{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# This file is part of nannos\n# License: GPLv3\n%matplotlib notebook"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Convergence\n\nConvergence of the various FMM formulations.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\n\nimport nannos as nn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We will study the convergence on a benchmark case from\n:cite:p:`Li1997`.\nFirst we define the main function that performs the simulation.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def checkerboard(nh, formulation):\n    la = 1\n    d = 2 * 1.25 * la\n    Nx = 2**9\n    Ny = 2**9\n    lattice = nn.Lattice(([d, 0], [0, d]), discretization=(Nx, Ny))\n    pw = nn.PlaneWave(wavelength=la, angles=(0, 0, 0))\n    epsgrid = lattice.ones() * 2.25\n    sq1 = lattice.square((0.25 * d, 0.25 * d), 0.5 * d)\n    sq2 = lattice.square((0.75 * d, 0.75 * d), 0.5 * d)\n    epsgrid[sq1] = 1\n    epsgrid[sq2] = 1\n\n    sup = lattice.Layer(\"Superstrate\", epsilon=2.25)\n    sub = lattice.Layer(\"Substrate\", epsilon=1)\n    st = lattice.Layer(\"Structured\", la)\n    st.epsilon = epsgrid\n\n    sim = nn.Simulation([sup, st, sub], pw, nh, formulation=formulation)\n    order = (\n        -1,\n        -1,\n    )  # this actually corresponds to order (0,-1) for the other unit cell in [Li1997]\n    R, T = sim.diffraction_efficiencies(orders=True)\n    t = sim.get_order(T, order)\n    return R, T, t, sim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Perform the simulation for different formulations and number\nof retained harmonics:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "NH = [100, 200, 300, 400, 600]\nformulations = [\"original\", \"tangent\", \"pol\", \"jones\"]\nnhs = {f: [] for f in formulations}\nts = {f: [] for f in formulations}\n\n\nfor nh in NH:\n    print(\"============================\")\n    print(\"number of harmonics = \", nh)\n    print(\"============================\")\n\n    for formulation in formulations:\n        Ri, Ti, t, sim = checkerboard(nh, formulation=formulation)\n        R = np.sum(Ri)\n        T = np.sum(Ti)\n        print(\"formulation = \", formulation)\n        print(\"nh0 = \", nh)\n        print(\"nh = \", sim.nh)\n        print(\"t = \", t)\n        print(\"R = \", R)\n        print(\"T = \", T)\n        print(\"R+T = \", R + T)\n        print(\"-----------------\")\n        nhs[formulation].append(sim.nh)\n        ts[formulation].append(t)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the results:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "markers = {\"original\": \"^\", \"tangent\": \"o\", \"jones\": \"s\", \"pol\": \"^\"}\ncolors = {\n    \"original\": \"#d4b533\",\n    \"tangent\": \"#d46333\",\n    \"jones\": \"#3395d4\",\n    \"pol\": \"#54aa71\",\n}\n\nfor formulation in formulations:\n    plt.plot(\n        nhs[formulation],\n        ts[formulation],\n        \"-\",\n        color=colors[formulation],\n        marker=markers[formulation],\n        label=formulation,\n    )\n    plt.pause(0.1)\nplt.legend()\nplt.xlabel(\"number of Fourier harmonics $n_h$\")\nplt.ylabel(\"$T_{0,-1}$\")\nplt.ylim(0.1255, 0.129)\nplt.tight_layout()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import nannos.utils.jupyter\n%nannos_version_table"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.13"
    }
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  "nbformat": 4,
  "nbformat_minor": 0
}