{
 "metadata": {
  "name": "",
  "signature": "sha256:d1c82017224d0c9a84cea8e4b6c0b3e3b3277c83922ded5c17cf0838d9e6e825"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "init_printing(use_latex='mathjax')\n",
      "\n",
      "x = symbols('x')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Code Generation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expr = R_nl(3, 1, x, 6)\n",
      "expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.utilities.autowrap import ufuncify\n",
      "from sympy.utilities.lambdify import lambdify\n",
      "\n",
      "fn_numpy   = lambdify(x, expr, 'numpy')\n",
      "fn_fortran = ufuncify([x], expr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### They work the same"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import linspace\n",
      "xx = linspace(0, 1, 5)\n",
      "fn_numpy(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fn_fortran(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot form with matplotlib"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib.pyplot import plot, show, legend\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xx = linspace(0, 5, 50000)  # A bigger \n",
      "plot(xx, fn_numpy(xx))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Time fn_numpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Time fn_fortran"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Theano"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import theano.tensor as T\n",
      "import theano"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tx = T.vector('x')\n",
      "ty = T.vector('y')\n",
      "tz = tx + 2 * ty\n",
      "tz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Print z, see expression"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make function\n",
      "f = theano.function([tx, ty], tz)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "xx = np.array([1, 2, 3], dtype=np.float32)\n",
      "yy = np.array([10, 20, 30], dtype=np.float32)\n",
      "f(xx, yy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Theano compiles symbolic trees down to numeric C and CUDA code\n",
      "\n",
      "Less sophisticated mathematics but more sophisticated code generation\n",
      "\n",
      "(Almost) all SymPy expressions can be transformed into Theano Expressions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = Symbol('a')\n",
      "from sympy.printing.theanocode import theano_code\n",
      "theano_code(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theano.printing.debugprint(theano_code(expr))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.printing.theanocode import theano_function\n",
      "\n",
      "fn_theano  = theano_function([x], [expr], dims={x: 1}, dtypes={x: 'float64'})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theano.printing.debugprint(fn_theano)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fn_theano(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# More complex problem\n",
      "\n",
      "Lets compute both the expression and its derivative simultaneously. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "outputs = expr, simplify(expr.diff(x))\n",
      "outputs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fn_numpy  = lambdify([x], outputs, 'numpy')\n",
      "fn_theano = theano_function([x], outputs, dims={x: 1}, dtypes={x: 'float64'})\n",
      "\n",
      "fns_fortran = [ufuncify([x], output) for output in outputs]\n",
      "fn_fortran  = lambda xx: [fn_fortran(xx) for fn_fortran in fns_fortran]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xx = linspace(0, 5, 50000)\n",
      "\n",
      "for y in fn_theano(xx):\n",
      "    plot(xx, y)\n",
      "legend(['$R_{31}$', \"$R'_{31}$\"])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit fn_numpy(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit fn_fortran(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit fn_theano(xx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Matrices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = Symbol('n', integer=True)\n",
      "X = MatrixSymbol('X', n, n)\n",
      "y = MatrixSymbol('y', n, 1)\n",
      "\n",
      "f = theano_function([X, y], [X*y])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nX = np.array([[1, 0], [0, 1]], dtype=np.float32)\n",
      "ny = np.array([[10], [1]], dtype=np.float32)\n",
      "\n",
      "f(nX, ny)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}