test_astropy_convolution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test the astropy convolution routine\n",
    "It treats NaNs robustly, but converts big regions of NaN to zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from astropy.io import fits\n",
    "from astropy.utils.data import get_pkg_data_filename\n",
    "from astropy.convolution import Gaussian2DKernel\n",
    "from scipy.signal import convolve as scipy_convolve\n",
    "from astropy.convolution import convolve\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.zeros((25,25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[12,12]= 1.\n",
    "a[10,10]= .5\n",
    "a[11,11]= np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1c8437d4ac8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAChdJREFUeJzt3U+onXedx/H3xyZNsSo0aEumdkbH\nCYPZGOVSCx2GSqkT3aQuCnYxZCFcFy3o4Ka40c1AN1pnIUKchmahFQftNIsyGoLQGZgpRgk2JQ4t\npaMxIRnpomVg+vc7i/sEbtPc3JN7/jz3zPf9gnDO+d3n3ufLQ955znPOSZKqQlI/7xl7AEnjMH6p\nKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmtqxyJ1dn111AzcucpdSK//L//B6vZZJtp0q/iQHgH8A\nrgP+saoevtr2N3Ajn87d0+xS0lU8Uycm3nbLT/uTXAd8F/gcsA+4P8m+rf48SYs1zTX/7cALVfVi\nVb0O/Ag4OJuxJM3bNPHfCvx+3eOzw5qkJTDNNf+VXlR4198PTrIKrALcwHun2J2kWZrmzH8WuG3d\n4w8D5y7fqKoOV9VKVa3sZNcUu5M0S9PE/0tgb5KPJrke+CJwbDZjSZq3LT/tr6o3kzwI/Iy1t/qO\nVNVzM5tM0lxN9T5/VT0FPDWjWSQtkB/vlZoyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6p\nKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp\n45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmtoxzTcneQl4FXgLeLOqVmYxlKT5myr+wWeq\n6o8z+DmSFsin/VJT08ZfwM+T/CrJ6pU2SLKa5GSSk2/w2pS7kzQr0z7tv7OqziW5GTie5LdV9fT6\nDarqMHAY4APZXVPuT9KMTHXmr6pzw+1F4Ang9lkMJWn+thx/khuTvP/SfeCzwOlZDSZpvqZ52n8L\n8ESSSz/nh1X1LzOZStLcbTn+qnoR+MQMZ5G0QL7VJzVl/FJTxi81ZfxSU8YvNWX8UlPGLzVl/FJT\nxi81ZfxSU8YvNWX8UlPGLzVl/FJTxi81ZfxSU8YvNWX8UlPGLzVl/FJTxi81ZfxSU8YvNWX8UlPG\nLzVl/FJTxi81ZfxSU8YvNWX8UlPGLzVl/FJTxi81tWPsATQbLzxyx6bb/MXf/ccCJtGy2PTMn+RI\nkotJTq9b253keJLnh9ub5jumpFmb5Gn/Y8CBy9YeAk5U1V7gxPBY0hLZNP6qehp4+bLlg8DR4f5R\n4N4ZzyVpzrb6gt8tVXUeYLi9eXYjSVqEub/gl2QVWAW4gffOe3eSJrTVM/+FJHsAhtuLG21YVYer\naqWqVnaya4u7kzRrW43/GHBouH8IeHI240halEne6nsc+HfgL5OcTfIl4GHgniTPA/cMjyUtkVTV\nwnb2geyuT+fuhe1P73T87X/adJt73nPfAibRvDxTJ3ilXs4k2/rxXqkp45eaMn6pKeOXmjJ+qSnj\nl5oyfqkp45ea8l/yaWSSD/D87Nypq379b/5k/6zG0cg880tNGb/UlPFLTRm/1JTxS00Zv9SU8UtN\n+T6/3sH38fvwzC81ZfxSU8YvNWX8UlPGLzVl/FJTxi81ZfxSU8YvNWX8UlPGLzVl/FJTxi81ZfxS\nU8YvNWX8UlPGLzVl/FJTm8af5EiSi0lOr1v7ZpI/JDk1/Pr8fMeUNGuTnPkfAw5cYf2Rqto//Hpq\ntmNJmrdN46+qp4GXFzCLpAWa5pr/wSS/GS4LbtpooySrSU4mOfkGr02xO0mztNX4vwd8DNgPnAe+\ntdGGVXW4qlaqamUnu7a4O0mztqX4q+pCVb1VVW8D3wdun+1YkuZtS/En2bPu4ReA0xttK2l72vR/\n7EnyOHAX8MEkZ4FvAHcl2Q8U8BLw5TnOKGkONo2/qu6/wvKjc5hF0gL5CT+pKeOXmjJ+qSnjl5oy\nfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+\nqSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5raNP4ktyX5RZIz\nSZ5L8pVhfXeS40meH25vmv+4kmZlkjP/m8DXqurjwB3AA0n2AQ8BJ6pqL3BieCxpSWwaf1Wdr6pf\nD/dfBc4AtwIHgaPDZkeBe+c1pKTZu6Zr/iQfAT4JPAPcUlXnYe0PCODmWQ8naX4mjj/J+4CfAF+t\nqleu4ftWk5xMcvINXtvKjJLmYKL4k+xkLfwfVNVPh+ULSfYMX98DXLzS91bV4apaqaqVneyaxcyS\nZmCSV/sDPAqcqapvr/vSMeDQcP8Q8OTsx5M0Lzsm2OZO4G+BZ5OcGta+DjwM/DjJl4DfAffNZ0RJ\n87Bp/FX1b0A2+PLdsx1H0qL4CT+pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp\n45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5oyfqkp45eaMn6pKeOXmjJ+qSnj\nl5oyfqkp45eaMn6pKeOXmjJ+qSnjl5pKVS1uZ8l/A/+1bumDwB8XNsD0lmneZZoVlmve7Tzrn1XV\nhybZcKHxv2vnycmqWhltgGu0TPMu06ywXPMu06xX49N+qSnjl5oaO/7DI+//Wi3TvMs0KyzXvMs0\n64ZGveaXNJ6xz/ySRjJa/EkOJPnPJC8keWisOSaR5KUkzyY5leTk2PNcLsmRJBeTnF63tjvJ8STP\nD7c3jTnjehvM+80kfxiO8akknx9zxkuS3JbkF0nOJHkuyVeG9W17fCc1SvxJrgO+C3wO2Afcn2Tf\nGLNcg89U1f5t+hbPY8CBy9YeAk5U1V7gxPB4u3iMd88L8MhwjPdX1VMLnmkjbwJfq6qPA3cADwy/\nV7fz8Z3IWGf+24EXqurFqnod+BFwcKRZll5VPQ28fNnyQeDocP8ocO9Ch7qKDebdlqrqfFX9erj/\nKnAGuJVtfHwnNVb8twK/X/f47LC2XRXw8yS/SrI69jATuqWqzsPab2Dg5pHnmcSDSX4zXBZsu6fR\nST4CfBJ4huU8vu8wVvy5wtp2ftvhzqr6FGuXKQ8k+euxB/p/6HvAx4D9wHngW+OO805J3gf8BPhq\nVb0y9jyzMFb8Z4Hb1j3+MHBupFk2VVXnhtuLwBOsXbZsdxeS7AEYbi+OPM9VVdWFqnqrqt4Gvs82\nOsZJdrIW/g+q6qfD8lId3ysZK/5fAnuTfDTJ9cAXgWMjzXJVSW5M8v5L94HPAqev/l3bwjHg0HD/\nEPDkiLNs6lJIgy+wTY5xkgCPAmeq6tvrvrRUx/dKRvuQz/BWzneA64AjVfX3owyyiSR/ztrZHmAH\n8MPtNmuSx4G7WPvbZheAbwD/DPwY+FPgd8B9VbUtXmTbYN67WHvKX8BLwJcvXVOPKclfAf8KPAu8\nPSx/nbXr/m15fCflJ/ykpvyEn9SU8UtNGb/UlPFLTRm/1JTxS00Zv9SU8UtN/R8jwE9F2D3SaQAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c83e5a10b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = Gaussian2DKernel(x_stddev=1,y_stddev=3)\n",
    "ac = convolve(a, kernel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1c8438b6320>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8ANJEX4gKcIPJEX4gaT+Bq6HJ+1yRSowAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c83e586fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(ac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1c84397a0b8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqf8Dh5ZSe+65DtkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8438ee358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a[14:,14:]=np.nan\n",
    "plt.imshow(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1c843920198>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c8438465f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ac2 = convolve(a, kernel)\n",
    "plt.imshow(ac2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}