{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pystencils.session import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 01: Getting Started\n",
    "\n",
    "\n",
    "## Overview\n",
    "\n",
    "*pystencils* is a package that can speed up computations on *numpy* arrays. All computations are carried out fully parallel on CPUs (single node with OpenMP, multiple nodes with MPI) or on GPUs.\n",
    "It is suited for applications that run the same operation on *numpy* arrays multiple times. It can be used to accelerate computations on images or voxel fields. Its main application, however, are numerical simulations using finite differences, finite volumes, or lattice Boltzmann methods. \n",
    "There already exist a variety of packages to speed up numeric Python code. One could use pure numpy or solutions that compile your code, like *Cython* and *numba*. See [this page](demo_benchmark.ipynb) for a comparison of these tools.\n",
    "\n",
    "![Stencil](../img/pystencils_stencil_four_points_with_arrows.svg)\n",
    "\n",
    "As the name suggests, *pystencils* was developed for **stencil codes**, i.e. operations that update array elements using only a local neighborhood. \n",
    "It generates C code, compiles it behind the scenes, and lets you call the compiled C function as if it was a native Python function. \n",
    "But lets not dive too deep into the concepts of *pystencils* here, they are covered in detail in the following tutorials. Let's instead look at a simple example, that computes the average neighbor values of a *numpy* array. Therefor we first create two rather large arrays for input and output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_arr = np.random.rand(1024, 1024)\n",
    "output_arr = np.zeros_like(input_arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first implement a version of this algorithm using pure numpy and benchmark it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def numpy_kernel():\n",
    "    output_arr[1:-1, 1:-1] = input_arr[2:, 1:-1] + input_arr[:-2, 1:-1] + \\\n",
    "                             input_arr[1:-1, 2:] + input_arr[1:-1, :-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.11 ms ± 137 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "numpy_kernel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets see how to run the same algorithm with *pystencils*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle {{dst}_{(0,0)}} \\leftarrow \\frac{{{src}_{(1,0)}}}{4} + \\frac{{{src}_{(0,1)}}}{4} + \\frac{{{src}_{(0,-1)}}}{4} + \\frac{{{src}_{(-1,0)}}}{4}$"
      ],
      "text/plain": [
       "         src_E   src_N   src_S   src_W\n",
       "dst_C := ───── + ───── + ───── + ─────\n",
       "           4       4       4       4  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "src, dst = ps.fields(src=input_arr, dst=output_arr)\n",
    "\n",
    "symbolic_description = ps.Assignment(dst[0,0], \n",
    "                                     (src[1, 0] + src[-1, 0] + src[0, 1] + src[0, -1]) / 4)\n",
    "symbolic_description"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3,3))\n",
    "ps.stencil.plot_expression(symbolic_description.rhs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we first have created a symbolic notation of the stencil itself. This representation is built on top of *sympy* and is explained in detail in the next section. \n",
    "This description is then compiled and loaded as a Python function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = ps.create_kernel(symbolic_description).compile()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This whole process might seem overly complicated. We have already spent more lines of code than we needed for the *numpy* implementation and don't have anything running yet! However, this multi-stage process of formulating the algorithm symbolically, and just in the end actually running it, is what makes *pystencils* faster and more flexible than other approaches.\n",
    "\n",
    "Now finally lets benchmark the *pystencils* kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pystencils_kernel():\n",
    "    kernel(src=input_arr, dst=output_arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.49 ms ± 5.93 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "pystencils_kernel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This benchmark shows that *pystencils* is a lot faster than pure *numpy*, especially for large arrays. \n",
    "If you are interested in performance details and comparison to other packages like Cython, have a look at [this page](demo_benchmark.ipynb).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Short *sympy* introduction\n",
    "\n",
    "In this tutorial we continue with a short *sympy* introduction, since the symbolic kernel definition is built on top of this package. If you already know *sympy* you can skip this section. \n",
    "You can also read the full [sympy documentation here](http://docs.sympy.org/latest/index.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()  # enable nice LaTeX output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*sympy* is a package for symbolic calculation. So first we need some symbols:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sp.Symbol(\"x\")\n",
    "y = sp.Symbol(\"y\")\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The usual mathematical operations are defined for symbols:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} \\left(x + y + 5\\right) + x^{2}$"
      ],
      "text/plain": [
       " 2                2\n",
       "x ⋅(x + y + 5) + x "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = x**2 * ( y + x + 5) + x**2\n",
    "expr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can do all sorts of operations on these expressions: expand them, factor them, substitute variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{3} + x^{2} y + 6 x^{2}$"
      ],
      "text/plain": [
       " 3    2        2\n",
       "x  + x ⋅y + 6⋅x "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} \\left(x + y + 6\\right)$"
      ],
      "text/plain": [
       " 2            \n",
       "x ⋅(x + y + 6)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} \\left(x + \\cos{\\left(x \\right)} + 5\\right) + x^{2}$"
      ],
      "text/plain": [
       " 2                     2\n",
       "x ⋅(x + cos(x) + 5) + x "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.subs(y, sp.cos(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also built equations and solve them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} \\left(x + y + 5\\right) + x^{2} = 1$"
      ],
      "text/plain": [
       " 2                2    \n",
       "x ⋅(x + y + 5) + x  = 1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = sp.Eq(expr, 1)\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - x - 6 + \\frac{1}{x^{2}}\\right]$"
      ],
      "text/plain": [
       "⎡         1 ⎤\n",
       "⎢-x - 6 + ──⎥\n",
       "⎢          2⎥\n",
       "⎣         x ⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.solve(sp.Eq(expr, 1), y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A *sympy* expression is represented by an abstract syntax tree (AST), which can be inspected and modified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} \\left(x + y + 5\\right) + x^{2}$"
      ],
      "text/plain": [
       " 2                2\n",
       "x ⋅(x + y + 5) + x "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"426pt\" height=\"260pt\"\n",
       " viewBox=\"0.00 0.00 426.00 260.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 256)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-256 422,-256 422,4 -4,4\"/>\n",
       "<!-- Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_() -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_()</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"136\" cy=\"-234\" rx=\"29.4969\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"136\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Add</text>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(0,) -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"98\" cy=\"-162\" rx=\"30.5947\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"98\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Pow</text>\n",
       "</g>\n",
       "<!-- Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_()&#45;&gt;Pow(Symbol(&#39;x&#39;), Integer(2))_(0,) -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_()&#45;&gt;Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M126.8013,-216.5708C122.3203,-208.0807 116.8379,-197.6929 111.8634,-188.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"114.877,-186.4789 107.114,-179.2687 108.6863,-189.7462 114.877,-186.4789\"/>\n",
       "</g>\n",
       "<!-- Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,) -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"175\" cy=\"-162\" rx=\"28.6953\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"175\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Mul</text>\n",
       "</g>\n",
       "<!-- Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_()&#45;&gt;Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,) -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>Add(Pow(Symbol(&#39;x&#39;), Integer(2)), Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))))_()&#45;&gt;Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M145.4408,-216.5708C150.0396,-208.0807 155.6664,-197.6929 160.7718,-188.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"163.9608,-189.7286 165.6461,-179.2687 157.8057,-186.3946 163.9608,-189.7286\"/>\n",
       "</g>\n",
       "<!-- Symbol(&#39;x&#39;)_(0, 0) -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Symbol(&#39;x&#39;)_(0, 0)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)&#45;&gt;Symbol(&#39;x&#39;)_(0, 0) -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)&#45;&gt;Symbol(&#39;x&#39;)_(0, 0)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M82.5941,-146.3771C72.7854,-136.4302 59.9251,-123.3888 49.0442,-112.3547\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"51.4029,-109.7619 41.8893,-105.099 46.4187,-114.6769 51.4029,-109.7619\"/>\n",
       "</g>\n",
       "<!-- Integer(2)_(0, 1) -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Integer(2)_(0, 1)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)&#45;&gt;Integer(2)_(0, 1) -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(0,)&#45;&gt;Integer(2)_(0, 1)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M98.2523,-143.8314C98.3593,-136.131 98.4865,-126.9743 98.6053,-118.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.1049,-118.4609 98.7443,-108.4133 95.1056,-118.3637 102.1049,-118.4609\"/>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0) -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"175\" cy=\"-90\" rx=\"30.5947\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"175\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Pow</text>\n",
       "</g>\n",
       "<!-- Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)&#45;&gt;Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0) -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)&#45;&gt;Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M175,-143.8314C175,-136.131 175,-126.9743 175,-118.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"178.5001,-118.4132 175,-108.4133 171.5001,-118.4133 178.5001,-118.4132\"/>\n",
       "</g>\n",
       "<!-- Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1) -->\n",
       "<g id=\"node9\" class=\"node\">\n",
       "<title>Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"286\" cy=\"-90\" rx=\"29.4969\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"286\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Add</text>\n",
       "</g>\n",
       "<!-- Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)&#45;&gt;Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1) -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>Mul(Pow(Symbol(&#39;x&#39;), Integer(2)), Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;)))_(1,)&#45;&gt;Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M195.1013,-148.9613C212.438,-137.7159 237.684,-121.3401 257.173,-108.6986\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"259.1882,-111.5633 265.6732,-103.185 255.3789,-105.6905 259.1882,-111.5633\"/>\n",
       "</g>\n",
       "<!-- Symbol(&#39;x&#39;)_(1, 0, 0) -->\n",
       "<g id=\"node7\" class=\"node\">\n",
       "<title>Symbol(&#39;x&#39;)_(1, 0, 0)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"103\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"103\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)&#45;&gt;Symbol(&#39;x&#39;)_(1, 0, 0) -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)&#45;&gt;Symbol(&#39;x&#39;)_(1, 0, 0)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M159.3771,-74.3771C149.4302,-64.4302 136.3888,-51.3888 125.3547,-40.3547\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"127.645,-37.6953 118.099,-33.099 122.6953,-42.645 127.645,-37.6953\"/>\n",
       "</g>\n",
       "<!-- Integer(2)_(1, 0, 1) -->\n",
       "<g id=\"node8\" class=\"node\">\n",
       "<title>Integer(2)_(1, 0, 1)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"175\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"175\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
       "</g>\n",
       "<!-- Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)&#45;&gt;Integer(2)_(1, 0, 1) -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>Pow(Symbol(&#39;x&#39;), Integer(2))_(1, 0)&#45;&gt;Integer(2)_(1, 0, 1)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M175,-71.8314C175,-64.131 175,-54.9743 175,-46.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"178.5001,-46.4132 175,-36.4133 171.5001,-46.4133 178.5001,-46.4132\"/>\n",
       "</g>\n",
       "<!-- Integer(5)_(1, 1, 0) -->\n",
       "<g id=\"node10\" class=\"node\">\n",
       "<title>Integer(5)_(1, 1, 0)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"247\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"247\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">5</text>\n",
       "</g>\n",
       "<!-- Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Integer(5)_(1, 1, 0) -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Integer(5)_(1, 1, 0)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M276.5592,-72.5708C271.9604,-64.0807 266.3336,-53.6929 261.2282,-44.2674\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"264.1943,-42.3946 256.3539,-35.2687 258.0392,-45.7286 264.1943,-42.3946\"/>\n",
       "</g>\n",
       "<!-- Symbol(&#39;x&#39;)_(1, 1, 1) -->\n",
       "<g id=\"node11\" class=\"node\">\n",
       "<title>Symbol(&#39;x&#39;)_(1, 1, 1)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"319\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"319\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "</g>\n",
       "<!-- Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Symbol(&#39;x&#39;)_(1, 1, 1) -->\n",
       "<g id=\"edge10\" class=\"edge\">\n",
       "<title>Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Symbol(&#39;x&#39;)_(1, 1, 1)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M293.9884,-72.5708C297.8392,-64.1691 302.5417,-53.9091 306.8256,-44.5623\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"310.1003,-45.8177 311.0852,-35.2687 303.7369,-42.901 310.1003,-45.8177\"/>\n",
       "</g>\n",
       "<!-- Symbol(&#39;y&#39;)_(1, 1, 2) -->\n",
       "<g id=\"node12\" class=\"node\">\n",
       "<title>Symbol(&#39;y&#39;)_(1, 1, 2)</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"391\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"391\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y</text>\n",
       "</g>\n",
       "<!-- Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Symbol(&#39;y&#39;)_(1, 1, 2) -->\n",
       "<g id=\"edge11\" class=\"edge\">\n",
       "<title>Add(Integer(5), Symbol(&#39;x&#39;), Symbol(&#39;y&#39;))_(1, 1)&#45;&gt;Symbol(&#39;y&#39;)_(1, 1, 2)</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M305.7497,-76.4574C322.0864,-65.2551 345.4675,-49.2223 363.6128,-36.7798\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"365.7782,-39.5388 372.0461,-30.997 361.8194,-33.7657 365.7782,-39.5388\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x7f9701574250>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ps.to_dot(expr, graph_style={'size': \"9.5,12.5\"} )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Programatically the children node type is acessible as ``expr.func`` and its children as ``expr.args``.\n",
    "With these members a tree can be traversed and modified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.add.Add"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.func"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAaCAYAAAAXMNbWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGkElEQVR4Ae2b7XHVOhCGDxkKOIQKbm4HAToIHQRuBYQOwvAr+ZcJHRAq4KMDoAJIOggd3HA6CO+jSELWkWU7tmVncnZGyJJWu6/Xq9VKJzy4vr5eDEnHx8dLyXtrZe7Y+pX6V0Pq6SJrjpi64N/w1lvgYTykj32gvl+qv8VjLdunmvva8er5vZ7PVf51fRPUc8Q0gRnurkr8KPQr9yZb7oFaDPuqnqi+rfMi5kDz93iwdKp6R327rmOCeo6YJjDDnVZJEPoav4F3YA2arV+1j54xc8s283+25C3F1huT7OLSoVKY742eNrYVzy8Z5LPqw9Aw3oEZVGG770VScKYS5rs4DynJRS/BPSb3xaT5GG3KHaTH2087VbZbs5v6liphQGCHrjhmCrV4ztT/mvlu3OTAVthT1c/dwBC15AHepCVDyBtCRldM4gf/Y9XvhtB/D2V8l+1wOBfAnPM9cbbQ+DeVXRVSPZw0RwTZDyovYHIR+I2emybC35oEhBVG/ktOHUbk1jKGZuyKSfwY+61q7LOh21ngStP4/gQz7PlFZc0nZGMCRCW6qp0i/HTffpuFu4Xg5mGw6CvhOO8b1UambS9Uk8dMQhZDV0wswN5pVZcXFk4OwGypgwaULhhC3gHwXEiGiZah3JpnbI3Na89hkrVSIZq/VDnbUsPlKIMcvCQP5wUI1x5sC8gngrESJ6EemF5qbmlHIkpR5kLF8FhbY/Om98dXzaIgArPiOWStBrIYd74AoPYk+bWryjON99AZk/CS+062Y4xnitlLxuYmumaQXloek0I8UyPrvHZFkGZA8L9SIdL+pwL9EA+5zUL1I+qxqQAm0p/sfXgXDGPbA/kBHn40Olfb7x527IPqttv5YJClE98hqD1WwW9O1OcOdWpWCJtje4+9MnrTYC43GcstHlSatncukd9RxPtDhVPgntqkBswnbylNY2N6qhdipedobAw53akxDpx8Iy78429CVGNXKU34xyfrP/gLhcXFzp8ibI6T58j56w4OvK2yquOWIlZPaAx4MYRbIcwPx9UclwphwvDOUGsvVAjDmt66DuHhrEFwgYhgMfbGHcXMHPgf4Xqu4v1Lz6QIRNm6wzG4mxzYydsmB85+KI3/tEr1aIj7O06WRojq4luS9JfAlF3YfTHIbnzAVBRC70LjqTND7kQf/lhEtD1BTkDoivv88Ah4vOzEA07MDs5tS3zOoI1P5sgvThwYRzRGS82QgouoP2WciGXc5hww9cWg+SkHXaif3Y0P2+mHE/G7gIKj4gBuh0Qm0Zm+2pxePIPikS70kspsq/Y/WtAfEJhiagoc8Dt/vSKFaE0C4oxjDmxMVJ9JplsLGZhxREys8pSB195gRAxrulp0sCP6HdLy893c/WkLEYOxcI5I2dA4oOwWB0cUw+8jLB0JcjJXOHBtyLbO+dV+IOSwSjFEGPY5OKwY7ELI7sLveJmnMgomp8PWvGMyFyuIIYLUqgnm8PswaZL8V3r5u5jUn9GyoOp2A5w7xq+uClUiMIk/KyVFKKJc8dGoQyb1MeYODuFQ9tnK+q26clecnfR3cBRMf8X7J6IDV4YpKoUhpbupr/Lx7TcCL9t5aeLHrMphTe1DC6Lu7GTOWA1AWaQE0tVDPfChiGqUOJKySsilMMBC4/xWTfQDFM6HY/t0Ap42pDkox9B1enNiRsGUUPhRfZ8T/XSVwlCjPtvNNRX3vdwM/a/iImBdxMsK6zPINwaHinNiIidB8B/1xb7mVOFryXzcMajGyW/eh/9SdHR09Ftlj+eSRTr3VZYldXbRJWyXKrtd5vTltTY57CvHzZe8U5Vz1+5aD40np1+6dlQuczyM8T4qBzyTA0OfVMiTStOzzEosjSWljyjWFA1S8/r0EZnqolNWro12Pi1Te6kJ3OOfZCfmB2+NJy82Ocrukf1Nwb7Trvjw2QUpBESI/66CgCJkgbDFzZaEkUMIKVPqvnIU3NLVZ6vnCs5t1+DjF1PeoXOax2SoJ54bIS3+lR7yWuzcFDC4xv0iPrPITQRWgzyYPyrGAKXoQPo63XWWAhbp4bAROkU0PKsmAYjzxaEKmDlEFQtKPS0B3ibnRQXv49/pAXkEpBdlu+Gv5+sunQ3fffxHNiE68EfUd2HB3blPJLtyM0FUrdygxC+icfNHQeF38A4MswaIwOSl3sNjIZv2xgJTWEA+SRBhR6mc1UwK4QBpkFzpUrW5NnP9m3pjgRlYgKC6dnf8B+NFxn0ejbbTAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left( x^{2}, \\  x^{2} \\left(x + y + 5\\right)\\right)$"
      ],
      "text/plain": [
       "⎛ 2   2            ⎞\n",
       "⎝x , x ⋅(x + y + 5)⎠"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.args"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using *pystencils* \n",
    "\n",
    "\n",
    "### Fields\n",
    "\n",
    "*pystencils* is a module to generate code for stencil operations. \n",
    "One has to specify an update rule for each element of an array, with optional dependencies to neighbors.\n",
    "This is done use pure *sympy* with one addition: **Fields**.\n",
    "\n",
    "Fields represent a multidimensional array, where some dimensions are considered *spatial*, and some as *index* dimensions. Spatial coordinates are given relative (i.e. one can specify \"the current cell\" and \"the left neighbor\") whereas index dimensions are used to index multiple values per cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_field = ps.fields(\"f(3) : double[2D]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neighbors are labeled according to points on a compass where the first coordinate is west/east, second coordinate north/south and third coordinate top/bottom. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle {{f}_{(1,0)}^{1}}$"
      ],
      "text/plain": [
       "f_E__1"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "field_access = my_field[1, 0](1)\n",
    "field_access"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of indexing a field is an instance of ``Field.Access``. This class is a subclass of a *sympy* Symbol and thus can be used whereever normal symbols can be used. It is just like a normal symbol with some additional information attached to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isinstance(field_access, sp.Symbol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building our first stencil kernel\n",
    "\n",
    "Lets start by building a simple filter kernel. We create a field representing an image, then define a edge detection filter on the third pixel component which is blue for an RGB image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "img_field = ps.fields(\"img(4): [2D]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left({{img}_{(1,0)}^{2}} w_{2} - {{img}_{(1,1)}^{2}} w_{1} - {{img}_{(-1,1)}^{2}} w_{1} + {{img}_{(1,-1)}^{2}} w_{1} - {{img}_{(-1,-1)}^{2}} w_{1} - {{img}_{(-1,0)}^{2}} w_{2}\\right)^{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "(img_E__2⋅w₂ - img_NE__2⋅w₁ - img_NW__2⋅w₁ + img_SE__2⋅w₁ - img_SW__2⋅w₁ - img\n",
       "\n",
       "         2\n",
       "_W__2⋅w₂) "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w1, w2 = sp.symbols(\"w_1 w_2\")\n",
    "color = 2\n",
    "sobel_x = (-w2 * img_field[-1,0](color) - w1 * img_field[-1,-1](color) - w1 * img_field[-1, +1](color) \\\n",
    "           +w2 * img_field[+1,0](color) + w1 * img_field[+1,-1](color) - w1 * img_field[+1, +1](color))**2\n",
    "sobel_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have mixed some standard *sympy* symbols into this expression to possibly give the different directions different weights. The complete expression is still a valid *sympy* expression, so all features of *sympy* work on it. Lets for example now fix one weight by substituting it with a constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left({{img}_{(1,0)}^{2}} w_{2} - 0.5 {{img}_{(1,1)}^{2}} - 0.5 {{img}_{(-1,1)}^{2}} + 0.5 {{img}_{(1,-1)}^{2}} - 0.5 {{img}_{(-1,-1)}^{2}} - {{img}_{(-1,0)}^{2}} w_{2}\\right)^{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "(img_E__2⋅w₂ - 0.5⋅img_NE__2 - 0.5⋅img_NW__2 + 0.5⋅img_SE__2 - 0.5⋅img_SW__2 -\n",
       "\n",
       "             2\n",
       " img_W__2⋅w₂) "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sobel_x = sobel_x.subs(w1, 0.5)\n",
    "sobel_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets built an executable kernel out of it, which writes the result to a second field. Assignments are created using *pystencils* `Assignment` class, that gets the left- and right hand side of the assignment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle {{dst}_{(0,0)}} \\leftarrow \\left({{img}_{(1,0)}^{2}} w_{2} - 0.5 {{img}_{(1,1)}^{2}} - 0.5 {{img}_{(-1,1)}^{2}} + 0.5 {{img}_{(1,-1)}^{2}} - 0.5 {{img}_{(-1,-1)}^{2}} - {{img}_{(-1,0)}^{2}} w_{2}\\right)^{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "dst_C := (img_E__2⋅w₂ - 0.5⋅img_NE__2 - 0.5⋅img_NW__2 + 0.5⋅img_SE__2 - 0.5⋅im\n",
       "\n",
       "                      2\n",
       "g_SW__2 - img_W__2⋅w₂) "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dst_field = ps.fields('dst: [2D]' )\n",
    "update_rule = ps.Assignment(dst_field[0,0], sobel_x)\n",
    "update_rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we can see *pystencils* in action which creates a kernel for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pystencils import create_kernel\n",
    "ast = create_kernel(update_rule, cpu_openmp=False)\n",
    "compiled_kernel = ast.compile()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This compiled kernel is now just an ordinary Python function. \n",
    "Now lets grab an image to apply this filter to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "try:\n",
    "    import requests\n",
    "    import imageio\n",
    "    from io import BytesIO\n",
    "\n",
    "    response = requests.get(\"https://www.python.org/static/community_logos/python-logo-master-v3-TM.png\")\n",
    "    img = imageio.imread(BytesIO(response.content)).astype(np.double)\n",
    "    img /= img.max()\n",
    "    plt.imshow(img);\n",
    "except ImportError:\n",
    "    print(\"No requests installed\")\n",
    "    img = np.random.random((82, 290, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "filtered_image = np.zeros_like(img[..., 0])\n",
    "# here we call the compiled stencil function\n",
    "compiled_kernel(img=img, dst=filtered_image, w_2=0.5)\n",
    "plt.imshow(filtered_image, cmap='gray');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Digging into *pystencils*\n",
    "\n",
    "On our way we have created an ``ast``-object. We can inspect this, to see what *pystencils* actually does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"684pt\" height=\"384pt\"\n",
       " viewBox=\"0.00 0.00 684.00 383.91\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(.8065 .8065) rotate(0) translate(4 472)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-472 844.0784,-472 844.0784,4 -4,4\"/>\n",
       "<!-- 140286538387600 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>140286538387600</title>\n",
       "<ellipse fill=\"#a056db\" stroke=\"#000000\" cx=\"269.1436\" cy=\"-450\" rx=\"135.6761\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"269.1436\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Func: kernel (dst,img,w_2)</text>\n",
       "</g>\n",
       "<!-- 140286539358736 -->\n",
       "<g id=\"node11\" class=\"node\">\n",
       "<title>140286539358736</title>\n",
       "<ellipse fill=\"#dbc256\" stroke=\"#000000\" cx=\"269.1436\" cy=\"-378\" rx=\"37.0935\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"269.1436\" y=\"-374.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Block</text>\n",
       "</g>\n",
       "<!-- 140286538387600&#45;&gt;140286539358736 -->\n",
       "<g id=\"edge10\" class=\"edge\">\n",
       "<title>140286538387600&#45;&gt;140286539358736</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M269.1436,-431.8314C269.1436,-424.131 269.1436,-414.9743 269.1436,-406.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"272.6437,-406.4132 269.1436,-396.4133 265.6437,-406.4133 272.6437,-406.4132\"/>\n",
       "</g>\n",
       "<!-- 140286538521232 -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>140286538521232</title>\n",
       "<ellipse fill=\"#56db7f\" stroke=\"#000000\" cx=\"179.1436\" cy=\"-306\" rx=\"75.2868\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"179.1436\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">_data_img_22</text>\n",
       "</g>\n",
       "<!-- 140286575500560 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>140286575500560</title>\n",
       "<ellipse fill=\"#3498db\" stroke=\"#000000\" cx=\"359.1436\" cy=\"-306\" rx=\"86.3847\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"359.1436\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Loop over dim 0</text>\n",
       "</g>\n",
       "<!-- 140286539326864 -->\n",
       "<g id=\"node10\" class=\"node\">\n",
       "<title>140286539326864</title>\n",
       "<ellipse fill=\"#dbc256\" stroke=\"#000000\" cx=\"359.1436\" cy=\"-234\" rx=\"37.0935\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"359.1436\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Block</text>\n",
       "</g>\n",
       "<!-- 140286575500560&#45;&gt;140286539326864 -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>140286575500560&#45;&gt;140286539326864</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M359.1436,-287.8314C359.1436,-280.131 359.1436,-270.9743 359.1436,-262.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"362.6437,-262.4132 359.1436,-252.4133 355.6437,-262.4133 362.6437,-262.4132\"/>\n",
       "</g>\n",
       "<!-- 140286538492944 -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>140286538492944</title>\n",
       "<ellipse fill=\"#56db7f\" stroke=\"#000000\" cx=\"72.1436\" cy=\"-162\" rx=\"72.2875\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"72.1436\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">_data_dst_00</text>\n",
       "</g>\n",
       "<!-- 140286538522128 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>140286538522128</title>\n",
       "<ellipse fill=\"#56db7f\" stroke=\"#000000\" cx=\"254.1436\" cy=\"-162\" rx=\"91.784\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"254.1436\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">_data_img_22_01</text>\n",
       "</g>\n",
       "<!-- 140286538519184 -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>140286538519184</title>\n",
       "<ellipse fill=\"#56db7f\" stroke=\"#000000\" cx=\"464.1436\" cy=\"-162\" rx=\"100.9827\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"464.1436\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">_data_img_22_0m1</text>\n",
       "</g>\n",
       "<!-- 140286539326928 -->\n",
       "<g id=\"node7\" class=\"node\">\n",
       "<title>140286539326928</title>\n",
       "<ellipse fill=\"#3498db\" stroke=\"#000000\" cx=\"669.1436\" cy=\"-162\" rx=\"86.3847\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"669.1436\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Loop over dim 1</text>\n",
       "</g>\n",
       "<!-- 140286538390928 -->\n",
       "<g id=\"node9\" class=\"node\">\n",
       "<title>140286538390928</title>\n",
       "<ellipse fill=\"#dbc256\" stroke=\"#000000\" cx=\"669.1436\" cy=\"-90\" rx=\"37.0935\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"669.1436\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Block</text>\n",
       "</g>\n",
       "<!-- 140286539326928&#45;&gt;140286538390928 -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>140286539326928&#45;&gt;140286538390928</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M669.1436,-143.8314C669.1436,-136.131 669.1436,-126.9743 669.1436,-118.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"672.6437,-118.4132 669.1436,-108.4133 665.6437,-118.4133 672.6437,-118.4132\"/>\n",
       "</g>\n",
       "<!-- 140286538593616 -->\n",
       "<g id=\"node8\" class=\"node\">\n",
       "<title>140286538593616</title>\n",
       "<ellipse fill=\"#56db7f\" stroke=\"#000000\" cx=\"669.1436\" cy=\"-18\" rx=\"170.8697\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"669.1436\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">_data_dst_00[_stride_dst_1*ctr_1]</text>\n",
       "</g>\n",
       "<!-- 140286538390928&#45;&gt;140286538593616 -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>140286538390928&#45;&gt;140286538593616</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M669.1436,-71.8314C669.1436,-64.131 669.1436,-54.9743 669.1436,-46.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"672.6437,-46.4132 669.1436,-36.4133 665.6437,-46.4133 672.6437,-46.4132\"/>\n",
       "</g>\n",
       "<!-- 140286539326864&#45;&gt;140286538492944 -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>140286539326864&#45;&gt;140286538492944</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M326.221,-225.7407C279.2459,-213.956 192.1579,-192.1081 133.1881,-177.3143\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"133.8004,-173.8595 123.2492,-174.8209 132.097,-180.6491 133.8004,-173.8595\"/>\n",
       "</g>\n",
       "<!-- 140286539326864&#45;&gt;140286538522128 -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>140286539326864&#45;&gt;140286538522128</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M337.6419,-219.256C323.4673,-209.5363 304.5958,-196.5958 288.3799,-185.4764\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"289.9177,-182.287 279.691,-179.5182 285.959,-188.0601 289.9177,-182.287\"/>\n",
       "</g>\n",
       "<!-- 140286539326864&#45;&gt;140286538519184 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>140286539326864&#45;&gt;140286538519184</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M380.6453,-219.256C394.8199,-209.5363 413.6914,-196.5958 429.9073,-185.4764\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"432.3282,-188.0601 438.5962,-179.5182 428.3695,-182.287 432.3282,-188.0601\"/>\n",
       "</g>\n",
       "<!-- 140286539326864&#45;&gt;140286539326928 -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>140286539326864&#45;&gt;140286539326928</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M392.6136,-226.2263C442.3238,-214.6807 536.7265,-192.7549 601.2727,-177.7636\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"602.4153,-181.0914 611.3642,-175.4197 600.8316,-174.2729 602.4153,-181.0914\"/>\n",
       "</g>\n",
       "<!-- 140286539358736&#45;&gt;140286538521232 -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>140286539358736&#45;&gt;140286538521232</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M249.6149,-362.3771C237.7129,-352.8555 222.2663,-340.4982 208.8691,-329.7804\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"210.8374,-326.8729 200.8422,-323.3589 206.4645,-332.3389 210.8374,-326.8729\"/>\n",
       "</g>\n",
       "<!-- 140286539358736&#45;&gt;140286575500560 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>140286539358736&#45;&gt;140286575500560</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M288.6723,-362.3771C300.4886,-352.924 315.7988,-340.6758 329.1287,-330.0119\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"331.5013,-332.5961 337.1235,-323.6161 327.1284,-327.13 331.5013,-332.5961\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x7f9700dfd5d0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ps.to_dot(ast, graph_style={'size': \"9.5,12.5\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*pystencils* also builds a tree structure of the program, where each `Assignment` node internally again has a *sympy* AST which is not printed here. Out of this representation *C* code can be generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.highlight .hll { background-color: #ffffcc }\n",
       ".highlight  { background: #f8f8f8; }\n",
       ".highlight .c { color: #408080; font-style: italic } /* Comment */\n",
       ".highlight .err { border: 1px solid #FF0000 } /* Error */\n",
       ".highlight .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".highlight .o { color: #666666 } /* Operator */\n",
       ".highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".highlight .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".highlight .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".highlight .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".highlight .ge { font-style: italic } /* Generic.Emph */\n",
       ".highlight .gr { color: #FF0000 } /* Generic.Error */\n",
       ".highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".highlight .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".highlight .go { color: #888888 } /* Generic.Output */\n",
       ".highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".highlight .gs { font-weight: bold } /* Generic.Strong */\n",
       ".highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".highlight .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".highlight .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".highlight .kt { color: #B00040 } /* Keyword.Type */\n",
       ".highlight .m { color: #666666 } /* Literal.Number */\n",
       ".highlight .s { color: #BA2121 } /* Literal.String */\n",
       ".highlight .na { color: #7D9029 } /* Name.Attribute */\n",
       ".highlight .nb { color: #008000 } /* Name.Builtin */\n",
       ".highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".highlight .no { color: #880000 } /* Name.Constant */\n",
       ".highlight .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".highlight .nf { color: #0000FF } /* Name.Function */\n",
       ".highlight .nl { color: #A0A000 } /* Name.Label */\n",
       ".highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".highlight .nv { color: #19177C } /* Name.Variable */\n",
       ".highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".highlight .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".highlight .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".highlight .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".highlight .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".highlight .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".highlight .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".highlight .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       ".highlight .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".highlight .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       ".highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".highlight .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".highlight .sx { color: #008000 } /* Literal.String.Other */\n",
       ".highlight .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".highlight .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".highlight .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".highlight .fm { color: #0000FF } /* Name.Function.Magic */\n",
       ".highlight .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".highlight .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".highlight .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".highlight .vm { color: #19177C } /* Name.Variable.Magic */\n",
       ".highlight .il { color: #666666 } /* Literal.Number.Integer.Long */</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"k\">const</span> <span class=\"n\">_data_img</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_size_dst_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_size_dst_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_dst_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_dst_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_2</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"n\">w_2</span><span class=\"p\">)</span>\n",
       "<span class=\"p\">{</span>\n",
       "   <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22</span> <span class=\"o\">=</span> <span class=\"n\">_data_img</span> <span class=\"o\">+</span> <span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">_stride_img_2</span><span class=\"p\">;</span>\n",
       "   <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">&lt;</span> <span class=\"n\">_size_dst_0</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "   <span class=\"p\">{</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst_00</span> <span class=\"o\">=</span> <span class=\"n\">_data_dst</span> <span class=\"o\">+</span> <span class=\"n\">_stride_dst_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22_01</span> <span class=\"o\">=</span> <span class=\"n\">_stride_img_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_0</span> <span class=\"o\">+</span> <span class=\"n\">_data_img_22</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22_0m1</span> <span class=\"o\">=</span> <span class=\"n\">_stride_img_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_0</span> <span class=\"o\">+</span> <span class=\"n\">_data_img_22</span><span class=\"p\">;</span>\n",
       "      <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">&lt;</span> <span class=\"n\">_size_dst_1</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "      <span class=\"p\">{</span>\n",
       "         <span class=\"n\">_data_dst_00</span><span class=\"p\">[</span><span class=\"n\">_stride_dst_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">((</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">])</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]));</span>\n",
       "      <span class=\"p\">}</span>\n",
       "   <span class=\"p\">}</span>\n",
       "<span class=\"p\">}</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "FUNC_PREFIX void kernel(double * RESTRICT _data_dst, double * RESTRICT const _data_img, int64_t const _size_dst_0, int64_t const _size_dst_1, int64_t const _stride_dst_0, int64_t const _stride_dst_1, int64_t const _stride_img_0, int64_t const _stride_img_1, int64_t const _stride_img_2, double w_2)\n",
       "{\n",
       "   double * RESTRICT _data_img_22 = _data_img + 2*_stride_img_2;\n",
       "   for (int ctr_0 = 1; ctr_0 < _size_dst_0 - 1; ctr_0 += 1)\n",
       "   {\n",
       "      double * RESTRICT _data_dst_00 = _data_dst + _stride_dst_0*ctr_0;\n",
       "      double * RESTRICT _data_img_22_01 = _stride_img_0*ctr_0 + _stride_img_0 + _data_img_22;\n",
       "      double * RESTRICT _data_img_22_0m1 = _stride_img_0*ctr_0 - _stride_img_0 + _data_img_22;\n",
       "      for (int ctr_1 = 1; ctr_1 < _size_dst_1 - 1; ctr_1 += 1)\n",
       "      {\n",
       "         _data_dst_00[_stride_dst_1*ctr_1] = ((w_2*_data_img_22_01[_stride_img_1*ctr_1] - w_2*_data_img_22_0m1[_stride_img_1*ctr_1] - 0.5*_data_img_22_01[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 - _stride_img_1] + 0.5*_data_img_22_01[_stride_img_1*ctr_1 - _stride_img_1])*(w_2*_data_img_22_01[_stride_img_1*ctr_1] - w_2*_data_img_22_0m1[_stride_img_1*ctr_1] - 0.5*_data_img_22_01[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 - _stride_img_1] + 0.5*_data_img_22_01[_stride_img_1*ctr_1 - _stride_img_1]));\n",
       "      }\n",
       "   }\n",
       "}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ps.show_code(ast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Behind the scenes this code is compiled into a shared library and made available as a Python function. Before compiling this function we can modify the AST object, for example to parallelize it with OpenMP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.highlight .hll { background-color: #ffffcc }\n",
       ".highlight  { background: #f8f8f8; }\n",
       ".highlight .c { color: #408080; font-style: italic } /* Comment */\n",
       ".highlight .err { border: 1px solid #FF0000 } /* Error */\n",
       ".highlight .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".highlight .o { color: #666666 } /* Operator */\n",
       ".highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".highlight .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".highlight .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".highlight .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".highlight .ge { font-style: italic } /* Generic.Emph */\n",
       ".highlight .gr { color: #FF0000 } /* Generic.Error */\n",
       ".highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".highlight .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".highlight .go { color: #888888 } /* Generic.Output */\n",
       ".highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".highlight .gs { font-weight: bold } /* Generic.Strong */\n",
       ".highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".highlight .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".highlight .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".highlight .kt { color: #B00040 } /* Keyword.Type */\n",
       ".highlight .m { color: #666666 } /* Literal.Number */\n",
       ".highlight .s { color: #BA2121 } /* Literal.String */\n",
       ".highlight .na { color: #7D9029 } /* Name.Attribute */\n",
       ".highlight .nb { color: #008000 } /* Name.Builtin */\n",
       ".highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".highlight .no { color: #880000 } /* Name.Constant */\n",
       ".highlight .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".highlight .nf { color: #0000FF } /* Name.Function */\n",
       ".highlight .nl { color: #A0A000 } /* Name.Label */\n",
       ".highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".highlight .nv { color: #19177C } /* Name.Variable */\n",
       ".highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".highlight .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".highlight .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".highlight .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".highlight .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".highlight .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".highlight .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".highlight .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       ".highlight .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".highlight .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       ".highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".highlight .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".highlight .sx { color: #008000 } /* Literal.String.Other */\n",
       ".highlight .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".highlight .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".highlight .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".highlight .fm { color: #0000FF } /* Name.Function.Magic */\n",
       ".highlight .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".highlight .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".highlight .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".highlight .vm { color: #19177C } /* Name.Variable.Magic */\n",
       ".highlight .il { color: #666666 } /* Literal.Number.Integer.Long */</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"k\">const</span> <span class=\"n\">_data_img</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_size_dst_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_size_dst_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_dst_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_dst_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_0</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">,</span> <span class=\"kt\">int64_t</span> <span class=\"k\">const</span> <span class=\"n\">_stride_img_2</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"n\">w_2</span><span class=\"p\">)</span>\n",
       "<span class=\"p\">{</span>\n",
       "   <span class=\"cp\">#pragma omp parallel num_threads(2)</span>\n",
       "   <span class=\"p\">{</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22</span> <span class=\"o\">=</span> <span class=\"n\">_data_img</span> <span class=\"o\">+</span> <span class=\"mi\">2</span><span class=\"o\">*</span><span class=\"n\">_stride_img_2</span><span class=\"p\">;</span>\n",
       "      <span class=\"cp\">#pragma omp for schedule(static)</span>\n",
       "      <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">&lt;</span> <span class=\"n\">_size_dst_0</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "      <span class=\"p\">{</span>\n",
       "         <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst_00</span> <span class=\"o\">=</span> <span class=\"n\">_data_dst</span> <span class=\"o\">+</span> <span class=\"n\">_stride_dst_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span><span class=\"p\">;</span>\n",
       "         <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22_01</span> <span class=\"o\">=</span> <span class=\"n\">_stride_img_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_0</span> <span class=\"o\">+</span> <span class=\"n\">_data_img_22</span><span class=\"p\">;</span>\n",
       "         <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_img_22_0m1</span> <span class=\"o\">=</span> <span class=\"n\">_stride_img_0</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_0</span> <span class=\"o\">+</span> <span class=\"n\">_data_img_22</span><span class=\"p\">;</span>\n",
       "         <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">&lt;</span> <span class=\"n\">_size_dst_1</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "         <span class=\"p\">{</span>\n",
       "            <span class=\"n\">_data_dst_00</span><span class=\"p\">[</span><span class=\"n\">_stride_dst_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">((</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">])</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">w_2</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_0m1</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">_data_img_22_01</span><span class=\"p\">[</span><span class=\"n\">_stride_img_1</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"n\">_stride_img_1</span><span class=\"p\">]));</span>\n",
       "         <span class=\"p\">}</span>\n",
       "      <span class=\"p\">}</span>\n",
       "   <span class=\"p\">}</span>\n",
       "<span class=\"p\">}</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "FUNC_PREFIX void kernel(double * RESTRICT _data_dst, double * RESTRICT const _data_img, int64_t const _size_dst_0, int64_t const _size_dst_1, int64_t const _stride_dst_0, int64_t const _stride_dst_1, int64_t const _stride_img_0, int64_t const _stride_img_1, int64_t const _stride_img_2, double w_2)\n",
       "{\n",
       "   #pragma omp parallel num_threads(2)\n",
       "   {\n",
       "      double * RESTRICT _data_img_22 = _data_img + 2*_stride_img_2;\n",
       "      #pragma omp for schedule(static)\n",
       "      for (int ctr_0 = 1; ctr_0 < _size_dst_0 - 1; ctr_0 += 1)\n",
       "      {\n",
       "         double * RESTRICT _data_dst_00 = _data_dst + _stride_dst_0*ctr_0;\n",
       "         double * RESTRICT _data_img_22_01 = _stride_img_0*ctr_0 + _stride_img_0 + _data_img_22;\n",
       "         double * RESTRICT _data_img_22_0m1 = _stride_img_0*ctr_0 - _stride_img_0 + _data_img_22;\n",
       "         for (int ctr_1 = 1; ctr_1 < _size_dst_1 - 1; ctr_1 += 1)\n",
       "         {\n",
       "            _data_dst_00[_stride_dst_1*ctr_1] = ((w_2*_data_img_22_01[_stride_img_1*ctr_1] - w_2*_data_img_22_0m1[_stride_img_1*ctr_1] - 0.5*_data_img_22_01[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 - _stride_img_1] + 0.5*_data_img_22_01[_stride_img_1*ctr_1 - _stride_img_1])*(w_2*_data_img_22_01[_stride_img_1*ctr_1] - w_2*_data_img_22_0m1[_stride_img_1*ctr_1] - 0.5*_data_img_22_01[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 + _stride_img_1] - 0.5*_data_img_22_0m1[_stride_img_1*ctr_1 - _stride_img_1] + 0.5*_data_img_22_01[_stride_img_1*ctr_1 - _stride_img_1]));\n",
       "         }\n",
       "      }\n",
       "   }\n",
       "}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ast = ps.create_kernel(update_rule)\n",
    "ps.cpu.add_openmp(ast, num_threads=2)\n",
    "ps.show_code(ast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loops = list(ast.atoms(ps.astnodes.LoopOverCoordinate))\n",
    "l1 = loops[0]\n",
    "l1.prefix_lines.append(\"#pragma someting\")\n",
    "l1.is_outermost_loop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixed array sizes\n",
    "\n",
    "Since we already know the arrays to which the kernel should be applied, we can \n",
    "create *Field* objects with fixed size, based on a numpy array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.highlight .hll { background-color: #ffffcc }\n",
       ".highlight  { background: #f8f8f8; }\n",
       ".highlight .c { color: #408080; font-style: italic } /* Comment */\n",
       ".highlight .err { border: 1px solid #FF0000 } /* Error */\n",
       ".highlight .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".highlight .o { color: #666666 } /* Operator */\n",
       ".highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".highlight .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".highlight .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".highlight .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".highlight .ge { font-style: italic } /* Generic.Emph */\n",
       ".highlight .gr { color: #FF0000 } /* Generic.Error */\n",
       ".highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".highlight .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".highlight .go { color: #888888 } /* Generic.Output */\n",
       ".highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".highlight .gs { font-weight: bold } /* Generic.Strong */\n",
       ".highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".highlight .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".highlight .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".highlight .kt { color: #B00040 } /* Keyword.Type */\n",
       ".highlight .m { color: #666666 } /* Literal.Number */\n",
       ".highlight .s { color: #BA2121 } /* Literal.String */\n",
       ".highlight .na { color: #7D9029 } /* Name.Attribute */\n",
       ".highlight .nb { color: #008000 } /* Name.Builtin */\n",
       ".highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".highlight .no { color: #880000 } /* Name.Constant */\n",
       ".highlight .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".highlight .nf { color: #0000FF } /* Name.Function */\n",
       ".highlight .nl { color: #A0A000 } /* Name.Label */\n",
       ".highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".highlight .nv { color: #19177C } /* Name.Variable */\n",
       ".highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".highlight .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".highlight .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".highlight .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".highlight .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".highlight .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".highlight .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".highlight .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       ".highlight .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".highlight .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       ".highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".highlight .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".highlight .sx { color: #008000 } /* Literal.String.Other */\n",
       ".highlight .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".highlight .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".highlight .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".highlight .fm { color: #0000FF } /* Name.Function.Magic */\n",
       ".highlight .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".highlight .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".highlight .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".highlight .vm { color: #19177C } /* Name.Variable.Magic */\n",
       ".highlight .il { color: #666666 } /* Literal.Number.Integer.Long */</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"kt\">void</span> <span class=\"nf\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"k\">const</span> <span class=\"n\">_data_I</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst</span><span class=\"p\">)</span>\n",
       "<span class=\"p\">{</span>\n",
       "   <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_21</span> <span class=\"o\">=</span> <span class=\"n\">_data_I</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
       "   <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">&lt;</span> <span class=\"mi\">81</span><span class=\"p\">;</span> <span class=\"n\">ctr_0</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "   <span class=\"p\">{</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst_00</span> <span class=\"o\">=</span> <span class=\"n\">_data_dst</span> <span class=\"o\">+</span> <span class=\"mi\">290</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_21_01</span> <span class=\"o\">=</span> <span class=\"n\">_data_I_21</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_21_0m1</span> <span class=\"o\">=</span> <span class=\"n\">_data_I_21</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">;</span>\n",
       "      <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"kt\">int</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"mi\">1</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">&lt;</span> <span class=\"mi\">289</span><span class=\"p\">;</span> <span class=\"n\">ctr_1</span> <span class=\"o\">+=</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n",
       "      <span class=\"p\">{</span>\n",
       "         <span class=\"n\">_data_dst_00</span><span class=\"p\">[</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mf\">2.0</span><span class=\"o\">*</span><span class=\"n\">_data_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">2.0</span><span class=\"o\">*</span><span class=\"n\">_data_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">_data_I_21_01</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_21_0m1</span><span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"mi\">4</span><span class=\"p\">];</span>\n",
       "      <span class=\"p\">}</span>\n",
       "   <span class=\"p\">}</span>\n",
       "<span class=\"p\">}</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "FUNC_PREFIX void kernel(double * RESTRICT const _data_I, double * RESTRICT _data_dst)\n",
       "{\n",
       "   double * RESTRICT _data_I_21 = _data_I + 1;\n",
       "   for (int ctr_0 = 1; ctr_0 < 81; ctr_0 += 1)\n",
       "   {\n",
       "      double * RESTRICT _data_dst_00 = _data_dst + 290*ctr_0;\n",
       "      double * RESTRICT _data_I_21_01 = _data_I_21 + 1160*ctr_0 + 1160;\n",
       "      double * RESTRICT _data_I_21_0m1 = _data_I_21 + 1160*ctr_0 - 1160;\n",
       "      for (int ctr_1 = 1; ctr_1 < 289; ctr_1 += 1)\n",
       "      {\n",
       "         _data_dst_00[ctr_1] = -2.0*_data_I_21_0m1[4*ctr_1] + 2.0*_data_I_21_01[4*ctr_1] - _data_I_21_01[4*ctr_1 + 4] + _data_I_21_01[4*ctr_1 - 4] - _data_I_21_0m1[4*ctr_1 + 4] - _data_I_21_0m1[4*ctr_1 - 4];\n",
       "      }\n",
       "   }\n",
       "}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img_field, dst_field = ps.fields(\"I(4), dst : [2D]\", I=img.astype(np.double), dst=filtered_image)\n",
    "\n",
    "sobel_x = -2 * img_field[-1,0](1) - img_field[-1,-1](1) - img_field[-1, +1](1) \\\n",
    "         +2 * img_field[+1,0](1) + img_field[+1,-1](1) - img_field[+1, +1](1)\n",
    "update_rule = ps.Assignment(dst_field[0,0], sobel_x)\n",
    "\n",
    "ast = create_kernel(update_rule)\n",
    "ps.show_code(ast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare this code to the version above. In this code the loop bounds and array offsets are constants, which usually leads to faster kernels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running on GPU\n",
    "\n",
    "If you have a CUDA enabled graphics card and [pycuda](https://mathema.tician.de/software/pycuda/) installed, *pystencils* can run your kernel on the GPU as well. You can find more details about this in the GPU tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "gpu_ast = create_kernel(update_rule, target='gpu', gpu_indexing=ps.gpucuda.indexing.BlockIndexing, \n",
    "                        gpu_indexing_params={'blockSize': (8,8,4)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.highlight .hll { background-color: #ffffcc }\n",
       ".highlight  { background: #f8f8f8; }\n",
       ".highlight .c { color: #408080; font-style: italic } /* Comment */\n",
       ".highlight .err { border: 1px solid #FF0000 } /* Error */\n",
       ".highlight .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".highlight .o { color: #666666 } /* Operator */\n",
       ".highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".highlight .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".highlight .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".highlight .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".highlight .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".highlight .ge { font-style: italic } /* Generic.Emph */\n",
       ".highlight .gr { color: #FF0000 } /* Generic.Error */\n",
       ".highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".highlight .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".highlight .go { color: #888888 } /* Generic.Output */\n",
       ".highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".highlight .gs { font-weight: bold } /* Generic.Strong */\n",
       ".highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".highlight .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".highlight .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".highlight .kt { color: #B00040 } /* Keyword.Type */\n",
       ".highlight .m { color: #666666 } /* Literal.Number */\n",
       ".highlight .s { color: #BA2121 } /* Literal.String */\n",
       ".highlight .na { color: #7D9029 } /* Name.Attribute */\n",
       ".highlight .nb { color: #008000 } /* Name.Builtin */\n",
       ".highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".highlight .no { color: #880000 } /* Name.Constant */\n",
       ".highlight .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".highlight .nf { color: #0000FF } /* Name.Function */\n",
       ".highlight .nl { color: #A0A000 } /* Name.Label */\n",
       ".highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".highlight .nv { color: #19177C } /* Name.Variable */\n",
       ".highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".highlight .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".highlight .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".highlight .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".highlight .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".highlight .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".highlight .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".highlight .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       ".highlight .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".highlight .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       ".highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".highlight .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".highlight .sx { color: #008000 } /* Literal.String.Other */\n",
       ".highlight .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".highlight .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".highlight .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".highlight .fm { color: #0000FF } /* Name.Function.Magic */\n",
       ".highlight .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".highlight .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".highlight .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".highlight .vm { color: #19177C } /* Name.Variable.Magic */\n",
       ".highlight .il { color: #666666 } /* Literal.Number.Integer.Long */</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div class=\"highlight\"><pre><span></span><span class=\"n\">FUNC_PREFIX</span> <span class=\"nf\">__launch_bounds__</span><span class=\"p\">(</span><span class=\"mi\">256</span><span class=\"p\">)</span> <span class=\"kt\">void</span> <span class=\"n\">kernel</span><span class=\"p\">(</span><span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"k\">const</span> <span class=\"n\">_data_I</span><span class=\"p\">,</span> <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst</span><span class=\"p\">)</span>\n",
       "<span class=\"p\">{</span>\n",
       "   <span class=\"k\">if</span> <span class=\"p\">(</span><span class=\"n\">blockDim</span><span class=\"p\">.</span><span class=\"n\">x</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\">&lt;</span> <span class=\"mi\">81</span> <span class=\"o\">&amp;&amp;</span> <span class=\"n\">blockDim</span><span class=\"p\">.</span><span class=\"n\">y</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\">&lt;</span> <span class=\"mi\">289</span><span class=\"p\">)</span>\n",
       "   <span class=\"p\">{</span>\n",
       "      <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">ctr_0</span> <span class=\"o\">=</span> <span class=\"n\">blockDim</span><span class=\"p\">.</span><span class=\"n\">x</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
       "      <span class=\"k\">const</span> <span class=\"kt\">int64_t</span> <span class=\"n\">ctr_1</span> <span class=\"o\">=</span> <span class=\"n\">blockDim</span><span class=\"p\">.</span><span class=\"n\">y</span><span class=\"o\">*</span><span class=\"n\">blockIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"n\">threadIdx</span><span class=\"p\">.</span><span class=\"n\">y</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_dst_10</span> <span class=\"o\">=</span> <span class=\"n\">_data_dst</span> <span class=\"o\">+</span> <span class=\"n\">ctr_1</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_11_21</span> <span class=\"o\">=</span> <span class=\"n\">_data_I</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">5</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_1m1_21</span> <span class=\"o\">=</span> <span class=\"n\">_data_I</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">-</span> <span class=\"mi\">3</span><span class=\"p\">;</span>\n",
       "      <span class=\"kt\">double</span> <span class=\"o\">*</span> <span class=\"n\">RESTRICT</span> <span class=\"n\">_data_I_10_21</span> <span class=\"o\">=</span> <span class=\"n\">_data_I</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">ctr_1</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">;</span>\n",
       "      <span class=\"n\">_data_dst_10</span><span class=\"p\">[</span><span class=\"mi\">290</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mf\">2.0</span><span class=\"o\">*</span><span class=\"n\">_data_I_10_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"mf\">2.0</span><span class=\"o\">*</span><span class=\"n\">_data_I_10_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_11_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_11_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">_data_I_1m1_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">+</span> <span class=\"mi\">1160</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">_data_I_1m1_21</span><span class=\"p\">[</span><span class=\"mi\">1160</span><span class=\"o\">*</span><span class=\"n\">ctr_0</span> <span class=\"o\">-</span> <span class=\"mi\">1160</span><span class=\"p\">];</span>\n",
       "   <span class=\"p\">}</span> \n",
       "<span class=\"p\">}</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "FUNC_PREFIX __launch_bounds__(256) void kernel(double * RESTRICT const _data_I, double * RESTRICT _data_dst)\n",
       "{\n",
       "   if (blockDim.x*blockIdx.x + threadIdx.x + 1 < 81 && blockDim.y*blockIdx.y + threadIdx.y + 1 < 289)\n",
       "   {\n",
       "      const int64_t ctr_0 = blockDim.x*blockIdx.x + threadIdx.x + 1;\n",
       "      const int64_t ctr_1 = blockDim.y*blockIdx.y + threadIdx.y + 1;\n",
       "      double * RESTRICT _data_dst_10 = _data_dst + ctr_1;\n",
       "      double * RESTRICT _data_I_11_21 = _data_I + 4*ctr_1 + 5;\n",
       "      double * RESTRICT _data_I_1m1_21 = _data_I + 4*ctr_1 - 3;\n",
       "      double * RESTRICT _data_I_10_21 = _data_I + 4*ctr_1 + 1;\n",
       "      _data_dst_10[290*ctr_0] = -2.0*_data_I_10_21[1160*ctr_0 - 1160] + 2.0*_data_I_10_21[1160*ctr_0 + 1160] - _data_I_11_21[1160*ctr_0 + 1160] - _data_I_11_21[1160*ctr_0 - 1160] + _data_I_1m1_21[1160*ctr_0 + 1160] - _data_I_1m1_21[1160*ctr_0 - 1160];\n",
       "   } \n",
       "}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ps.show_code(gpu_ast)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}