{ "cells": [ { "cell_type": "markdown", "id": "cb1d5eb9-cf28-46a8-9495-4e5346fcf67e", "metadata": {}, "source": [ "# 2025-09-12 Formulation\n", "\n", "* Goal sharing\n", "\n", "* Exploration\n", "\n", "* Multiple roots\n", "\n", "* Conditioning of the rootfinding problem\n", "\n", "* Forward and backward stability" ] }, { "cell_type": "code", "execution_count": 1, "id": "1b71447f-9300-4a9e-89d6-d09175fd7df6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "newton_hist (generic function with 1 method)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n", "\n", "# Here's the Newton's method with history we've been using\n", "function newton_hist(f, fp, x0; tol=1e-12)\n", " x = x0\n", " hist = []\n", " for k in 1:100 # max number of iterations\n", " fx = f(x)\n", " fpx = fp(x)\n", " push!(hist, [x fx fpx])\n", " if abs(fx) < tol\n", " return vcat(hist...)\n", " end\n", " x = x - fx / fpx\n", " end\n", "end" ] }, { "cell_type": "markdown", "id": "f8e0f515-7d2f-4f56-8b23-4fad5e91f8dc", "metadata": {}, "source": [ "## Exploration\n", "\n", "* Find a function $f \\left( x \\right)$ that models something you're interested in.\n", "You could consider nonlinear physical models (aerodynamic drag, nonlinear elasticity), behavioral models, probability distributions, or anything else that that catches your interest.\n", "Implement the function in Julia or another language.\n", "\n", "* Consider how you might know the output of such functions, but not an input.\n", "Think from the position of different stakeholders: is the equation used differently by an experimentalist collecting data versus by someone making predictions through simulation?\n", "How about a company or government reasoning about people versus the people their decisions may impact?\n", "\n", "* Formulate the map from known to desired data as a rootfinding problem and try one or more methods (Newton, bisection, etc., or use a rootfinding library).\n", "\n", "* Plot the inverse function (output versus input) from the standpoint of one or more stakeholder.\n", "Are there interesting inflection points?\n", "Are the methods reliable?\n", "\n", "* If there are a hierarchy of models for the application you're interested in, consider using a simpler model to provide an initial guess to a more complicated model." ] }, { "cell_type": "markdown", "id": "643c9fe9-b6ca-44dd-9b2e-a779165385ae", "metadata": {}, "source": [ "## Roots with multiplicity\n", "\n", "There are multiple ways to represent (monic) polynomials\n", "\n", "$$ f \\left( x \\right) = \\left( x - a_1 \\right) \\left( x - a_2 \\right) $$\n", "$$ g \\left( x \\right) = x^2 - \\left( a_1 + a_2 \\right) x + a_1 a_2 $$" ] }, { "cell_type": "code", "execution_count": 2, "id": "635a0f6a-94a6-47a4-8808-6c0dfcf09e22", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "g (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Here is the f(x) style above\n", "function poly_eval_prod(x, a) \n", " product = 1\n", " for c in a\n", " product *= (x - c)\n", " end\n", " product\n", "end\n", "# Note, compactly poly_eval_prod(x, a) = prod(x .- a)\n", "\n", "# And here is the g(x) style\n", "function poly_eval_sum(x, b)\n", " sum = 1\n", " for c in b\n", " # This is known as Horner's rule\n", " sum = x * sum + c\n", " end\n", " sum\n", "end\n", "\n", "# Let's make a couple of functions and compare the effect of perturbations ot each\n", "eps = 1e-10\n", "a = [1e5, 1e5*(1+eps)] # tiny perturbation to root\n", "b = [-(a[1] + a[2])*(1+eps), # tiny perturbation to monomial coefficent\n", " a[1]*a[2]]\n", "f(x) = poly_eval_prod(x, a)\n", "g(x) = poly_eval_sum(x, b)" ] }, { "cell_type": "code", "execution_count": 3, "id": "5dcb0ddb-c340-492e-958e-9ac7c0037e97", "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" ], "text/html": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# And let's plot these two and look at their roots\n", "plot([f, g], xlim=(a[1]-2, a[2]+2), ylim=(-3, 3), label=[\"\\$f(x)\\$\" \"\\$g(x)\\$\"])\n", "plot!(zero, color=:black, label=:none)" ] }, { "cell_type": "markdown", "id": "85df8582-b03b-495e-b066-6d06270572ff", "metadata": {}, "source": [ "* Perturbing the coefficient in the 10th digit made the difference between one root or two\n", "\n", "* The distance between the roots was large when $b_1$ was perturbed" ] }, { "cell_type": "markdown", "id": "40647b04-8d46-4db6-a3ca-f0db5486b6a2", "metadata": {}, "source": [ "## How did this happen?\n", "\n", "Take a polynomial with two roots at $x = a$ and perturb the middle coefficient.\n", "\n", "$$ x^2 + b_1 x + b_2 = 0 $$\n", "$$ x^2 - 2a \\left( 1 + \\epsilon \\right) x + a^2 = 0 $$\n", "\n", "Using the quadratic formula, we know that the roots are at\n", "\n", "$$ \\begin{align} x_* = \\frac{b_1}{2} \\pm \\sqrt{\\frac{b_1^2}{4} - b_2} &= a \\left(1 + \\epsilon \\right) \\pm \\sqrt{a^2 \\left( 1 + \\epsilon \\right)^2 - a^2}\\\\\n", "&= a \\left( 1 + \\epsilon \\right) \\pm a \\sqrt{2 \\epsilon + \\epsilon^2}\\\\\n", "&\\approx a \\left( 1 + \\epsilon \\pm \\sqrt{2 \\epsilon} \\right)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "4c5790dc-cc5f-4d9a-8cbc-3eab19d89b43", "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" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# What happens to small values when we take their square root?\n", "plot([x -> x, sqrt], xlims=(0, .001), label=[\"\\$x\\$\" \"\\$\\\\sqrt{x}\\$\"])" ] }, { "cell_type": "markdown", "id": "a6f0bc7b-2194-481c-9bc0-3cfc2806c87f", "metadata": {}, "source": [ "Note that the condition number is well behaved.\n", "\n", "$$ \\kappa \\left( \\sqrt{\\epsilon} \\right) = \\frac{1}{2 \\sqrt{\\epsilon}} \\frac{\\epsilon}{\\sqrt{\\epsilon}} = \\frac{1}{2} $$" ] }, { "cell_type": "markdown", "id": "18eb6f76-50c4-4788-a7c2-e051676f13e8", "metadata": {}, "source": [ "## Which root does Newton find?" ] }, { "cell_type": "code", "execution_count": 5, "id": "36c80819-6142-47d7-8fa3-bc8fa07d1c7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_k, g(x_k), g'(x_k)\n" ] }, { "data": { "text/plain": [ "17×3 Matrix{Float64}:\n", " 110000.0 1.0e8 20000.0\n", " 105000.0 2.5e7 10000.0\n", " 102500.0 6.25e6 5000.0\n", " 101250.0 1.5625e6 2500.0\n", " 100625.0 3.90624e5 1250.0\n", " 1.00313e5 97655.6 625.004\n", " 1.00156e5 24413.4 312.509\n", " 1.00078e5 6102.85 156.267\n", " 1.00039e5 1525.21 78.1591\n", " 1.0002e5 380.804 39.1307\n", " 1.0001e5 94.7036 19.6676\n", " 100005.0 23.1862 10.0372\n", " 1.00003e5 5.33626 5.41711\n", " 1.00002e5 0.970375 3.44696\n", " 1.00001e5 0.0792503 2.88392\n", " 1.00001e5 0.00075531 2.82896\n", " 1.00001e5 0.0 2.82843" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Note the rather slow convergence\n", "println(\"x_k, g(x_k), g'(x_k)\")\n", "hist = newton_hist(g, x -> 2*x + b[1], 1.1e5; tol=1e-14)" ] }, { "cell_type": "code", "execution_count": 6, "id": "dded298a-ede8-4568-9b8f-28333cd1a0ea", "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", "\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": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's plot the newton iterations\n", "plot(hist[:,1], hist[:,2], seriestype=:path, marker=:auto, label=\"\\$g(x_k)\\$\")\n", "plot!(g, title=\"Root $(hist[end,1])\", alpha=.5, label=\"\\$g(x)\\$\")\n", "plot!(zero, color=:black, label=:none)" ] }, { "cell_type": "markdown", "id": "e9abb500-a0b6-417b-ace8-cc17bb4f1926", "metadata": {}, "source": [ "* Convergence is slower than we've seen before\n", "\n", "* The solution is not nearly as accurate as machine precision" ] }, { "cell_type": "markdown", "id": "e6254f75-2442-4c74-a86f-7788e863409c", "metadata": {}, "source": [ "## Using [Polynomials](https://juliamath.github.io/Polynomials.jl/stable/)\n", "\n", "Julia has a package for evaluating and manipulating polynomials.\n", "Lets, use it instead of our own hand-rolled approach.\n", "\n", "
\n", "\n", "Note that the coefficients are given in the order $b_0 + b_1 x + b_2 x^2 + \\cdots$." ] }, { "cell_type": "code", "execution_count": 7, "id": "6670d275-3e51-4ea6-9e03-de87d62c7c92", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Defining roots (x - a_0)(x - a_1)...\n", "fpoly = fromroots([1, 2] .+ 100000.0) = Polynomial(1.0000300002e10 - 200003.0*x + 1.0*x^2)\n", "derivative(fpoly) = Polynomial(-200003.0 + 2.0*x)\n", "\n", "Defining coefficients b_0, b_1, ...\n", "gpoly = Polynomial([2, -3, 1]) = Polynomial(2 - 3*x + x^2)\n", "derivative(gpoly) = Polynomial(-3 + 2*x)\n" ] } ], "source": [ "using Polynomials\n", "\n", "# Here's how we'd call the equivelent of our two functions above\n", "println(\"Defining roots (x - a_0)(x - a_1)...\")\n", "@show fpoly = fromroots([1, 2] .+ 1e5)\n", "@show derivative(fpoly);\n", "\n", "println()\n", "println(\"Defining coefficients b_0, b_1, ...\")\n", "@show gpoly = Polynomial([2, -3, 1])\n", "@show derivative(gpoly);" ] }, { "cell_type": "code", "execution_count": 8, "id": "6cd78520-aa1f-4cc7-bfb3-08b0cdd823d9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "24×3 Matrix{Float64}:\n", " 300000.0 3.99994e10 399997.0\n", " 2.00001e5 9.99985e9 1.99999e5\n", " 1.50001e5 2.49996e9 99999.3\n", " 1.25001e5 6.24991e8 49999.6\n", " 1.12501e5 1.56248e8 24999.8\n", " 1.06251e5 3.90619e7 12499.9\n", " 1.03126e5 9.76548e6 6249.95\n", " 101564.0 2.44137e6 3124.98\n", " 1.00783e5 6.10342e5 1562.49\n", " 1.00392e5 1.52586e5 781.245\n", " 1.00197e5 38146.3 390.623\n", " 1.00099e5 9536.52 195.313\n", " 1.0005e5 2384.07 97.6589\n", " 1.00026e5 595.954 48.8346\n", " 1.00014e5 148.926 24.4275\n", " 1.00008e5 37.1691 12.2342\n", " 1.00005e5 9.2302 6.15799\n", " 1.00003e5 2.2467 3.16019\n", " 1.00002e5 0.505433 1.73831\n", " 1.00002e5 0.0845417 1.15679\n", " 100002.0 0.00534111 1.01063\n", " 100002.0 2.79307e-5 1.00006\n", " 100002.0 7.85803e-10 1.0\n", " 100002.0 0.0 1.0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# And we can feed this directly into our Newton function\n", "newton_hist(fpoly, derivative(fpoly), 3e5)" ] }, { "cell_type": "markdown", "id": "0def07da-2fc9-453e-9b98-14fdefbc68d1", "metadata": {}, "source": [ "## Finding *all* roots of polynomials" ] }, { "cell_type": "code", "execution_count": 9, "id": "baf1ead0-7af1-4eab-ac51-00d787b85754", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2-element Vector{Float64}:\n", " 99998.58579643762\n", " 100001.41422356237" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# There's a convenient function to call!\n", "roots(Polynomial([1e10, -2e5*(1 + 1e-10), 1]))" ] }, { "cell_type": "code", "execution_count": 10, "id": "9bd1083a-dc25-4650-abb0-3d7c2270322c", "metadata": {}, "outputs": [ { "data": { "image/png": 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color=:red)\n", "\n", "# Let's add little random perturbations and find the roots\n", "for i in 1:100\n", " r = randn(length(p)) # normally distributed mean 0, stddev 1\n", " q = copy(p)\n", " q[:] .*= 1 .+ 1e-10 * r\n", " xs = roots(q)\n", " scatter!(real(xs), imag(xs), markersize=1)\n", "end\n", "plot!(legend=:none)" ] }, { "cell_type": "markdown", "id": "6286626c-ed1d-4259-ab24-8a0fecd907ed", "metadata": {}, "source": [ "## [Fundamental Theorem of Algebra](https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra)\n", "\n", "Every non-zero, single-variable, degree $n$ polynomial with complex coefficients has, counted with multiplicity, exactly $n$ complex roots." ] }, { "cell_type": "markdown", "id": "e894c2c1-b6bf-4a44-a336-bd3cba02e09d", "metadata": {}, "source": [ "## Exploring - Wilkinson's polynomial\n", "\n", "Let's add more terms\n", "\n", "$$ w \\left( x \\right) = \\prod_{k = 1}^{20} \\left( x - k \\right) = \\left( x - 1 \\right) \\left( x - 2 \\right) \\cdots \\left( x - 20 \\right) = \\sum_{k = 0}^{20} b_k x^k $$" ] }, { "cell_type": "code", "execution_count": 11, "id": "c0026859-ded4-47e3-bbdf-2a09223a021a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" } }, "cell_type": "markdown", "id": "f9a71b9c-04b8-4ea7-a7fd-f38678a652fa", "metadata": {}, "source": [ "### Figure from Trefethen and Bau (1999)\n", "\n", "![image.png](attachment:78b75a91-2439-46bf-b073-eaa462c669d0.png)" ] }, { "cell_type": "markdown", "id": "41bb5a85-b23d-4a9f-8765-3a8c56e10bbc", "metadata": {}, "source": [ "## So which is better for modeling inputs to a rootfinder?\n", "\n", "A) coefficients $a_k$ in\n", "\n", "$$ p \\left( x \\right) = \\prod_k \\left( x - a_k \\right) $$\n", "\n", "B) coefficients $b_k$ in\n", "\n", "$$ p \\left( x \\right) = \\sum_k b_k x^k $$" ] }, { "attachments": { "fc8473cb-1760-4f04-9b70-4270618a4c2a.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "506d2aab-1cb3-4d26-820b-fa7aba4bfcbd", "metadata": {}, "source": [ "## Back to forward/backward error and stability\n", "\n", "See [FNC](https://tobydriscoll.net/fnc-julia/intro/stability.html#backward-error)\n", "\n", "![image2.png](attachment:fc8473cb-1760-4f04-9b70-4270618a4c2a.png)" ] }, { "cell_type": "markdown", "id": "221b4025-e3d0-4888-b880-a6c20dc6fcd8", "metadata": {}, "source": [ "### Stability\n", "\n", "**\"nearly the right answer to nearly the right question\"**\n", "\n", "$$ \\frac{\\left\\lvert \\tilde{f} \\left( x \\right) - f \\left( \\tilde{x} \\right) \\right\\rvert}{\\left\\lvert f \\left( \\tilde{x} \\right) \\right\\rvert} \\in \\mathcal{O} \\left( \\epsilon_\\text{machine} \\right) $$\n", "\n", "for some $\\tilde{x}$ that is close to $x$." ] }, { "cell_type": "markdown", "id": "bcf215e7-3900-455d-a376-9663298cb44f", "metadata": {}, "source": [ "### Backward stability\n", "\n", "**\"exactly the right answer to nearly the right question\"**\n", "\n", "$$ \\tilde{f} \\left( x \\right) = f \\left( \\tilde{x} \\right) $$\n", "\n", "for some $\\tilde{x}$ that is close to $x$.\n", "\n", "* Every backward stable algorithm is stable\n", "\n", "* Not every stable algorithm is backward stable" ] }, { "cell_type": "markdown", "id": "d91a7826-77f4-47ed-bc62-ad26bb31023d", "metadata": {}, "source": [ "### Example - mapping angle to the unit circle" ] }, { "cell_type": "code", "execution_count": 13, "id": "e8598272-40d0-4baa-be80-cf303eba91de", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"text": [ "GKS: Possible loss of precision in routine SET_WINDOW\n" ] } ], "source": [ "# The points on the unit circle *should* make a smooth curve\n", "theta = 1 .+ LinRange(0, 3e-15, 100)\n", "scatter(cos.(theta), sin.(theta), legend=:none, aspect_ratio=:equal)" ] }, { "cell_type": "code", "execution_count": 14, "id": "7866ef82-bc4b-49b1-b0a9-81261ce0f852", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"execute_result" } ], "source": [ "# Let's shift the range of the inputs for sin\n", "theta = LinRange(1., 1+2e-5, 100)\n", "mysin(t) = cos(t - (1e10+1)*pi/2)\n", "\n", "plot(cos.(theta), sin.(theta), aspect_ratio=:equal, label=\"1-1.00005\")\n", "scatter!(cos.(theta), mysin.(theta), label=\"shifted 10^10\")" ] }, { "cell_type": "markdown", "id": "c37787dd-c45d-4711-aaf1-09bdf74c715b", "metadata": {}, "source": [ "Is this\n", "\n", "a) stability\n", "\n", "b) backward stability\n", "\n", "c) neither\n", "\n", "* The numbers $\\left( \\tilde{\\cos} \\left( \\theta \\right), \\tilde{\\sin} \\left( \\theta \\right) \\right) = \\left( fl \\left( \\cos \\left( \\theta \\right) \\right), fl \\left( \\sin \\left( \\theta \\right) \\right) \\right)$ do not lie exactly on the unit circles\n", "\n", "* There does not exist a $\\tilde{\\theta}$ such that $\\left( \\tilde{\\cos} \\left( \\theta \\right), \\tilde{\\sin} \\left( \\theta \\right) \\right) = \\left( \\cos \\left( \\tilde{\\theta} \\right), \\sin \\left( \\tilde{\\theta} \\right) \\right)$" ] }, { "cell_type": "markdown", "id": "c1096859-9a94-46a2-b147-f1cfcd35e855", "metadata": {}, "source": [ "## Theorem - accuracy of backward stable algorithms\n", "\n", "A backward stable algorithm for computing $f \\left( x \\right)$ has relative accuracy\n", "\n", "$$ \\frac{\\left\\lvert \\tilde{f} \\left( x \\right) - f \\left( \\tilde{x} \\right) \\right\\rvert}{\\left\\lvert f \\left( \\tilde{x} \\right) \\right\\rvert} \\lesssim \\kappa \\left( f \\right) \\epsilon_\\text{machine} $$\n", "\n", "Backward stability is generally the best we can hope for.\n", "\n", "
\n", "\n", "In practice, it is rarely possible for a function to be backward stable when the output space is higher dimensional than the input space." ] } ], "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 }