{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lumped BDDC Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dependencies\n",
    "using LFAToolkit\n",
    "using LinearAlgebra\n",
    "using Pkg\n",
    "Pkg.activate(\"./\")\n",
    "Pkg.instantiate()\n",
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "# setup\n",
    "p = 3\n",
    "mesh = Mesh2D(1.0, 1.0)\n",
    "\n",
    "# diffusion operator\n",
    "diffusion = GalleryOperator(\"diffusion\", p + 1, p + 1, mesh)\n",
    "\n",
    "# bddc smoother\n",
    "bddc = LumpedBDDC(diffusion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     14,
     16,
     27
    ],
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# full operator symbols\n",
    "numbersteps = 250\n",
    "maxeigenvalue = 0\n",
    "θ_min = -π/2\n",
    "θ_max = 3π/2\n",
    "θ_step = 2π/(numbersteps-1)\n",
    "θ_range = θ_min:θ_step:θ_max\n",
    "\n",
    "# compute and plot smoothing factor\n",
    "# setup\n",
    "ω = [0.2]\n",
    "maxeigenvalues = zeros(numbersteps, numbersteps)\n",
    "\n",
    "# compute\n",
    "for i in 1:numbersteps, j in 1:numbersteps\n",
    "    θ = [θ_range[i], θ_range[j]]\n",
    "    if sqrt(abs(θ[1])^2 + abs(θ[2])^2) > π/128\n",
    "        A = computesymbols(bddc, ω, θ)\n",
    "        eigenvalues = [abs(val) for val in eigvals(A)]\n",
    "        maxeigenvalues[i, j] = max(eigenvalues...)\n",
    "        maxeigenvalue = max(maxeigenvalue, maxeigenvalues[i, j])\n",
    "    end\n",
    "end\n",
    "\n",
    "# plot\n",
    "println(\"max eigenvalue: \", maxeigenvalue)\n",
    "xrange = θ_range/π\n",
    "heatmap(\n",
    "    xrange,\n",
    "    xlabel=\"θ/π\",\n",
    "    xtickfont=font(12, \"Courier\"),\n",
    "    xrange,\n",
    "    ylabel=\"θ/π\",\n",
    "    ytickfont=font(12, \"Courier\"),\n",
    "    maxeigenvalues,\n",
    "    title=\"Lumped BDDC Error Symbol\",\n",
    "    transpose=true,\n",
    "    aspect_ratio=:equal\n",
    ")\n",
    "xlims!(θ_min/π, θ_max/π)\n",
    "ylims!(θ_min/π, θ_max/π)"
   ]
  }
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