{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "57a2b335-a7f3-4ace-a2d8-52219c4febc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"thinQR.jl\")\n",
    "using .thinQR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "afd34800-7b9a-4006-9849-071fa197d962",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [5.810770900369532e-16, 0.4999999999999994]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 0.9999999999999993\n",
       " 1.9999999999999993\n",
       " 2.999999999999999"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra: \\, qr\n",
    "A = [1. 2.; 3. 4.; 5. 6.]\n",
    "(Q, R) = qr(A)\n",
    "x = A \\ [1., 2, 3]\n",
    "@show x\n",
    "A * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8b3d71f8-2f4f-44f0-8c97-dd9d78706163",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " -1.5012955407352218e-16\n",
       "  0.5000000000000001"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [1. 2; 3. 4.; 5. 6.]\n",
    "A = qrhous!(A)\n",
    "b = [1., 2, 3]\n",
    "x = A \\ b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1883485c-b026-4a8a-8c34-b7c74ad79868",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 0.9999999999999991\n",
       " 1.9999999999999996\n",
       " 2.9999999999999996"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * x"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.3",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}