{
  "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# Computing gradients\n\nIn this tutorial we will see how to compute gradients of quantities \nwith respect to input values automatically.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n\nimport nannos as nn\n\nnn.set_backend(\"torch\")\n# nn.set_backend(\"autograd\")\nfrom nannos import grad\n\nbk = nn.backend"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's define a function that will return the reflection coefficient for\na metasurface:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def f(thickness):\n    lattice = nn.Lattice(([1, 0], [0, 1]))\n    sup = lattice.Layer(\"Superstrate\")\n    sub = lattice.Layer(\"Substrate\", epsilon=2)\n    ms = lattice.Layer(\"ms\", thickness=thickness, epsilon=6)\n    sim = nn.Simulation(\n        [sup, ms, sub],\n        nn.PlaneWave(1.5),\n        nh=1,\n    )\n    R, T = sim.diffraction_efficiencies()\n    return R\n\n\nx = bk.array([0.3], dtype=bk.float64)\nprint(f(x))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We will compute the finite difference approximation\nof the gradient:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def first_finite_differences(f, x):\n    eps = 1e-4\n    return nn.backend.array(\n        [(f(x + eps * v) - f(x - eps * v)) / (2 * eps) for v in nn.backend.eye(len(x))],\n    )\n\n\ndf_fd = first_finite_differences(f, x)\nprint(df_fd)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Automatic differentiation:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "df = grad(f)\ndf_auto = df(x)\nprint(df_auto)\n\nassert nn.backend.allclose(df_fd, df_auto, atol=1e-7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "A random pattern:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import random\n\nrandom.seed(2022)\n\ndiscretization = 2**4, 2**4\n\n\ndef f(var):\n    lattice = nn.Lattice(([1, 0], [0, 1]), discretization=discretization)\n    xa = var.reshape(lattice.discretization)\n    sup = lattice.Layer(\"Superstrate\")\n    sub = lattice.Layer(\"Substrate\")\n    ms = lattice.Layer(\"ms\", 1)\n    ms.epsilon = 9 + 1 * xa + 0j\n    sim = nn.Simulation(\n        [sup, ms, sub],\n        nn.PlaneWave(1.5),\n        nh=51,\n    )\n    R, T = sim.diffraction_efficiencies()\n    return R\n\n\nnvar = discretization[0] * discretization[1]\nprint(nvar)\n\nxlist = [random.random() for _ in range(nvar)]\nx = bk.array(xlist, dtype=bk.float64)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Finite differences:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "t0 = nn.tic()\ndf_fd = first_finite_differences(f, x)\ntfd = nn.toc(t0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Automatic differentiation:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "df = grad(f)\nt0 = nn.tic()\ndf_auto = df(x)\ntauto = nn.toc(t0)\n\n\nassert nn.backend.allclose(df_fd, df_auto, atol=1e-7)\n\nprint(\"speedup: \", tfd / tauto)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot gradients\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "fig, ax = plt.subplots(1, 2, figsize=(8, 3))\n_ = ax[0].imshow(df_auto.reshape(*discretization).real)\nplt.colorbar(_, ax=ax[0])\nax[0].set_title(\"autodiff\")\n_ = ax[1].imshow(df_fd.reshape(*discretization).real)\nplt.colorbar(_, ax=ax[1])\nax[1].set_title(\"finite differences\")\nplt.tight_layout()\n\n\nnn.set_backend(\"numpy\")"
      ]
    },
    {
      "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"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}