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   "source": [
    "# Numexpr\n",
    "\n",
    "**Numexpr** is a fast numerical expression evaluator for NumPy. \n",
    "\n",
    "With it, expressions that operate on arrays (like `3*a+4*b`) are accelerated and use less memory than doing the same calculation in Python.\n",
    "\n",
    "In addition, its **multi-threaded capabilities** can make use of all your cores, which may accelerate computations, most specially if they are not memory-bounded.\n",
    "\n",
    "Last but not least, `numexpr` can make use of Intel's VML (Vector Math Library, normally integrated in its Math Kernel Library, or MKL). This allows further acceleration of transcendent (i.e., non polynomial) expressions.\n",
    "\n",
    "**GitHub**: [https://github.com/pydata/numexpr#what-it-is-numexpr]()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Examples \n",
    "\n",
    "(gathered from `numexpr` documentation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numexpr as ne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(1e6)   # Choose large arrays for better speedups\n",
    "b = np.arange(1e6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e+00,   2.00000000e+00,   3.00000000e+00, ...,\n",
       "         9.99998000e+05,   9.99999000e+05,   1.00000000e+06])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ne.evaluate(\"a + 1\")   # a simple expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ...,  True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ne.evaluate('a*b-4.1*a > 2.5*b')   # a more complex one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([        nan,  1.72284457,  1.79067101, ...,  1.09567006,\n",
       "        0.17523598, -0.09597844])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ne.evaluate(\"sin(a) + arcsinh(a/b)\")   # you can also use functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Comparison with Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 3.11 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit a+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 2.8 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit ne.evaluate(\"a + 1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 15.9 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit a*b-4.1*a > 2.5*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 3.13 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit ne.evaluate('a*b-4.1*a > 2.5*b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (some) preliminary conclusions\n",
    "\n",
    "* numexpr is (generally) slow with small arrays\n",
    "* numexpr is very fast with large arrays and complex operations\n",
    "* numpy is terrific with in-place operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumExpr supported Datatypes\n",
    "\n",
    "* 8-bit boolean (bool)\n",
    "* 32-bit signed integer (int or int32)\n",
    "* 64-bit signed integer (long or int64)\n",
    "* 32-bit single-precision floating point number (float or float32)\n",
    "* 64-bit, double-precision floating point number (double or float64)\n",
    "* 2x64-bit, double-precision complex number (complex or complex128)\n",
    "* Raw string of bytes (str)"
   ]
  }
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