Added Project and Report
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elvis
176
project/testing/QR/QR.ipynb
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176
project/testing/QR/QR.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "57a2b335-a7f3-4ace-a2d8-52219c4febc5",
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"metadata": {},
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"outputs": [],
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"source": [
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"include(\"../../QR/housQR.jl\")\n",
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"include(\"../../utilities/genFunc.jl\")\n",
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"using .housQR\n",
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"using LinearAlgebra, BenchmarkTools, CSV, DataFrames\n",
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"\n",
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"baseDir = joinpath(\"../\", \"results/QR\")\n",
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"mkpath(baseDir);"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "356e3edd",
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"metadata": {},
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"outputs": [],
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"source": [
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"### time with respect to lambda\n",
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"\n",
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"# parameters\n",
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"lambdas = 10. .^(-15:6)\n",
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"epss = [nothing]\n",
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"m = 300\n",
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"n = 20\n",
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"\n",
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"\n",
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"# output csv\n",
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"outputvsc = joinpath(baseDir, \"statisticsQR-lambda-m\" * string(m) * \"n\" * string(n) * \"--time.csv\");\n",
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"accData = Dict(\n",
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" :lambda => Array{Float64}(undef, 0),\n",
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" :meantime => Array{Float64}(undef, 0),\n",
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" :stdtime => Array{Float64}(undef, 0)\n",
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" )\n",
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"\n",
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"# computation\n",
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"for (λ, ϵ) ∈ Iterators.product(lambdas, epss) |> collect\n",
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" gf = genFunc(:exactRandDataset, λ=λ, m=m, n=n)\n",
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"\n",
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" t = @benchmark begin\n",
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" QR = qrfact($gf[:X_hat])\n",
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" w = QR \\ $gf[:y_hat]\n",
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" end\n",
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"\n",
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" push!(accData[:lambda], λ)\n",
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" push!(accData[:meantime], mean(t.times))\n",
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" push!(accData[:stdtime], std(t.times))\n",
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" println(\"Done: λ \" * string(λ))\n",
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" flush(stdout)\n",
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"end\n",
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"\n",
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"CSV.write(outputvsc, DataFrame(accData));"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8b3d71f8-2f4f-44f0-8c97-dd9d78706163",
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"metadata": {},
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"outputs": [],
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"source": [
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"### error with respect to lambda\n",
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"\n",
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"# parameters\n",
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"lambdas = 10. .^(-15:6)\n",
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"epss = [nothing]\n",
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"m = 300\n",
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"n = 20\n",
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"\n",
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"\n",
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"# output csv\n",
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"outputvsc = joinpath(baseDir, \"statisticsQR-lambda-m\" * string(m) * \"n\" * string(n) * \"--error.csv\");\n",
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"accData = Dict(\n",
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" :lambda => Array{Float64}(undef, 0),\n",
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" :relative => Array{Float64}(undef, 0),\n",
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" :residual => Array{Float64}(undef, 0),\n",
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" :stability => Array{Float64}(undef, 0)\n",
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" )\n",
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"\n",
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"# computation\n",
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"for (λ, ϵ) ∈ Iterators.product(lambdas, epss) |> collect\n",
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" gf = genFunc(:exactRandDataset, λ=λ, m=m, n=n)\n",
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"\n",
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" QR = qrfact(gf[:X_hat])\n",
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" w = QR \\ gf[:y_hat]\n",
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" \n",
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" relative_error = norm(w - gf[:w_star]) / norm(gf[:w_star])\n",
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" residual = norm(gf[:X_hat] * w - gf[:y_hat]) / norm(gf[:y_hat])\n",
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" stability = norm(Q_times_R - gf[:X_hat]) / norm(gf[:X_hat])\n",
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"\n",
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" push!(accData[:lambda], λ)\n",
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" push!(accData[:relative], relative_error)\n",
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" push!(accData[:residual], residual)\n",
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" push!(accData[:stability], stability)\n",
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" println(\"Done: λ \" * string(λ))\n",
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" flush(stdout)\n",
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"end\n",
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"\n",
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"CSV.write(outputvsc, DataFrame(accData));"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "387520b7",
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"metadata": {},
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"outputs": [],
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"source": [
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"### error with respect to lambda\n",
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"\n",
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"# parameters\n",
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"lambdas = 10. .^(-15:6)\n",
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"epss = [nothing]\n",
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"m = 300\n",
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"n = 20\n",
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"perturbation = 1e-10\n",
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"\n",
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"\n",
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"# output csv\n",
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"outputvsc = joinpath(baseDir, \"statisticsQR-forward-m\" * string(m) * \"n\" * string(n) * \"--error.csv\");\n",
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"accData = Dict(\n",
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" :lambda => Array{Float64}(undef, 0),\n",
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" :forwardQ => Array{Float64}(undef, 0),\n",
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" :forwardR => Array{Float64}(undef, 0),\n",
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" )\n",
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"\n",
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"# computation\n",
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"for (λ, ϵ) ∈ Iterators.product(lambdas, epss) |> collect\n",
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" gf = genFunc(:exactRandDataset, λ=λ, m=m, n=n)\n",
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"\n",
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" QR = qrfact(gf[:X_hat])\n",
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" w = QR \\ gf[:y_hat]\n",
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"\n",
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" X_hat_p = gf[:X_hat] + perturbation * randn(size(gf[:X_hat]))\n",
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" cond(gf[:X_hat]) |> display\n",
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" # cond(X_hat_p) |> display\n",
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" QR_p = qrfact(X_hat_p)\n",
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"\n",
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" forwardQ = norm(QR.Q - QR_p.Q)\n",
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" forwardR = norm(QR.R - QR_p.R) / norm(QR.R)\n",
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"\n",
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" push!(accData[:lambda], λ)\n",
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" push!(accData[:forwardQ], forwardQ)\n",
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" push!(accData[:forwardR], forwardR)\n",
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"\n",
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" println(\"Done: λ \" * string(λ))\n",
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" flush(stdout)\n",
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"end\n",
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"\n",
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"CSV.write(outputvsc, DataFrame(accData));"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.9.3",
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"language": "julia",
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"name": "julia-1.9"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.9.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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