{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a812668f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ChatGPT wrote this basedon the prompt\n",
    "# I'm teaching a class in computational optimization that wants a demo of sparse direct methods. Can you come up with a fun Julia example to show off a sparse lu or cholesky factorization. Maybe throw in a few spy plots to illustrate the sparsity patterns of the factors and the fill in? \n",
    "\n",
    "using SparseArrays\n",
    "using LinearAlgebra\n",
    "using SuiteSparse\n",
    "using Plots\n",
    "\n",
    "# Create a 2D finite difference Laplacian matrix on an n x n grid\n",
    "\n",
    "function poisson_2d(n)\n",
    "    e = ones(n)\n",
    "    T = spdiagm(-1 => -e, 0 => 2e, 1 => -e)\n",
    "    I = spdiagm(0 => ones(n))\n",
    "    return kron(I, T) + kron(T, I)\n",
    "end\n",
    "\n",
    "# Visualize the sparsity pattern\n",
    "function spyplot(A, title_str)\n",
    "    spy(A, markersize=1)\n",
    "    title!(title_str)\n",
    "end\n",
    "\n",
    "n = 10            # Grid size, gives n^2 x n^2 matrix\n",
    "A = poisson_2d(n)  # Sparse symmetric positive definite matrix\n",
    "\n",
    "spyplot(A, \"original\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8ead13bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparseArrays.CHOLMOD.FactorComponent{Float64, :L, Int64}\n",
       "type:    LLt\n",
       "method:  simplicial\n",
       "maxnnz:  783\n",
       "nnz:     783\n",
       "success: true\n"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cholesky factorization\n",
    "F = cholesky(A + I)\n",
    "L = F.L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e82a29e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "783"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nnz(sparse(L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "78ad8b9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spyplot(sparse(L), \"Cholesky Factor L (with Fill-In)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "49033a1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what happens without the ordering\n",
    "Fdense = cholesky(Matrix(A+I)) \n",
    "spyplot(sparse(Fdense.U),\"dense cholesky\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e5925853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1119"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nnz(sparse(Fdense.U))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "403eb9a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# LU factorization (non-symmetric version for fun)\n",
    "    A_nonsym = copy(A)\n",
    "    A_nonsym[1, end] = 0.1  # Break symmetry\n",
    "    F_lu = lu(A_nonsym)\n",
    "\n",
    "    # Show LU factors\n",
    "    plot(layout=(1,2), size=(800,400))\n",
    "    plot!(spy(sparse(F_lu.L), markersize=1), title=\"LU Factor L\")\n",
    "    plot!(spy(sparse(F_lu.U), markersize=1), title=\"LU Factor U\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0b8aeb8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(spy(sparse(F_lu.L)), spy(sparse(F_lu.U)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "60dd5db8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "300×300 SparseMatrixCSC{Float64, Int64} with 3023 stored entries:\n",
       "⎡⠀⡨⠲⢮⢥⠓⡐⡀⠄⣷⡉⢀⢢⡛⢚⡰⡞⢧⢨⡒⣇⠼⡺⢶⡈⡃⠗⣠⣠⡂⠂⢲⣦⢰⡐⡤⠦⢈⠄⠥⎤\n",
       "⎢⡤⣡⠁⢅⢅⢪⡏⣊⢰⠇⠐⠯⣊⠬⣊⡴⣦⣙⡢⡮⡧⡹⠉⡦⡷⡢⣣⠅⠴⠛⠎⠤⠆⡡⡡⢧⠐⢈⡁⡄⎥\n",
       "⎢⠤⠧⠈⡁⠋⣶⡈⠞⣕⠘⠈⡁⢨⠪⢅⠆⠦⢠⠄⢆⠑⢉⣊⢄⡡⡁⣂⢌⠌⠜⠰⢀⢀⡞⢑⢆⣊⢸⡋⠑⎥\n",
       "⎢⢀⢂⡂⢡⠏⡠⠿⠀⣒⡄⠃⡞⢳⢤⠝⣉⡟⢕⠠⣒⠚⠃⣀⡂⠔⡰⠀⡈⠋⢪⣌⠏⣀⢋⠩⡤⡅⢻⣃⢂⎥\n",
       "⎢⣭⠠⡮⡰⣌⠜⠂⢈⡡⢊⠇⢋⢗⣩⠉⠘⠝⡺⠷⠐⣅⠐⠪⢖⡫⡂⡀⣂⣽⢐⢒⣒⠄⠞⣒⠂⢀⠚⢉⠄⎥\n",
       "⎢⠂⠅⠁⠩⢏⠓⡷⠋⣱⡄⠍⠦⡢⣥⢶⠩⢟⠞⠢⠔⡃⠏⠈⢅⢝⢵⡾⡁⠢⢘⢙⢔⡍⡅⠡⠩⡃⠝⢉⠂⎥\n",
       "⎢⠢⠋⡡⣓⡊⠐⣉⣀⠜⣧⢞⡐⡾⢧⠀⡦⠢⢔⣂⡄⡠⠻⢕⠆⣃⠉⡖⡎⡠⡧⠤⢍⡠⠹⣲⠣⣇⡐⣿⡃⎥\n",
       "⎢⢰⢭⢑⠲⡉⠥⣼⢰⠠⠏⠆⡓⠲⠀⠄⠗⢁⣇⠃⡨⠸⣡⡕⢃⠔⡄⠥⠗⠜⣐⠠⡔⢀⣸⡐⢢⢁⢀⠗⠍⎥\n",
       "⎢⠠⡊⢣⢈⢜⠤⣀⢘⢌⣡⡢⠀⠃⢒⠭⢡⣀⢐⢁⠩⡘⡾⢄⠌⠤⠑⣡⡈⢩⠕⡘⡒⠢⠧⠗⢀⡏⢂⢲⠐⎥\n",
       "⎢⣨⡤⢄⠉⡧⠵⠠⢺⠮⡀⢁⣘⠓⡵⣅⡄⡧⡀⢀⠂⠄⠄⡕⢌⢂⣋⠿⣀⠀⢀⠐⡳⡈⡃⡘⢨⠦⠈⣲⡆⎥\n",
       "⎢⣙⡑⡁⢨⡒⢀⠀⢀⡃⡒⠞⣑⢫⠑⢍⠕⡏⢛⢈⡈⢇⢉⣐⣈⢸⡘⠁⠒⢊⠂⣀⡠⢓⠍⣢⣘⡆⢹⡈⠄⎥\n",
       "⎢⢂⢝⡵⠸⣃⢡⡚⡀⣘⡏⠉⡒⠮⣬⡙⡋⠂⢙⡐⣐⡦⡃⣂⢕⢖⠁⠇⢩⠤⡇⠁⢑⠅⢝⢒⢑⢊⣣⡄⠁⎥\n",
       "⎢⢤⠠⢀⠐⢂⠈⠌⡈⠕⢀⠌⠀⡈⠙⣰⢎⢗⣸⠣⠩⠊⡢⡃⠭⠟⢇⠊⠕⠐⣄⠠⠰⠘⣠⠌⢋⠈⢨⡌⡃⎥\n",
       "⎢⠑⠄⢠⠊⡐⢞⢜⣈⣊⠃⢩⠞⡄⢆⠉⠃⡊⢽⢌⣌⠈⠢⢓⡽⠄⠻⢇⢄⠢⢎⢓⢁⣟⡆⡣⠆⠰⠐⠃⢣⎥\n",
       "⎢⠎⠤⠄⣺⣀⣬⢸⢢⢰⢆⢵⡰⡆⣽⠝⠣⠥⢿⡆⠨⣧⠑⠐⠧⢯⡈⠄⡤⠨⠁⣑⠲⡇⡆⣗⠡⣅⢂⠀⡃⎥\n",
       "⎢⡊⢨⢙⡀⢃⣤⡂⠌⢄⢠⡚⠥⢅⢈⠁⠪⠫⣌⢷⡡⠧⠔⢇⣔⠐⢽⢣⣇⢐⣄⣠⡈⡁⠬⢿⠈⣑⠄⡢⢄⎥\n",
       "⎢⡾⢔⢣⡈⢀⠂⡫⢄⣸⠜⣝⠥⡰⠸⠢⠡⡑⠢⠣⡀⡠⠄⠈⠝⣘⡂⡭⠵⡸⠚⡔⠈⡹⢑⣒⠈⢋⡂⣥⡁⎥\n",
       "⎢⢈⢮⠀⣂⢂⠪⢀⢴⠉⢃⠕⢃⣄⡜⡰⠴⠣⣬⠞⡣⣡⡘⠘⠲⡰⣡⣉⡘⠰⠐⢈⣂⢢⠆⣺⠒⠍⢦⢪⠢⎥\n",
       "⎢⢣⢐⠗⠚⡅⠒⢬⠤⠢⡁⢂⢅⠀⠙⢽⠽⠇⡀⢦⡤⠄⠨⡳⠋⠘⠟⠢⠥⢰⡂⣕⠱⠊⠩⡁⢀⡒⠐⡊⠅⎥\n",
       "⎣⡢⠿⠅⠩⠋⠚⢘⡄⠇⠂⠦⢶⠼⠌⢛⠘⣨⡼⠌⠃⠘⠄⢌⠟⡎⠰⠨⣡⡪⢗⢆⡒⣪⡁⣬⠁⠆⣔⡤⠀⎦"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Abad = sprand(300,300,10/300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "867bfde0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "300×300 SparseMatrixCSC{Float64, Int64} with 19062 stored entries:\n",
       "⎡⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤\n",
       "⎢⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠄⡄⢊⠵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⢑⠠⢐⠀⠉⠨⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠠⢬⠐⠤⠀⠄⠡⠄⡵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠁⠐⠸⠥⢴⠤⣒⡝⢭⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⡂⠚⢉⢠⣀⠡⠸⣠⣒⢼⢱⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠜⢑⠐⣴⢂⣣⣚⠲⣽⣭⣳⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠁⣡⢁⣨⡄⡙⡬⣡⡉⣫⣉⣫⣽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⡠⡆⢀⠉⠇⠦⡭⡩⣼⢧⡦⡵⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⢐⠈⢦⠠⠩⠱⠊⢐⢚⣳⡼⠛⢟⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠈⢒⠀⣧⠀⠭⡏⢟⣢⣾⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠠⣥⠥⠒⠒⠗⠛⣬⢚⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⢦⡐⢀⠋⠄⣃⡢⣾⠟⡗⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠄⢈⡭⢀⠪⡶⢼⠨⡧⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⢀⢀⠘⡡⢠⣀⣮⢠⣻⠡⣥⣦⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠡⡔⠡⣀⠠⠊⡬⠃⢽⣩⡠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⡀⢣⢀⠳⡐⢩⡀⡣⡉⠜⡅⣟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⎥\n",
       "⎢⠔⠀⠊⡠⠠⣈⣸⠀⡇⣴⣵⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⎥\n",
       "⎣⠐⣂⡄⠨⠊⢟⡮⢭⠻⢿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⎦"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_bad = lu(Abad+10I)\n",
    "#plot(spy(sparse(F_lu.L)), spy(sparse(F_lu.U)))\n",
    "F_bad.L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4fcd7522",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10100×10100 SparseMatrixCSC{Float64, Int64} with 50099 stored entries:\n",
       "⎡⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤\n",
       "⎢⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⎥\n",
       "⎣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "n = 100            # Grid size, gives n^2 x n^2 matrix\n",
    "Abig = poisson_2d(n)  # Sparse symmetric positive definite matrix\n",
    "\n",
    "Abig "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c2ac1b13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10100×10100 SparseMatrixCSC{Float64, Int64} with 373145 stored entries:\n",
       "⎡⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤\n",
       "⎢⣀⣘⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⢈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠠⠄⠸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠠⠄⠤⠠⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠂⠒⠒⠒⠚⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠷⣄⠀⠀⠀⠀⎥\n",
       "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⢀⣀⣀⣘⣳⣄⠀⠀⎥\n",
       "⎣⣠⣤⢤⣤⠴⠶⠶⠦⢤⣶⣖⡦⠴⠖⠆⠐⠶⠒⢲⠿⠿⠛⠛⠻⠿⣡⣿⠛⠛⠉⠛⠚⢉⡁⣓⡚⠉⢘⣷⣄⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fbig = cholesky(Abig+I)\n",
    "sparse(Fbig.L)"
   ]
  }
 ],
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   "name": "julia-1.11"
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   "file_extension": ".jl",
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   "name": "julia",
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