "* Rootfinding examples\n", "\n", "* Bisection\n", "\n", "See also [FNC](https://tobydriscoll.net/fnc-julia/nonlineqn/rootproblem.html)" ] }, { "cell_type": "markdown", "id": "9151fd85-7c64-49cd-8a7b-1381732856fc", "metadata": {}, "source": [ "## Reliability\n", "\n", "**Reliablility** comes from well-conditioned operations and stable algorithms" ] }, { "cell_type": "markdown", "id": "f4014251-3687-4608-9e23-da1d6afec038", "metadata": {}, "source": [ "### Well-conditioned operations\n", "\n", "* Modeling turns an abstract question into a mathematical function\n", "\n", "* We want well-conditioned models ($\\kappa$)\n", "\n", "* Some systems are inherantly sensitive though (fracture, chaotic systems, combustion, etc)" ] }, { "cell_type": "markdown", "id": "05b2d92f-429f-41ea-9008-cf2b63d348cd", "metadata": {}, "source": [ "### Stable algorithms\n", "\n", "* An algorithm `f(x)` may be unstable\n", "\n", "* These algorithms are unreliable, but may be practical\n", "\n", "* Unstable algorithms are constructed from ill-conditioned parts" ] }, { "cell_type": "markdown", "id": "490713cb-4945-4dd3-b6e4-22a90b272543", "metadata": {}, "source": [ "## Forward and backward error" ] }, { "cell_type": "markdown", "id": "879c85e2-fc23-461f-a99a-4b41c6975b76", "metadata": {}, "source": [ "* **Forward error** is the difference between our result and the true solution\n", "\n", "* **Backward error** tells us which problem our result is the solution for\n", "\n", "Additional reading: [FNC](https://fncbook.com/stability)" ] }, { "attachments": { "ae0ef1fe-0b38-48d1-9079-cf7fd417347d.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "39a3889d-e2b3-482c-bee4-d2ce222413fe", "metadata": {}, "source": [ "![image.png](attachment:ae0ef1fe-0b38-48d1-9079-cf7fd417347d.png)" ] }, { "cell_type": "markdown", "id": "d383e28c-7598-482a-8077-b508aad473a7", "metadata": {}, "source": [ "## An ill-conditioned problem from Paul Olum\n", "\n", "From [Surely You're Joking, Mr. Feynman](https://sistemas.fciencias.unam.mx/%7Ecompcuantica/RICHARD%20P.%20FEYNMAN-SURELY%20YOU%27RE%20JOKING%20MR.%20FEYNMAN.PDF) (p 113)\n", "\n", "> So Paul is walking past the lunch place and these guys are all excited. “Hey, Paul!” they call out. “Feynman’s terrific! We give him a problem that can be stated in ten seconds, and in a minute he gets the answer to 10 percent. Why don’t you give him one?” Without hardly stopping, he says, “The tangent of 10 to the 100th.” I was sunk: you have to divide by pi to 100 decimal places! It was hopeless." ] }, { "cell_type": "code", "execution_count": 1, "id": "938e9b0d-e87b-4172-a821-fc9f467d0939", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4012319619908143541857543436532949583238702611292440683194415381168718098221194" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tan(BigFloat(\"1e100\", precision=400))" ] }, { "cell_type": "code", "execution_count": 2, "id": "7f1d3c76-89a1-41b0-9d69-e1e131f4f095", "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" ], "text/html": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# what values could have answered this question?\n", "using Plots\n", "default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n", "\n", "plot(tan, ylims=(-10, 10), x=LinRange(-10, 10, 1000), label=\"tan(x)\")" ] }, { "cell_type": "markdown", "id": "c1feb4fb-e7df-4a15-bc75-110af572c326", "metadata": {}, "source": [ "* For ill-conditioned problems, the best we can hope for is small backward error\n", "\n", "* Feynman could have answered with any real number and the relative backward error would have been less than $10^{-100}$. All vaues on the graph above have tiny backward error, as $\\tan \\left( \\text{fl} \\left( 10^{100} \\right) \\right) = \\tan \\left( 10^{100} \\left( 1 + \\epsilon \\right) \\right)$ for some $\\epsilon < 10^{-100}$" ] }, { "cell_type": "markdown", "id": "e208e093-1b93-4e1c-a5b3-233c67f922e8", "metadata": {}, "source": [ "## Stability - Volume of a polygon\n", "\n", "If error exceeds what we can explain via condition numbers, then we call our algorithm **unstable**." ] }, { "cell_type": "code", "execution_count": 3, "id": "b6b89023-aeb0-4a78-89d9-25d09a1180f2", "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", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R(θ) = [cos(θ) -sin(θ); sin(θ) cos(θ)]\n", "Y = X * R(deg2rad(30))' .+ [0 0]\n", "plot(Y[:,1], Y[:,2], seriestype=:shape, aspect_ratio=:equal, xlims=(-3, 3), ylims=(-3, 3))" ] }, { "cell_type": "code", "execution_count": 5, "id": "5e8774e9-0777-4545-a67a-b0d392adcec3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "vol_X = pvolume(X) = 9.25\n", "vol_Y = pvolume(Y) = 9.25\n" ] }, { "data": { "text/plain": [ "8×2 Matrix{Float64}:\n", " 1.0 0.0\n", " 2.0 1.0\n", " 1.0 3.0\n", " 0.0 1.0\n", " -1.0 1.5\n", " -2.0 -1.0\n", " 0.5 -2.0\n", " 1.0 0.0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using LinearAlgebra\n", "function pvolume(X)\n", " n = size(X, 1)\n", " vol = sum(det(X[i:i+1, :]) / 2 for i in 1:n-1)\n", "end\n", "\n", "@show vol_X = pvolume(X)\n", "@show vol_Y = pvolume(Y)\n", "[det(Y[i:i+1, :]) for i in 1:size(Y, 1)-1]\n", "X" ] }, { "cell_type": "markdown", "id": "549c4546-5262-415d-8251-926b4fd13939", "metadata": {}, "source": [ "What happens to this algorithm if the polygon is translated, perhaps far away?" ] }, { "cell_type": "markdown", "id": "09ff9e96-fc11-4546-8e2f-8fb5b61d9406", "metadata": {}, "source": [ "## Rootfinding\n", "\n", "Given $f \\left( x \\right)$, find $\\tilde{x}$ such that $f \\left( \\tilde{x} \\right) = 0$.\n", "\n", "We will start with scalars ($x$ is a single value and $f$ returns a single value) and come back to this with vectors later." ] }, { "cell_type": "markdown", "id": "7462cfaa-6c3e-4abb-a103-aa95cf72b3a7", "metadata": {}, "source": [ "* We don't have $f \\left( x \\right)$ but rather the algorithm `f(x)` that approximates it.\n", "\n", "* Sometimes we have extra information, such as `fp(x)` that approximates $f' \\left( x \\right)$.\n", "\n", "* If we have the source code for `f(x)`, we might be able to transform it to provide `fp(x)`." ] }, { "cell_type": "markdown", "id": "b0f7d2b0-0029-43fe-95b1-948f9d801fb0", "metadata": {}, "source": [ "### Example: Queueing\n", "\n", "In a [simple queueing model](https://en.wikipedia.org/wiki/Queueing_theory#Simple_two-equation_queue), there is an arrival rate and a departure (serving) rate. While waiting in the queue, there is a probability of “dropping out”. The length of the queue in this model is\n", "\n", "$$ \\text{length} = \\frac{\\text{arrival} - \\text{drop}}{\\text{departure}} $$\n", "\n", "One model for waiting time (with exponential distributions for rates) is" ] }, { "cell_type": "code", "execution_count": 6, "id": "820296d7-6be8-4e22-8603-539fdb29e8dc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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"\n", "#### Strain-energy formulation\n", "\n", "$$ W = C_1 \\left( I_1 - 3 - 2 \\log \\left( J \\right) \\right) + D_1 \\left( J - 1 \\right)^2 $$\n", "\n", "where $I_1 = \\lambda_1^2 + \\lambda_2^2 + \\lambda_3^2$ and $J = \\lambda_1 \\lambda_2 \\lambda_3$ are *invariants* defined in terms of th eprinciple stretches $\\lambda_i$" ] }, { "cell_type": "markdown", "id": "161f8cd6-3116-4112-a243-133b61c99517", "metadata": {}, "source": [ "#### [Uniaxial extension](https://en.wikipedia.org/wiki/Neo-Hookean_solid#Compressible_neo-Hookean_material_3)\n", "\n", "In that experiment, we want to know the stress as a function of the stretch $\\lambda_1$. We don't know $J$, and will have to determine it by solving an equation.\n", "\n", "[https://www.youtube.com/watch?v=9N5SS8f1auI&t=60](https://www.youtube.com/watch?v=9N5SS8f1auI&t=60)" ] }, { "cell_type": "markdown", "id": "4a633a5a-e23b-4f14-b057-a841ac407b3b", "metadata": {}, "source": [ "#### What is the change of volume?\n", "\n", "Using symmetries of uniaxial extension, we can write an equation $f \\left( \\lambda, J \\right) = 0$ that must be satisfield. We'll need to solve a rootfinding problem to compute $J \\left( \\lambda \\right)$." ] }, { "cell_type": "code", "execution_count": 9, "id": "61d5190e-3d79-4c22-95c1-1a6e41b731c2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"code", "execution_count": 11, "id": "48173e13-599b-4d44-9d20-6d8c01a40179", "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" ], "text/html": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hasroot(f, a, b) = f(a) * f(b) < 0\n", "\n", "f(x) = cos(x) - x\n", "plot(f, label=\"\\$cos(x) - x\\$\")" ] }, { "cell_type": "markdown", "id": "0dcbf3bb-0cb0-4c95-a3c3-23ca48982971", "metadata": {}, "source": [ "### Bisection" ] }, { "cell_type": "code", "execution_count": 12, "id": "654e0ef8-0b3f-4415-8a70-b4e4f71e3647", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(x0, f(x0)) = (0.7390861511230469, -1.7035832658995886e-6)\n" ] } ], "source": [ "function bisect(f, a, b, tol)\n", " mid = (a + b) / 2\n", " if abs(b - a) < tol\n", " return mid\n", " elseif hasroot(f, a, mid)\n", " return bisect(f, a, mid, tol)\n", " else\n", " return bisect(f, mid, b, tol)\n", " end\n", "end\n", "\n", "x0 = bisect(f, -1, 3, 1e-5)\n", "@show (x0, f(x0));" ] }, { "cell_type": "markdown", "id": "465a1163-5c7d-4290-a461-705848bf6875", "metadata": {}, "source": [ "#### What is my convergence rate?" ] }, { "cell_type": "code", "execution_count": 13, "id": "ae8c8cff-f9c3-4a88-bffb-707d5d78b42d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17-element Vector{Float64}:\n", " 1.0\n", " 0.0\n", " 0.5\n", " 0.75\n", " 0.625\n", " 0.6875\n", " 0.71875\n", " 0.734375\n", " 0.7421875\n", " 0.73828125\n", " 0.740234375\n", " 0.7392578125\n", " 0.73876953125\n", " 0.739013671875\n", " 0.7391357421875\n", " 0.73907470703125\n", " 0.739105224609375" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function bisect_hist(f, a, b, tol)\n", " mid = (a + b) / 2\n", " if abs(b - a) < tol\n", " return [mid]\n", " elseif hasroot(f, a, mid)\n", " return prepend!(bisect_hist(f, a, mid, tol), [mid])\n", " else\n", " return prepend!(bisect_hist(f, mid, b, tol), [mid])\n", " end\n", "end\n", "\n", "bisect_hist(f, -1, 3, 1e-4)" ] }, { "cell_type": "markdown", "id": "8cc43091-f3c4-4d33-b8f6-9bb6d071077d", "metadata": {}, "source": [ "### Iterative Bisection" ] }, { "cell_type": "code", "execution_count": 14, "id": "6a2605e2-5b09-4e0f-9d5c-72446601bbab", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16-element Vector{Float64}:\n", " 1.0\n", " 0.0\n", " 0.5\n", " 0.75\n", " 0.625\n", " 0.6875\n", " 0.71875\n", " 0.734375\n", " 0.7421875\n", " 0.73828125\n", " 0.740234375\n", " 0.7392578125\n", " 0.73876953125\n", " 0.739013671875\n", " 0.7391357421875\n", " 0.73907470703125" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function bisect_iter(f, a, b, tol)\n", " hist = Float64[]\n", " while abs(b - a) > tol\n", " mid = (a + b) / 2\n", " push!(hist, mid)\n", " if hasroot(f, a, mid)\n", " b = mid\n", " else\n", " a = mid\n", " end\n", " end\n", " hist\n", "end\n", "\n", "bisect_iter(f, -1, 3, 1e-4)" ] }, { "cell_type": "markdown", "id": "f9cf7ae9-7471-4668-bb0e-051d50fca66d", "metadata": {}, "source": [ "### Let's plot the error\n", "\n", "$$ \\lvert \\text{bisect}^k \\left( f, a, b \\right) - x_* \\rvert, k = 1, 2, \\dots $$\n", "\n", "where $r$ is the true root ($f \\left( x_* \\right) = 0$)." ] }, { "cell_type": "code", "execution_count": 15, "id": "873d0236-fce9-42ab-8e32-ec36d1a7c211", "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", "\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": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = bisect(f, -1, 3, 1e-15) # is this a good 'true' root?\n", "\n", "hist = bisect_hist(f, -1, 3, 1e-10)\n", "scatter( abs.(hist .- r), yscale=:log10, label=\"\\$x_k\\$\")\n", "\n", "ks = 1:length(hist)\n", "plot!(ks, 4 * (.5 .^ ks), label=\"~\\$2^{-k}\\$\")" ] }, { "cell_type": "markdown", "id": "8854c005-36aa-4cb9-a2b5-c6dcb515ab71", "metadata": {}, "source": [ "So the error $e_k = x_k - x_*$ satisfies the bound\n", "\n", "$$ \\left\\lvert e_k \\right\\rvert \\leq c 2^{-k} $$" ] }, { "cell_type": "markdown", "id": "a051c0e1-de46-4f3f-b5b3-f6c9b42f4c45", "metadata": {}, "source": [ "## Exploration\n", "\n", "* Share an equation on Zulip that is useful for one task but requires rootfinding for another task.\n", "\n", "* Or explain a system in which one stakeholder has the natural inputs but a different stakeholder only knows the outputs.\n", "\n", "Collaborate!" ] } ], "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 }