Raster regrid

example-raster-single-src-cell-target-cell.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# %matplotlib nbagg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from agg_regrid._agg import raster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the simple toy example to explore the behaviour of a raster regrid of a single source cell to a single target cell. The target cell has been back projected into the same co-ordinate system as the source cell, and for the purpose of this example, the source cell is regular and larger than the target cell. The target cell covers 1/8th of the source cell, as a diamond in the centre of the source cell ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# The source cell point value.\n",
    "src_value = 80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def grid(n, value, plot=True, quiet=False):\n",
    "    \"\"\"\n",
    "    Basic raster regrid of a single target cell within a single source cell.\n",
    "    \n",
    "    Args:\n",
    "    n : int\n",
    "        Number of (n x n) raster cells.\n",
    "    value : float\n",
    "        The point value of the source cell.\n",
    "    plot : boolean\n",
    "        Plot the raster target cell within the source cell.\n",
    "    quiet : boolean\n",
    "        Control verbosity of diagnostics.\n",
    "    \n",
    "    \"\"\"\n",
    "    # Create the raster cell space that covers the source cell.\n",
    "    shape = (n, n)\n",
    "    cells = np.ones(shape, dtype=np.float16) * value / np.prod(shape)\n",
    "    # Raster the target cell within the source cell.\n",
    "    weights = np.zeros(shape, dtype=np.uint8)\n",
    "    xi = np.array([[0.5, 0.75], [0.25, 0.5]], dtype=np.float64) * n\n",
    "    yi = np.array([[0.25, 0.5], [0.5, 0.75]], dtype=np.float64) * n\n",
    "    raster(weights, xi, yi)\n",
    "    # Calculate the contribution of the source cell to the target cell.\n",
    "    result = np.sum((weights / 255.) * cells)\n",
    "    if not quiet:\n",
    "        print weights\n",
    "        print 'weights sum = {}'.format(weights.sum())\n",
    "        print '{} of {} elements populated'.format(len(np.where(weights > 0)[0]), weights.size)\n",
    "        fraction = np.sum((weights / 255.) * cells) / value\n",
    "        print 'result = {}'.format(result)\n",
    "        print 'fraction = {} -> {}'.format(fraction, 1. / 8)\n",
    "        print 'error = {} %'.format(((value / 8.) - result) / (value / 8.) * 100)\n",
    "    if plot:\n",
    "        plt.pcolormesh(weights, vmin=0, vmax=255, cmap='gray_r')\n",
    "        plt.colorbar()\n",
    "        plt.xlim(0, n)\n",
    "        plt.ylim(0, n)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's now crank up the raster cell space (represented by a pixel buffer) that covers the source cell, to determine the speed and accuracy of this particular example scenario raster regrid. AGG will render the target cell in the pixel buffer using a filled grey-scale image, where each pixel is represented by a uint8, thus giving rather crude quantized valued in the range 0...255. But it's rather surprising the accuracy that can be achieved ...\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[31]]\n",
      "weights sum = 31\n",
      "1 of 1 elements populated\n",
      "result = 9.72549019608\n",
      "fraction = 0.121568627451 -> 0.125\n",
      "error = 2.74509803922 %\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb7c56d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use a single pixel to represent the source cell, and exercise the sub-pixel accuracy of AGG ...\n",
    "grid(1, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 21.89 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 108 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(1, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[31 31]\n",
      " [31 31]]\n",
      "weights sum = 124\n",
      "4 of 4 elements populated\n",
      "result = 9.72549019608\n",
      "fraction = 0.121568627451 -> 0.125\n",
      "error = 2.74509803922 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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krUlek+SuJN9PcmeSU4atb1w/zD0InFFVzyfZAnwVeMN8Dbdu3Xr49caNG9m0adOYSpB0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb78a42d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 2x2 pixel buffer for the raster cells ...\n",
    "grid(2, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 112 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(2, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0   0   0   0]\n",
      " [  0 127 127   0]\n",
      " [  0 127 127   0]\n",
      " [  0   0   0   0]]\n",
      "weights sum = 508\n",
      "4 of 16 elements populated\n",
      "result = 9.96078431373\n",
      "fraction = 0.124509803922 -> 0.125\n",
      "error = 0.392156862745 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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Sfvnll3n55Zd7rfMrwKXAbzWdTj1KrJmTsJlVWqckPHfuXObOnXv0/Q9/+MOOVSSvI/Vd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb56c7410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 4x4 pixel buffer for the raster cells ...\n",
    "grid(4, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 113 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(4, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0]\n",
      " [  0   0   0 127 127   0   0   0]\n",
      " [  0   0 127 255 255 127   0   0]\n",
      " [  0   0 127 255 255 127   0   0]\n",
      " [  0   0   0 127 127   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0]]\n",
      "weights sum = 2036\n",
      "12 of 64 elements populated\n",
      "result = 9.98039215686\n",
      "fraction = 0.124754901961 -> 0.125\n",
      "error = 0.196078431373 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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A/w54H3Ai8G8lLQYuB+61/avAfcAVvdZXplvg3cAKSXPohPHNtu/q9YIREYPQZ7fAEuDB\nN5bQlvRPwB8AS+msCguwAmjTCdzdVmYo1lrg5F5OHhFRlT7D9QngvxXdAD8DPgI8AhxmexuA7a2S\n3tXrBfKEVkQ00kzhum7dOtavXz/rZ20/JekLwD3AdmACeG26Q3utL+EaEY00U7iecMIJnHDCCbte\n33bbbdMeZ3s5sLw4138HNgPbJB1me5ukw4Hne62v3jMfRETMoN9xrpLeWfw+Avh94AbgTuDi4pCL\ngDt6rS8t14hopAHMivU3kg4BdgCX2P5J0VVwi6RPAM8A5/d68oRrRDRSvw8R2P7tafa9CJzV14kL\nCdeIaKS6P6GVcI2IRkq4RkRUIOEaEVGBhGtERAUSrhERFcgChRERFUjLNSKiAgnXiIgKJFwjIiqQ\ncI2IqEDCNSKiAgnXiIgKZChWREQF6t5yLbP660JJ90l6UtJaSZcOo7CIiNn0O1l21cq0XHcCn7W9\nRtIBwKOS7rad5bUjYmTq3nIts/rrVmBrsb1d0npgAZBwjYiRqXu47laPsKSjgBOBB6soJiKirAGs\noTVP0q2S1hfdnqdKeoekuyV9T9K3JM3rtb7SN7SKLoFVwGW2t093zPj4+K7tVqtFq9Xqta7o09jY\n2KhLiACg3W7TbrcHft4BjBa4BrjL9h9JmgvsD1wJ3Gv7i5I+D1wBXN7LyWV3X5a7uPDfA/9g+5oZ\njnGZc0XEW5skbPf1nV6S77///lLHnnHGGb90PUkHARO2F0/Z/xRwxqSltdu239tLjWWj/2vAupmC\nNSJi2PrsFjga+LGk5ZIek3StpP2Aw2xvg133m97Va31duwUknQZ8DFgraQIwcKXtb/Z60YiIfs0U\nnBMTE0xMTHT7+FzgZODTth+RdDWdr/9Tv373/HW8VLdAqROlWyAiShhUt8ADDzxQ6tjTTz99um6B\nw4DVto8pXp9OJ1wXA61J3QL/aHtJLzXW+/mxiIgZ9NMtUHz13yzpuGLXmcCTwJ3AxcW+i4A7eq0v\nj79GRCMNYJzrpcBKSW8DNgIfB/YCbpH0CeAZ4PxeT55wjYhG6ncolu3vAr85zVtn9XXiQsI1Ihqp\n7k9oJVwjopESrhERFUi4RkRUIOEaEVGBhGtERAUSrhERFcgaWhERFUjLNSKiAgnXiIgKJFwjIiqQ\ncI2IqEDCNSKiAgnXiIgKZChWREQF6t5y7Rr9kq6TtE3S48MoKCKijD4XKKxcmXb1cuDDVRcSEbE7\nGh+uth8AXhpCLRERpfUTrpL2kfSgpAlJayWNFfvfIeluSd+T9C1J83qtr949whERM+hzgcKfAR+0\nfRJwInCupFPorAB7r+1fBe4Drui1voRrRDRSv90Ctl8tNvehc3PfwHnAimL/CuD3eq1voKMFxsfH\nd223Wi1ardYgTx8RDdRut2m32wM/b79DsSTNAR4FFgN/ZfthSYcVy25je6ukd/V8fttlijgK+Dvb\nvzbLMS5zroh4a5OE7b7uNEnyM888U+rYI488ctbrSToIuJ3OUtv/x/Yhk957wfahvdTYteUq6Qag\nBRwq6VlgzPbyXi4WETEoM33lX716NatXry59Hts/kdQGzgG2vdF6lXQ48HzP9Q2qtZmWa0SUMaiW\n6+bNm0sdu2jRol+6nqT5wA7br0jaF/gW8GfAGcCLtr8g6fPAO2xf3kuNeUIrIhqpzzGs7wZWFP2u\nc4Cbbd8l6TvALZI+ATwDnN9zfWm5RsQwDarlumXLllLHLliwoO/r9SIt14hopLrPLZBwjYhGyqxY\nEREVSMs1IqICCdeIiAokXCMiKpBwjYioQMI1IqICGS0QEVGBtFwjIiqQcI2IqEDCNSKiAgnXiIgK\nJFwjIiqQcI2IqECGYkVEVCAt14iICtQ9XEu1qyWdI+kpSd8v1pWJiBgpSaV+Zvl8pbnWNVyLNWb+\nJ/Bh4ATgo5LeO+hCBqGKtdF7UYc6UsOb6lBHHWqA+tQxCP2E6zByrUzL9RRgg+1nbO8AbgLOG2QR\ng1KXvzh1qCM1vKkOddShBqhPHYPQZ8u18lwrE64LgMlr2P6g2BcRMTJ9hmvluZYbWhHRSHUfitV1\naW1J7wfGbZ9TvL4csO0vTDku62pHRCkDWFp7E3BkycO32T58yudL5VpfNZYI172A7wFnAj8EHgI+\nanv9oIqIiBimYeRa124B269J+lPgbjp9tNclWCOiyYaRa11brhERsfv67hGuwwMGkq6TtE3S46O4\nflHDQkn3SXpS0lpJl46ojn0kPShpoqhjbBR1FLXMkfSYpDtHWMMmSd8t/jweGlEN8yTdKml98ffj\n1BHUcFzxZ/BY8fuVUfwdlfQZSU9IelzSSkl7D7uGYemr5VoMxP0+nX6L54CHgQtsPzWY8krXcTqw\nHbje9q8P89qTajgcONz2GkkHAI8C5w37z6KoZT/brxb9Sv8MXGp76MEi6TPAbwAH2V467OsXNWwE\nfsP2S6O4flHD14H7bS+XNBfYz/ZPRljPHDpDj061vbnb8QO87nuAB4D32v65pJuB/237+mHVMEz9\ntlxr8YCB7QeAkf3PU9Sw1faaYns7sJ4RjQe2/WqxuQ+dfvWh9/1IWgh8BPjqsK89tRQG8A2t54tL\nBwG/ZXs5gO2dowzWwlnAvwwzWCfZC9j/jX9k6DTK9kj9/qXLAwbTkHQUcCLw4IiuP0fSBLAVuMf2\nwyMo42rgc4wg2KcwcI+khyV9cgTXPxr4saTlxVfyayXtO4I6Jvtj4MZhX9T2c8CXgGeBLcDLtu8d\ndh3DUu9RuA1UdAmsAi4rWrBDZ/t12ycBC4FTJR0/zOtL+h06YwvX0Gk5jnL6otNsn0ynFf3pogtp\nmOYCJwN/VdTxKnD5kGvYRdLbgKXArSO49sF0vtkeCbwHOEDShcOuY1j6DdctwBGTXi8s9r0lFV91\nVgHfsH3HqOspvn7+I3DOkC99GrC06O+8EfigpJH0q9n+YfH7R8DtdLqyhukHwGbbjxSvV9EJ21E5\nF3i0+PMYtrOAjbZftP0acBvwgRHUMRT9huvDwLGSjizu+l0AjOrO8KhbSABfA9bZvmZUBUiaL2le\nsb0v8CFgqDfVbF9p+wjbx9D5O3Gf7T8ZZg3QubFXfJNA0v7A2cATw6zB9jZgs6Tjil1nAuuGWcMU\nH2UEXQKFZ4H3S3q7Og/9n0nn3sQeqa+5BerygIGkG4AWcKikZ4GxN24gDLGG04CPAWuL/k4DV9r+\n5jDrAN4NrCjuCM8BbrZ915BrqIvDgNuLR7PnAitt3z2COi4FVhZfyTcCHx9BDUjaj07r8VOjuL7t\nhyStAiaAHcXva0dRyzDkIYKIiArkhlZERAUSrhERFUi4RkRUIOEaEVGBhGtERAUSrhERFUi4RkRU\nIOEaEVGB/w8VHUUcdPyifQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb56d79d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 8x8 pixel buffer for the raster cells ...\n",
    "grid(8, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 121 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(8, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0 127 127   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0 127 255 255 127   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0 127 255 255 255 255 127   0   0   0   0   0]\n",
      " [  0   0   0   0 127 255 255 255 255 255 255 127   0   0   0   0]\n",
      " [  0   0   0   0 127 255 255 255 255 255 255 127   0   0   0   0]\n",
      " [  0   0   0   0   0 127 255 255 255 255 127   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0 127 255 255 127   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0 127 127   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]]\n",
      "weights sum = 8152\n",
      "40 of 256 elements populated\n",
      "result = 9.99019607843\n",
      "fraction = 0.12487745098 -> 0.125\n",
      "error = 0.0980392156863 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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BL0paKulRSd+StH9VhUVE9GuYhxpmAKcAX7L9sKT/DFxDZ5mMt+iejKTVatFqtUo0GxHD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\nEVGzBG9ERM0SvBERNfv/EnQgyXt8FrQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb78a4290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 16x16 pixel buffer for the raster cells ...\n",
    "grid(16, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 131 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(16, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 32624\n",
      "144 of 1024 elements populated\n",
      "result = 9.99509803922\n",
      "fraction = 0.12493872549 -> 0.125\n",
      "error = 0.0490196078431 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb5580d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 32x32 pixel buffer for the raster cells ...\n",
    "grid(32, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 21.54 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "1000 loops, best of 3: 172 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(32, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 130528\n",
      "544 of 4096 elements populated\n",
      "result = 9.99754901961\n",
      "fraction = 0.124969362745 -> 0.125\n",
      "error = 0.0245098039215 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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YzGrHidfMrGROvGZmJXPita655lstI/28XdOtJideM7OSebNLM7OSucdrhfEKZ+XyULGJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb5587a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 64x64 pixel buffer for the raster cells ...\n",
    "grid(64, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 311 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(64, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 522176\n",
      "2112 of 16384 elements populated\n",
      "result = 9.9987745098\n",
      "fraction = 0.124984681373 -> 0.125\n",
      "error = 0.0122549019608 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb54a3110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 128x128 pixel buffer for the raster cells ...\n",
    "grid(128, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 865 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(128, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 2088832\n",
      "8320 of 65536 elements populated\n",
      "result = 9.9993872549\n",
      "fraction = 0.124992340686 -> 0.125\n",
      "error = 0.00612745098039 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb7954fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 256x256 pixel buffer for the raster cells ...\n",
    "grid(256, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 3.03 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(256, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 8355584\n",
      "33024 of 262144 elements populated\n",
      "result = 9.99969362745\n",
      "fraction = 0.124996170343 -> 0.125\n",
      "error = 0.00306372549016 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb55ae150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 512x512 pixel buffer for the raster cells ...\n",
    "grid(512, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 11.8 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(512, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 33422848\n",
      "131584 of 1048576 elements populated\n",
      "result = 9.99984681373\n",
      "fraction = 0.124998085172 -> 0.125\n",
      "error = 0.00153186274503 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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lwN2aY+MO6ooYGRnxyTqARkdH/e/eBWWDOiI2A69PW7YpIt5Jb58ChtLr5cCDETEZEXsp\nQvyc2drnGnXFuG49OBzQ3dOFc+oG4Nvp9WJgS83vxtOyuhzUFeSw7n8O6e7q5Pkk6d8Db0XEt+dc\nuQ4HdUVFBGvWrHHtug85pLuvXlDv2bOHPXv2lNnudcDngM/ULB4HltS8H0rL6nJQV9jUY5wc1v3D\nId0b9YL6pJNO4qSTTnr3/Q9+8INZN5N+prZ5KfAl4Lci4s2a9TYA90u6g6LkcTLwzGwb9mBixXmQ\nsT940LC32jA97wHgb4BTJb0s6XrgT4DDgSckPSfpboCI2Ak8BOwEHgVumut2oe5R9wnXratrdHTU\nD7ntsbLnTkRcPcPidbOsfxtwW6Pbd1D3EYd19bgXnYfczxuXPvqMr2SsDod0PnxTJus6DzLmzyGd\nF/eorSc8yJgnDxrmyT1q6ynXrfPhQcN85X6OOKgHgMO699yLzttsU+9ykHfrrG08yNg7Dun8ufRh\n2fAgY/c5pKsh9//jdI96wHiQsTs8aFgtufeoSwe1pHnp8sgN6f0CSRslvSjpcUlH1qzb1FMNrHMc\nIp3jQcPqyT2o21H6WElxzfrUY2ZWAZsi4nZJX6Z4qsGqaU81GAI2STplrmvcrXM8yNh+PpyrKffz\noFSPWtIQxS387qlZfDmwPr1eD1yRXjf9VAPrPA8yto9DurrK3pSp4+0r+fk7KG7jV3uELoyICYCI\n2A8cm5YvBvbVrDfnUw2sO/xMxvIc0tWWe+mj5aCW9DvARERso+YerDPwEVwBHmRsjQcN+0PuQV2m\nRn0+sFzS54DDgPmS7gP2S1oYEROSFgGvpvWbeqpBbQ9veHiY4eHhEk21Rrlu3TgPGvbG2NgYY2Nj\nbd1m7se82tEbkHQh8EcRsVzS7cD/iYi1aTBxQURMDSbeD5xLUfJ4AphxMFGSxxh7LPcDt9d8fOZD\nEhHR8gErKe69996G1r3xxhtLfVerOnHBy1eBhyTdALxEMdODiNgpaeqpBm/RwFMNrHfcs67Ph23/\nyf1Yb8swZkT8dUQsT69fi4jPRsRpEXFxRPyiZr3bIuLkiFgaERvb8d3WOZ4R8kEO6f6Ue43aVyba\nrDzIWPCgYX9rwzMTV0rakX5WpGV1L/5run2tftAGyyCHlAcN+1+ZHrWkM4AbgU8CZwGfl3QS7138\ndxrwJMXFfy3xTZmsYYNYtx7kP1CDpORxvRR4OiLeTNv6n8C/oLjIbzitsx4YowjvprlHbU0ZpOAa\npH0ddCVr1D8GPp1KHR+huFp7CfUv/muae9TWtIhgzZo1fT3Q6JAeLPVCeOfOnezatWvWz0bEC5LW\nUkw5PgBsBd6eadWW25fjAel51NXRb6UQ16Orpx3zqB944IGG1r366qvn/C5J/4HidhkrgeGai/9+\nGBFLW2mje9RWSj/Vrd05GFxlj2FJ/ygi/l7SccDvAucBJwLXAWuBa4FHWt2+g9pK64ewdkgPtjbc\nGe97ko7mvYv5/iGVQz5w8V8rHNTWFlUOa4e0lT12I+K3Zlj2GvDZUhtOPOvD2qaKVzI6pA18ZaIN\nmKpcyegrDa1W7kHt0od1RM6lEAe0TZfrsTrFQW0dk2NYO6RtJrkdp9M5qK2jcgprh7TVk8sxWo9r\n1NZxOQwyOqRtNrk/3NY9auuKqav9ehHYDmmbi3vUZkm3Z4REhEPaGuJZH2bTdKNu7YC2ZuTeo3ZQ\nW090Mqwd0tas3IPapQ/rmU4MMjqkrRW5lz4c1NZTIyMjbQlrX2loZeQe1L4ftWWj1RPBx8pga8f9\nqB9//PGG1r3kkktKfVerXKO2bLRSt3ZIWzvkXqN2UFtWmglrh7S1S+5B7Rq1ZaeRQUaHtLVT7jVq\nB7Vlqd7FMR40tE7IPahd+rCs1ZZCHNDWKW14ZuKRwD3AbwDvADcAPwG+AxwP7AWujIg3Wtm+e9SW\nPV8Kbp3Whpsy3Qk8mp4y/gngBWAVsCkiTgOeBFa33L5WP2hm1i/KlD4kHQF8OiLWAUTEZOo5Xw6s\nT6utB65otX0OajMbeCVr1CcCP5e0TtJzkr4h6SPAwoiYAIiI/cCxrbbPNWozG3j1Qnjr1q1s3bp1\nro8fDCwDbo6IH0m6g6LsMb1e13L9zlcmmlmltePKxM2bNze07gUXXPCB75K0ENgSER9L7y+gCOqT\ngOGImJC0CPhhqmE3zaUPMxt4ZUofqbyxT9KpadFFwPPABuC6tOxa4JFW2+fSh5kNvDbMkV4B3C/p\nQ8Ae4HrgIOAhSTcALwFXtrpxB7WZDbyyz0OMiL8DPjXDrz5basNJy62TNCTpSUnPS9ohaUVavkDS\nRkkvSno8TQSf+sxqSbsl7ZJ0cTt2wMysrNyvTCzzZ2QS+GJEnAH8U+BmSR+nziRvSadTdP2XApcB\ndyv3O6GY2UDo26COiP0RsS29PgDsAoaoP8l7OfBgmgy+F9gNnNPq95uZtUvfBnUtSScAZwFPUX+S\n92JgX83HxtMyM7Oeyj2oSw8mSjoceBhYGREHJLVlknftbS6Hh4cZHh5utYlm1kfGxsYYGxtr6zZz\nr8KWuuBF0sHAXwH/IyLuTMt2McMkb0mrgIiItWm9x4CRiHh6hu36ghcza0g7Lnh57rnnGlp32bJl\nPXkUV9nSxzeBnVMhndSb5L0BuErSIZJOBE4Gnin5/WZmpbXh7nkd1XLpQ9L5wDXADklbKUoctwJr\nmWGSd0TslPQQsBN4C7jJ3WYzy0Fflz46xaUPM2tUO0of27dvb2jdM888008hNzPrhdx71A5qMxt4\nDmozs8w5qM3MMuegNjPLXC+n3jXCQW1mA889ajOzzDmozcwyl3tQ512YMTPrgjJ3z5N0qKSnJW1N\nD1EZScvrPkSlWQ5qMxt4JR9u+ybw2xFxNsXtni+TdA51HqLSCge1mQ28svejjoj/m14eSlFSDuo/\nRKVpDmozG3hl754naV66Od1+4ImIeJb6D1FpmgcTzWzglR1MjIh3gLMlHQH8paQz+OBDU1q+05yD\n2swGXr2g3rJlC1u2bGl4OxHxD5LGgEuBCUkLax6i8mrL7cvxdqK+zamZNaodtzndt2/f3CsCS5Ys\n+cB3SToGeCsi3pB0GPA48FXgQuC1iFgr6cvAgohY1Uob3aM2s4FXsvTxj4H1kuZRjPt9JyIelfQU\nMzxEpaX25dhzdY/azBrVjh71+Ph4Q+suXrzYDw4wM+uF3K9MdFCb2cDz3fPMzDLnHrWZWeYc1GZm\nmXNQm5llzkFtZpY5B7WZWeY868PMLHPuUZuZZc5BbWaWOQe1mVnmHNRmZplzUJuZZc5BbWaWOU/P\nMzPLnHvUZmaZyz2ou97fl3SppBck/SQ9R8zMrKckNfQzy+c7mmtdDer0TLH/AlwCnAF8QdLHu9mG\nXhgbG+t1E9qq3/YH+m+fvD/NKRPU3ci1bveozwF2R8RLEfEW8CBweZfb0HU+afLXb/vk/WlOyR51\nx3Ot20G9GKh9LvvP0jIzs54pGdQdzzUPJprZwMt9ep4iontfJp0HjEbEpen9KiAiYu209brXKDOr\nvIhoedqGpL3A8Q2uPhERi6Z9vqFcK6PbQX0Q8CJwEfC/gWeAL0TErq41wsysjbqRa10tfUTE25L+\nENhIUR+/1yFtZlXWjVzrao/azMyal1UFvYoXw0gakvSkpOcl7ZC0Ii1fIGmjpBclPS7pyJrPrJa0\nW9IuSRf3rvX1SZon6TlJG9L7qu/PkZK+m9r4vKRzq7xPkm6R9GNJ2yXdL+mQqu2PpHslTUjaXrOs\n6X2QtCz9d/iJpP/c7f3oiojI4ofij8ZPKYr6HwK2AR/vdbsaaPci4Kz0+nCKWtXHgbXAv0vLvwx8\nNb0+HdhKUXY6Ie2zer0fM+zXLcCfAxvS+6rvz58B16fXBwNHVnWfgF8H9gCHpPffAa6t2v4AFwBn\nAdtrljW9D8DTwKfS60eBS3q9b+3+yalHXcmLYSJif0RsS68PALuAIYq2r0+rrQeuSK+XAw9GxGRE\n7AV2U+x7NiQNAZ8D7qlZXOX9OQL4dESsA0htfYMK7xNwEPBRSQcDhwHjVGx/ImIz8Pq0xU3tg6RF\nwPyIeDat962az/SNnIK68hfDSDqBoofwFLAwIiagCHPg2LTa9P0cJ7/9vAP4ElA7gFHl/TkR+Lmk\ndamc8w1JH6Gi+xQRrwBfA16maNsbEbGJiu7PNMc2uQ+LKbJiSuVyoxE5BXWlSToceBhYmXrW00dp\nKzFqK+l3KOaKbgNmm5taif1JDgaWAV+PiGXAL4FVVPff6CiKnufxFGWQj0q6horuzxz6YR9Kyymo\nx4Hjat4PpWXZS//7+TBwX0Q8khZPSFqYfr8IeDUtHweW1Hw8t/08H1guaQ/wbeAzku4D9ld0f6Do\nZe2LiB+l99+jCO6q/ht9FtgTEa9FxNvAXwL/jOruT61m96FK+9aynIL6WeBkScdLOgS4CtjQ4zY1\n6pvAzoi4s2bZBuC69Ppa4JGa5VelUfoTgZMpJshnISJujYjjIuJjFP8GT0bE7wPfp4L7A5D+V3qf\npFPToouA56novxFFyeM8SR9WcQOKi4CdVHN/xPv/z62pfUjlkTcknZP+W/zLms/0j16PZtb+AJdS\nzJrYDazqdXsabPP5wNsUs1S2As+l/Tga2JT2ZyNwVM1nVlOMWu8CLu71Psyybxfy3qyPSu8P8AmK\nzsA24C8oZn1Udp+AkdS27RSDbh+q2v4ADwCvAG9S/PG5HljQ7D4A/wTYkXLjzl7vVyd+fMGLmVnm\ncip9mJnZDBzUZmaZc1CbmWXOQW1mljkHtZlZ5hzUZmaZc1CbmWXOQW1mlrn/D3D0svk7zk0YAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb53a18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 1024x1024 pixel buffer for the raster cells ...\n",
    "grid(1024, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 48.6 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(1024, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 133692416\n",
      "525312 of 4194304 elements populated\n",
      "result = 9.99992340686\n",
      "fraction = 0.124999042586 -> 0.125\n",
      "error = 0.000765931372424 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb5396290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 2048x2048 pixel buffer for the raster cells ...\n",
    "grid(2048, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 208 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(2048, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " ..., \n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]\n",
      " [0 0 0 ..., 0 0 0]]\n",
      "weights sum = 534771712\n",
      "2099200 of 16777216 elements populated\n",
      "result = 9.99996170343\n",
      "fraction = 0.124999521293 -> 0.125\n",
      "error = 0.00038296568583 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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BbWaWOQe1mVnmPOrDzCxzblGbmWXOQW1mljkHtZlZ5hzUZmaZc1CbmWXOQW1m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\nBC7HcAqfx64AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdb54b0ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try a 4096x4096 pixel buffer for the raster cells ...\n",
    "grid(4096, src_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 778 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "grid(4096, src_value, plot=False, quiet=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}