{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diffusion 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": [
     5,
     7
    ]
   },
   "outputs": [],
   "source": [
    "# setup\n",
    "p = 2\n",
    "dimension = 1\n",
    "\n",
    "mesh = []\n",
    "if dimension == 1\n",
    "   mesh = Mesh1D(1.0)\n",
    "elseif dimension == 2\n",
    "   mesh = Mesh2D(1.0, 1.0)\n",
    "end\n",
    "\n",
    "# operator\n",
    "diffusion = GalleryOperator(\"diffusion\", p + 1, p + 1, mesh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     10,
     14,
     25,
     38,
     42,
     53
    ]
   },
   "outputs": [],
   "source": [
    "# compute 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",
    "# -- 1D --\n",
    "if dimension == 1\n",
    "    # compute\n",
    "    maxeigenvalues = zeros(numbersteps)\n",
    "\n",
    "    for i in 1:numbersteps\n",
    "        θ = [θ_range[i]]\n",
    "        A = computesymbols(diffusion, θ)\n",
    "        eigenvalues = [abs(val) for val in eigvals(A)]\n",
    "        maxeigenvalues[i] = max(eigenvalues...)\n",
    "        maxeigenvalue = max(maxeigenvalue, maxeigenvalues[i])\n",
    "    end\n",
    "\n",
    "    # plot\n",
    "    println(\"max eigenvalue: \", maxeigenvalue)\n",
    "    xrange = θ_range/π\n",
    "    plot(\n",
    "        xrange,\n",
    "        xlabel=\"θ/π\",\n",
    "        xtickfont=font(12, \"Courier\"),\n",
    "        maxeigenvalues,\n",
    "        ytickfont=font(12, \"Courier\"),\n",
    "        ylabel=\"spectral radius\",\n",
    "        linewidth=3,\n",
    "        legend=:none,\n",
    "        title=\"Mass Operator Symbol\"\n",
    "    )\n",
    "    ylims!(0.0, max(maxeigenvalues...) * 1.1)\n",
    "# -- 2D --\n",
    "elseif dimension == 2\n",
    "    # compute\n",
    "    maxeigenvalues = zeros(numbersteps, numbersteps)\n",
    "\n",
    "    for i in 1:numbersteps, j in 1:numbersteps\n",
    "        θ = [θ_range[i], θ_range[j]]\n",
    "        A = computesymbols(diffusion, 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",
    "\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",
    "        maxeigenvalues,\n",
    "        ytickfont=font(12, \"Courier\"),\n",
    "        title=\"Mass Operator 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)\n",
    "end"
   ]
  }
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