{ "cells": [ { "cell_type": "markdown", "id": "b3b7bd81-52fb-487d-84a6-f396136d6cc2", "metadata": {}, "source": [ "# 2025-09-22 Gram-Schmidt\n", "\n", "* Revisit projections, rotations, and reflections\n", "\n", "* Constructing orthogonal bases\n", "\n", "* QR factorization" ] }, { "cell_type": "code", "execution_count": 1, "id": "3c5d83a7-2925-456d-b8c9-2e056a00403a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "vander (generic function with 2 methods)" ] }, "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" ] }, { "cell_type": "markdown", "id": "2bf69f06-f6c0-45c4-b8ad-dc7dd95195b3", "metadata": {}, "source": [ "## Polynomials can be orthogonal too" ] }, { "cell_type": "code", "execution_count": 2, "id": "94e5c095-0bce-44ab-960f-a48ac86a34c8", "metadata": {}, "outputs": [ { "data": { "image/png": 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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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": [ "x = LinRange(-1, 1, 50)\n", "A = vander(x, 4)\n", "M = A * [.5 0 0 0; # 0.5\n", " 0 1 0 0; # x\n", " 0 0 1 0]' # x^2\n", "\n", "scatter(x, M, label=[\"\\$0.5\\$\" \"\\$x\\$\" \"\\$x^2\\$\"])\n", "plot!(x, 0*x, label=:none, color=:black)" ] }, { "cell_type": "markdown", "id": "7fc4dd74-a2d3-439f-ae85-7a07a99bc0bd", "metadata": {}, "source": [ "Which inner products will be zero?\n", "\n", "Which functions are even and odd?" ] }, { "cell_type": "markdown", "id": "557f17fb-cf68-4d7f-b6aa-6eb8b4c3b74d", "metadata": {}, "source": [ "## Pairwise inner product\n", "\n", "The pairwise inner products between two sets of vectors can be expressed by collecting the sets as columns in matrices and writing $A = X^T Y$, where $A_{i, j} = x_i^T y_j$.\n", "It follows from this definition that\n", "\n", "$$ \\left( X^T Y \\right)^T = Y^T X $$" ] }, { "cell_type": "code", "execution_count": 3, "id": "8564dd60-ed7f-4da8-905d-962ce8981ae4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(M' * M)' == M' * M = true\n" ] }, { "data": { "text/plain": [ "3×3 Matrix{Float64}:\n", " 12.5 -1.11022e-15 8.67347\n", " -1.11022e-15 17.3469 -2.22045e-16\n", " 8.67347 -2.22045e-16 10.8272" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's verify this\n", "@show (M' * M)' == M' * M\n", "M' * M" ] }, { "cell_type": "markdown", "id": "9f7ad032-df8d-44aa-a6c1-0c0a76ecaabe", "metadata": {}, "source": [ "## Normalization and orthogonalization" ] }, { "cell_type": "code", "execution_count": 4, "id": "d4c0d721-5b0c-4636-a4a9-5112db37f6de", "metadata": {}, "outputs": [ { "data": { "image/png": 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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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": [ "# Let's normalize the first column\n", "q1 = M[:, 1]\n", "q1 /= norm(q1)\n", "\n", "# and then plot the new function\n", "Q = [q1 M[:, 2:end]]\n", "scatter(x, Q)" ] }, { "cell_type": "code", "execution_count": 5, "id": "e170c79b-f8de-4e58-8815-4e8a39d7879c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3×3 Matrix{Float64}:\n", " 1.0 -1.94289e-16 2.45323\n", " -1.94289e-16 17.3469 -2.22045e-16\n", " 2.45323 -2.22045e-16 10.8272" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This should still be symmetric\n", "Q' * Q" ] }, { "cell_type": "markdown", "id": "2e090bf2-3a90-41c1-9bbe-f4f61d409dc5", "metadata": {}, "source": [ "## Orthogonal matrices\n", "\n", "If $x^T y = 0$, then we say $x$ and $y$ are **orthogonal** (or $x$ is orthogonal to $y$).\n", "\n", "A vector is said to be **normalized** if $\\left\\lvert \\left\\lvert x \\right\\rvert \\right\\rvert = 1$.\n", "\n", "If $x$ is orthogonal to $y$ and $\\left\\lvert \\left\\lvert x \\right\\rvert \\right\\rvert = \\left\\lvert \\left\\lvert y \\right\\rvert \\right\\rvert = 1$, then we say $x$ and $y$ are **orthogonal**.\n", "\n", "A square matrix with orthonormal columns is said to be an **orthogonal matrix**.\n", "\n", "We typically use $Q$ or $U$ and $V$ for matrices that are know/constructed to be orthogonal.\n", "Orthogonal matrices are always full rank - the columns are linearly independent.\n", "The inverse of a orthogonal matrix is its transpose.\n", "\n", "$$ Q^T Q = Q Q^T = I $$\n", "\n", "Orthogonal matrices are a powerful building block for robust numerical algorithms." ] }, { "cell_type": "markdown", "id": "a9e0d0ce-cf1a-4cd0-a56b-e0886ccc19d9", "metadata": {}, "source": [ "## Gram-Schmidt orthogonalization\n", "\n", "Suppose we're given some vectors and want to find an orthogonal basis for their span.\n", "\n", "$$ A = \\begin{split} \\Bigg[ a_1 \\Bigg| a_2 \\Bigg] = \\Bigg[ q_1 \\Bigg| q_2 \\Bigg] \\begin{bmatrix} r_{11} & r_{12} \\\\ 0 & r_{22} \\end{bmatrix} \\end{split} = Q R$$" ] }, { "cell_type": "markdown", "id": "700ea717-5276-44e8-9410-2fae8af20b07", "metadata": {}, "source": [ "## A naive Gram-Schmidt algorithm" ] }, { "cell_type": "code", "execution_count": 6, "id": "c53d6b48-d3fb-4a31-9913-8eb50d68f2dc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gram_schmidt_naive (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's form Q and R by making each column orthonormal to all previous columns\n", "function gram_schmidt_naive(A)\n", " m, n = size(A)\n", " Q = zeros(m, n) # Orthonormal basis\n", " R = zeros(n, n) # Upper triangular\n", " for j in 1:n\n", " v = A[:, j] # current column to normalize\n", " for k in 1:j-1\n", " # We do a projection against the previous columns of Q. Why?\n", " r = Q[:, k]' * v \n", " v -= Q[:, k] * r\n", " R[k, j] = r # What is this factor?\n", " end\n", " # normalize and store our final v\n", " R[j, j] = norm(v)\n", " Q[:, j] = v / R[j, j]\n", " end\n", " Q, R\n", "end" ] }, { "cell_type": "code", "execution_count": 7, "id": "c7d63f22-63fe-4c70-829b-c151f0751414", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(Q' * Q - I) = 1.0245877047652434e-15\n", "norm(Q * R - A) = 4.3681794554507014e-16\n" ] } ], "source": [ "# Let's try it with the Vandermonde matrix\n", "A = vander(x, 4)\n", "Q, R = gram_schmidt_naive(A)\n", "\n", "# Check this is valid\n", "@show norm(Q' * Q - I)\n", "@show norm(Q * R - A);" ] }, { "cell_type": "markdown", "id": "c804e332-985c-42b8-8a7a-e42171d9206c", "metadata": {}, "source": [ "## What do orthogonal polynomials look like" ] }, { "cell_type": "code", "execution_count": 8, "id": "88b6fb1e-08b6-4e6d-be41-60785a09880a", "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" ], "text/html": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's look at 6 orthonormal polynomials\n", "x = LinRange(-1, 1, 50)\n", "A = vander(x, 6)\n", "Q, R = gram_schmidt_naive(A)\n", "plot(x, Q, legend=:none)" ] }, { "cell_type": "markdown", "id": "14684df8-54c1-4aa3-a4e7-924799a2da91", "metadata": {}, "source": [ "What happen if we use more than $50$ values of $x$?\n", "Is there a continuous limit?" ] }, { "cell_type": "markdown", "id": "39258c1d-62c3-4e78-b81c-b5af44b172fb", "metadata": {}, "source": [ "## Theorem\n", "\n", "Every full-rank $m \\times n$ matrix ($m \\geq n$) has a unique reduced $QR$ factorization with $R_{j, j} > 0$.\n", "\n", "The algorithm we're using generates this matrix due to the line:\n", "\n", "```julia\n", " R[j,j] = norm(v)\n", "```" ] }, { "cell_type": "markdown", "id": "d4a486f8-0414-43f1-8625-998b712db952", "metadata": {}, "source": [ "## Solving equations with $QR$\n", "\n", "If $A x = b$, then $R x = Q^T b$." ] }, { "cell_type": "code", "execution_count": 9, "id": "5546ca96-f002-4e87-ba8c-6c536e244ab9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p = [3.352100840336134, -9.476050420168065, -1.747899159663866, 12.98319327731092]\n" ] }, { "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" ], "text/html": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's fit a polynomial to these points\n", "x1 = [-0.9, 0.1, 0.5, 0.8]\n", "y1 = [1, 2.4, -0.2, 1.3]\n", "scatter(x1, y1, label=\"data\")\n", "\n", "Q, R = gram_schmidt_naive(vander(x1, 4))\n", "p = R \\ (Q' * y1) # Using \\ to solve R^-1, easy for upper triangular\n", "@show p\n", "plot!(x, vander(x, 4) * p, label=\"\\$R^{-1}Q^Tb\\$\")" ] }, { "cell_type": "markdown", "id": "bce164da-0616-4815-981e-0ebb718d678e", "metadata": {}, "source": [ "## How accurate is the result?" ] }, { "cell_type": "code", "execution_count": 10, "id": "3e505731-4a92-43aa-a0d3-572217f980b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(Q' * Q - I) = 7.868453407006443e-9\n", "norm(Q * R - A) = 7.6178704465113005e-16\n" ] } ], "source": [ "m = 20\n", "x = LinRange(-1, 1, m)\n", "A = vander(x, m)\n", "Q, R = gram_schmidt_naive(A)\n", "\n", "@show norm(Q' * Q - I)\n", "@show norm(Q * R - A);" ] }, { "cell_type": "markdown", "id": "a5392621-2419-4e4f-8305-e5b7582a4466", "metadata": {}, "source": [ "## A variant with more parallelism\n", "\n", "$$ q_2 q_2^T \\left( q_1 q_1^T v \\right) = q_2 \\left( q_2^T q_1 \\right) q_1^T v = 0 $$" ] }, { "cell_type": "code", "execution_count": 11, "id": "527936f2-3a92-4ce2-9fac-af2b9769794f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gram_schmidt_classical (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's form Q and R by making each column orthonormal to all previous columns\n", "function gram_schmidt_classical(A)\n", " m, n = size(A)\n", " # Same setup as our naive version\n", " Q = zeros(m, n)\n", " R = zeros(n, n)\n", " for j in 1:n\n", " v = A[: ,j]\n", " # Here we make the current column othogonal to all previous\n", " R[1:j-1, j] = Q[:, 1:j-1]' * v\n", " v -= Q[:, 1:j-1] * R[1:j-1, j]\n", " # And normalize the result\n", " R[j, j] = norm(v)\n", " Q[:, j] = v / norm(v)\n", " end\n", " Q, R\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "id": "006ca2d4-59cd-4e72-b89e-82a62e8886b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm(Q' * Q - I) = 1.5098459477938957\n", "norm(Q * R - A) = 8.582718086704977e-16\n" ] } ], "source": [ "m = 20\n", "x = LinRange(-1, 1, m)\n", "A = vander(x, m)\n", "Q, R = gram_schmidt_classical(A)\n", "\n", "@show norm(Q' * Q - I)\n", "@show norm(Q * R - A);" ] } ], "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 }