recurrence.ipynb

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   "metadata": {},
   "source": [
    "recurrence relation example\n",
    "https://jakevdp.github.io/blog/2013/06/15/numba-vs-cython-take-2/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    {
     "data": {
      "text/plain": [
       "0        0.471435\n",
       "1       -1.190976\n",
       "2        1.432707\n",
       "3       -0.312652\n",
       "4       -0.720589\n",
       "5        0.887163\n",
       "           ...   \n",
       "99994   -0.940113\n",
       "99995   -1.478211\n",
       "99996    0.279401\n",
       "99997    0.029286\n",
       "99998   -1.220531\n",
       "99999    0.384112\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import Series\n",
    "from numba import jit\n",
    "\n",
    "np.random.seed(1234)\n",
    "pd.set_option('max_row',12)\n",
    "s = Series(np.random.randn(1e5))\n",
    "com = 0.5\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   "source": [
    "def python(s):\n",
    "    output = Series(index=range(len(s)))\n",
    "\n",
    "    alpha = 1. / (1. + com)\n",
    "    old_weight = 1.0\n",
    "    new_weight = 1.0\n",
    "    weighted_avg = s[0]\n",
    "    output[0] = weighted_avg\n",
    "    \n",
    "    for i in xrange(1,len(s)):\n",
    "        v = s[i]\n",
    "        old_weight *= (1-alpha)\n",
    "        weighted_avg = ((old_weight * weighted_avg) + (new_weight * v)) / (old_weight + new_weight)\n",
    "        old_weight += new_weight\n",
    "        output[i] = weighted_avg\n",
    "        \n",
    "    return output\n",
    "\n",
    "def cython(s):\n",
    "    return pd.ewma(s,com=com,adjust=True)\n",
    "\n",
    "@jit\n",
    "def f(arr, output):\n",
    "    alpha = 1. / (1. + com)\n",
    "    old_weight = 1.0\n",
    "    new_weight = 1.0\n",
    "    weighted_avg = arr[0]\n",
    "    output[0] = weighted_avg\n",
    "\n",
    "    for i in range(1,arr.shape[0]):\n",
    "        v = arr[i]\n",
    "        old_weight *= (1-alpha)\n",
    "        weighted_avg = ((old_weight * weighted_avg) + (new_weight * v)) / (old_weight + new_weight)\n",
    "        old_weight += new_weight\n",
    "        output[i] = weighted_avg\n",
    "            \n",
    "def numba(s):    \n",
    "    output = np.empty(len(s),dtype='float64')\n",
    "    f(s.values, output)\n",
    "    return Series(output)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "result1 = python(s)\n",
    "result2 = cython(s)\n",
    "result3 = numba(s)\n",
    "result1.equals(result2) and result1.equals(result3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loops, best of 3: 1.73 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit python(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 4.82 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit cython(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 1.01 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit numba(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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