PDE Swift.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completion enabled!\n"
     ]
    }
   ],
   "source": [
    "import Foundation\n",
    "import TensorFlow\n",
    "import Python\n",
    "%include \"EnableIPythonDisplay.swift\"\n",
    "%enableCompletion\n",
    "//%include \"EnableJupyterDisplay.swift\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "//print(Python.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "let np = Python.import(\"numpy\")\n",
    "let pilImage = Python.import(\"PIL.Image\")\n",
    "let ip = Python.import(\"IPython.display\")\n",
    "let clear_output = ip.clear_output\n",
    "let bytesio = Python.import(\"io\").BytesIO()\n",
    "//let builtins = Python.builtins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "func DisplayArray(_ a: Tensor<Float>, fileName: String? = nil, fmt: String=\"jpeg\", rng: (Float, Float)=(0.0, 1.0)){\n",
    "    let a = (a-rng.0)/(rng.1-rng.0)*255\n",
    "    let b = a.clipped(min: 0, max: 255).makeNumpyArray()\n",
    "    let c = np.uint8(b)\n",
    "    let f = bytesio\n",
    "    let image = pilImage.fromarray(c)\n",
    "    if let fileName = fileName { // output to filesystem\n",
    "        image.save(fileName, \"JPEG\")\n",
    "    } else { //output inline in jupyter\n",
    "        clear_output(wait: true)\n",
    "        image.save(f, fmt)\n",
    "        ip.Image(data:f.getvalue()).display()\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "func make_kernel(_ a: Tensor<Float>) -> Tensor<Float>{\n",
    "    return a.reshaped(to: TensorShape(a.shape.dimensions + [1,1]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "func simple_conv(_ x: Tensor<Float>, _ k: Tensor<Float>) -> Tensor<Float>{\n",
    "    let x = x.expandingShape(at: 0).expandingShape(at: -1)\n",
    "    let y = Raw.depthwiseConv2dNative(x, filter: k, strides: [1,1,1,1], padding: .same)\n",
    "    return y[0,TensorRange.ellipsis,0...,0]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "func laplace(_ x: Tensor<Float>) -> Tensor<Float>{\n",
    "    let laplace_k = make_kernel([[0.5, 1.0, 0.5],\n",
    "                           [1.0, -6.0, 1.0],\n",
    "                           [0.5, 1.0, 0.5]])\n",
    "    return simple_conv(x, laplace_k)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "let N = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "var u_init = Tensor<Float>(repeating: 0.0, shape: [N,N])\n",
    "var ut_init = Tensor<Float>(repeating: 0.0, shape: [N,N])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n in 0..<40 {\n",
    "    let a = Int.random(in: 0..<N)\n",
    "    let b = Int.random(in: 0..<N)\n",
    "    let c = Float.random(in: 0.0..<1.0)\n",
    "    u_init[a,b] = Tensor<Float>(c)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "//DisplayArray(u_init, rng: (-0.1, 0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's specify the details of the differential equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "// Parameters:\n",
    "// eps -- time resolution\n",
    "// damping -- wave damping\n",
    "\n",
    "// Discretized PDE update rules\n",
    "\n",
    "var eps = Tensor<Float>(0.03)\n",
    "var damping = Tensor<Float>(0.04)\n",
    "\n",
    "// Create variables for simulation state\n",
    "var U = Tensor<Float>(u_init)\n",
    "var Ut = Tensor<Float>(ut_init)\n",
    "\n",
    "// Create variables for simulation state\n",
    "\n",
    "for _ in 1...1000 {\n",
    "  U = U + eps * Ut\n",
    "  Ut = Ut + eps * (laplace(U) - damping * Ut)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DisplayArray(U, rng: (-0.1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Swift",
   "language": "swift",
   "name": "swift"
  },
  "language_info": {
   "file_extension": ".swift",
   "mimetype": "text/x-swift",
   "name": "swift",
   "version": ""
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}