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