source-code/numpy/numexpr.ipynb

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   "source": [
    "# numpy & numexpr"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the required modules."
   ]
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   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import numexpr as ne\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "numexpr can be used to speed up arithmetic operations on numpy arrays, and conserve memory when doing so by avoiding the creation of unnecessary intermediate arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create some matrices to compute with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "a = np.random.uniform(0, 1, (1000, 1000))\n",
    "b = np.random.uniform(0, 1, (1000, 1000))\n",
    "c = np.random.uniform(0, 1, (1000, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "135 ms ± 28 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit d = 3*a + b*c**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.82 ms ± 206 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit d = ne.evaluate('3*a + b*c**3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Under the hood, numexpr uses Intel VML (Vector Math Library) that is part of MKL if that is available, hence ensuring that the vector/matrix aritmethic is vectorized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "numexpr also supports the `where` function to \"mask\" arrays according to boolean conditions on the elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.85 ms ± 1.23 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit e = np.where(a > 0.5, 1, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.13 ms ± 223 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit e = ne.evaluate('where(a > 0.5, 1, -1)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this result is not very impressive, keep in mind that this output was generated on a single core machine. VML will automatically use multithreading to further parallelize vector/matrix arithmetic operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Important note:** numexpr supports only element-wise operations, except for accumulation using `sum` and `prod`."
   ]
  }
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