{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Astrophysics background\n",
    "\n",
    "It is very common in Astrophysics to work with sky pixels. The sky is tassellated in patches with specific properties and a sky map is then a collection of intensity values for each pixel. The most common pixelization used in Cosmology is [HEALPix](http://healpix.jpl.nasa.gov)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Measurements from telescopes are then represented as an array of pixels that encode the pointing of the instrument at each timestamp and the measurement output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample timeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numba\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity let's assume we have a sky with 50K pixels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NPIX = 50000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we have 50 million measurement from our instrument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NTIME = int(50 * 1e6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pointing of our instrument is an array of pixels, random in our sample case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pixels = np.random.randint(0, NPIX-1, NTIME)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our data are also random:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "timeline = np.random.randn(NTIME)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a map of the sky with pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the most common operations is to sum all of our measurements in a sky map, so the value of each pixel in our sky map will be the sum of each individual measurement.\n",
    "The easiest way is to use the `groupby` operation in `pandas`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "timeline_pandas = pd.Series(timeline, index=pixels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11105   -0.498438\n",
       "16106   -1.103009\n",
       "44723    0.392057\n",
       "16687    0.086918\n",
       "15197    1.946979\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timeline_pandas.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.49 s, sys: 604 ms, total: 3.09 s\n",
      "Wall time: 3.1 s\n"
     ]
    }
   ],
   "source": [
    "%time m = timeline_pandas.groupby(level=0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a map of the sky with numba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We would like to improve the performance of this operation using `numba`, which allows to produce automatically C-speed compiled code from pure python functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need to develop a pure python version of the code, test it, and then have `numba` optimize it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def groupby_python(index, value, output):\n",
    "    for i in range(index.shape[0]):\n",
    "        output[index[i]] += value[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_python = np.zeros_like(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 25.8 s, sys: 5 ms, total: 25.8 s\n",
      "Wall time: 25.8 s\n"
     ]
    }
   ],
   "source": [
    "%time groupby_python(pixels, timeline, m_python)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.testing.assert_allclose(m_python, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pure Python is slower than the `pandas` version implemented in `cython`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimize the function with numba.jit\n",
    "\n",
    "`numba.jit` gets an input function and creates an compiled version with does not depend on slow Python calls, this is enforced by `nopython=True`, `numba` would throw an error if it would not be possible to run in `nopython` mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "groupby_numba = numba.jit(groupby_python, nopython=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_numba = np.zeros_like(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 411 ms, sys: 7 ms, total: 418 ms\n",
      "Wall time: 441 ms\n"
     ]
    }
   ],
   "source": [
    "%time groupby_numba(pixels, timeline, m_numba)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.testing.assert_allclose(m_numba, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performance improvement is about 50x compared to Python and up to 10x compared to Pandas, pretty good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use numba.jit as a decorator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exact same result is obtained if we use `numba.jit` as a decorator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@numba.jit(nopython=True)\n",
    "def groupby_numba(index, value, output):\n",
    "    for i in range(index.shape[0]):\n",
    "        output[index[i]] += value[i]"
   ]
  }
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