{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Making Python faster\n", "====\n", "\n", "The Julia website has a set of benchmarks to show how fast it is. These are for toy functions, but serve as a nice set of examples for the basics of using `cython` and `numba` in Python.\n", "\n", "These examples are adapted from [here](https://www.ibm.com/developerworks/community/blogs/jfp/entry/python_meets_julia_micro_performance?lang=en)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Fortran Julia Python R Matlab\n", "1 fib 0.70 2.11 77.76 533.52 26.89\n", "2 parse_int 5.05 1.45 17.02 45.73 802.52\n", "3 quicksort 1.31 1.15 32.89 264.54 4.92\n", "4 mandel 0.81 0.79 15.32 53.16 7.58\n", "5 pi_sum 1.00 1.00 21.99 9.56 1.00\n", "6 rand_mat_stat 1.45 1.66 17.93 14.56 14.52\n", "7 rand_mat_mul 3.48 1.02 1.14 1.57 1.12" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "benchmarks = pd.read_pickle('julia_benchmarks.pic')\n", "benchmarks.ix[:, :6]" ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import time\n", "import random\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from numba import njit, jit" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The cython extension is already loaded. To reload it, use:\n", " %reload_ext cython\n" ] } ], "source": [ "%load_ext cython" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Utility function" ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def timer(f, *args, **kwargs):\n", " start = time.clock()\n", " ans = f(*args, **kwargs)\n", " return ans, time.clock() - start" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def report(fs, *args, **kwargs):\n", " ans, t = timer(fs[0], *args, **kwargs)\n", " print('%s: %.1f' % (fs[0].__name__, 1.0)) \n", " for f in fs[1:]:\n", " ans_, t_ = timer(f, *args, **kwargs)\n", " print('%s: %.1f' % (f.__name__, t/t_))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fib\n", "----" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fib(n):\n", " if n<2:\n", " return n\n", " return fib(n-1)+fib(n-2)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "6765" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fib(20)" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 loops, best of 3: 5.84 ms per loop\n" ] } ], "source": [ "%timeit fib(20)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from functools import lru_cache\n", "\n", "@lru_cache()\n", "def fib_lru(n):\n", " if n<2:\n", " return n\n", " return fib(n-1)+fib(n-2)" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The slowest run took 92.76 times longer than the fastest. This could mean that an intermediate result is being cached \n", "1000000 loops, best of 3: 213 ns per loop\n" ] } ], "source": [ "%timeit fib_lru(20)" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_a7383439b4d9daca4b8a6d569c53a027.pyx\n", " \n", " \n", "\n", "\n", "

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" ], "text/plain": [ "" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a\n", "\n", "def fib_cython_seq(int n):\n", " cdef int i\n", " cdef long a, b, tmp\n", " a = 0\n", " b = 1\n", " for i in range(n-1):\n", " tmp = a\n", " a = b\n", " b += tmp\n", " return b" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The slowest run took 15.42 times longer than the fastest. This could mean that an intermediate result is being cached \n", "10000000 loops, best of 3: 122 ns per loop\n" ] } ], "source": [ "%timeit fib_cython_seq(20)" ] }, { "cell_type": "code", "execution_count": 131, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fib: 1.0\n", "fib_lru: 1151.4\n", "fib_cython: 26.0\n", "fib_numba: 639.7\n", "fib_cython_seq: 1919.0\n" ] } ], "source": [ "report([fib, fib_lru, fib_cython, fib_numba, fib_cython_seq], 20)" ] }, { "cell_type": "code", "execution_count": 442, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6765\n", "6765\n", "6765\n", "6765\n", "6765\n" ] } ], "source": [ "fs = fib, fib_lru, fib_cython, fib_numba, fib_cython_seq\n", "for f in fs:\n", " print(f(20))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parse_int\n", "----" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def parse_int():\n", " for i in range(1,1000):\n", " n = random.randint(0,2**31-1)\n", " s = hex(n)\n", "# if s[-1]=='L':\n", "# s = s[0:-1] \n", " m = int(s,16)\n", " assert m == n" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 loops, best of 3: 4.56 ms per loop\n" ] } ], "source": [ "%timeit parse_int()" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def parse_int_numpy():\n", " for i in range(1,1000):\n", " n = np.random.randint(0,2**31-1)\n", " s = hex(n) \n", " m = int(s,16)\n", " assert m == n" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 loops, best of 3: 1.51 ms per loop\n" ] } ], "source": [ "%timeit parse_int_numpy()" ] }, { "cell_type": "code", "execution_count": 169, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_2d3f37e15c7a44b97af38354a036490d.pyx\n", " \n", " \n", "\n", "\n", "

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 04: cimport numpy as np
\n", "
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\n", "
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\n", "
/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_2d3f37e15c7a44b97af38354a036490d_1parse_int_cython(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused); /*proto*/\n",
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 07:     cdef int i, n, m
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  for (__pyx_t_1 = 1; __pyx_t_1 < 0x3E8; __pyx_t_1+=1) {\n",
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\n", "
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\n", "
  __pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;}\n",
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\n", "
  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numpy, 0, -1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L1_error;}\n",
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 04:
\n", "
 05: @cython.boundscheck(False)
\n", "
 06: @cython.wraparound(False)
\n", "
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\n", "
static __Pyx_memviewslice __pyx_f_46_cython_magic_2e0923d1649b2de5c2ff7f8deca79258_qsort_kernel_cython(__Pyx_memviewslice __pyx_v_a, int __pyx_v_lo, int __pyx_v_hi) {\n",
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 08:     cdef int i, j
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 10:
\n", "
+11:     i = lo
\n", "
  __pyx_v_i = __pyx_v_lo;\n",
       "
+12:     j = hi
\n", "
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\n", "
  while (1) {\n",
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\n", "
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       "
+15:         while i <= j:
\n", "
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       "      __pyx_t_1 = ((__pyx_v_i <= __pyx_v_j) != 0);\n",
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       "
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\n", "
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+17:                 i += 1
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       "      }\n",
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+18:             while a[j] > pivot:
\n", "
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       "        *((double *) ( /* dim=0 */ (__pyx_v_a.data + __pyx_t_10 * __pyx_v_a.strides[0]) )) = __pyx_t_8;\n",
       "
+22:                 i += 1
\n", "
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+23:                 j -= 1
\n", "
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       "
+24:         if lo < j:
\n", "
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+25:             qsort_kernel_cython(a, lo, j)
\n", "
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       "      __PYX_XDEC_MEMVIEW(&__pyx_t_11, 1);\n",
       "
+26:         lo = i
\n", "
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       "
+27:         j = hi
\n", "
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       "  }\n",
       "
+28:     return a
\n", "
  __PYX_INC_MEMVIEW(&__pyx_v_a, 0);\n",
       "  __pyx_r = __pyx_v_a;\n",
       "  goto __pyx_L0;\n",
       "
 29:
\n", "
+30: def benchmark_qsort_cython():
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 06:     cdef double sum
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" ], "text/plain": [ "" ] }, "execution_count": 298, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a\n", "\n", "cimport cython\n", "\n", "@cython.cdivision(True)\n", "def pisum_cython(int t):\n", " cdef double sum\n", " cdef int j, k\n", "\n", " for j in range(1, 501):\n", " sum = 0.0\n", " for k in range(1, t+1):\n", " sum += 1.0/(k*k)\n", " return sum" ] }, { "cell_type": "code", "execution_count": 299, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 loops, best of 3: 35.8 ms per loop\n" ] } ], "source": [ "%timeit pisum_cython(10000)" ] }, { "cell_type": "code", "execution_count": 286, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pisum: 1.0\n", "pisum_numba: 35.6\n", "pisum_cython: 35.6\n" ] } ], "source": [ "report([pisum, pisum_numba, pisum_cython], 10000)" ] }, { "cell_type": "code", "execution_count": 455, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.6448340718480652\n", "1.6448340718480652\n", "1.6448340718480652\n" ] } ], "source": [ "for f in pisum, pisum_numba, pisum_cython:\n", " print(f(10000))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rand_mat_stat\n", "----" ] }, { "cell_type": "code", "execution_count": 287, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def randmatstat(t):\n", " n = 5\n", " v = np.zeros(t)\n", " w = np.zeros(t)\n", " for i in range(1,t):\n", " a = np.random.randn(n, n)\n", " b = np.random.randn(n, n)\n", " c = np.random.randn(n, n)\n", " d = np.random.randn(n, n)\n", " P = np.matrix(np.hstack((a, b, c, d)))\n", " Q = np.matrix(np.vstack((np.hstack((a, b)), np.hstack((c, d)))))\n", " v[i] = np.trace(np.linalg.matrix_power(np.transpose(P)*P, 4))\n", " w[i] = np.trace(np.linalg.matrix_power(np.transpose(Q)*Q, 4))\n", " return (np.std(v)/np.mean(v), np.std(w)/np.mean(w))" ] }, { "cell_type": "code", "execution_count": 288, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 3: 260 ms per loop\n" ] } ], "source": [ "%timeit randmatstat(1000)" ] }, { "cell_type": "code", "execution_count": 391, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def randmatstat_numba(t):\n", " n = 5\n", " v = np.zeros(t)\n", " w = np.zeros(t)\n", " for i in range(1,t):\n", " a, b, c, d = np.random.randn(4, n, n)\n", " P = np.hstack((a, b, c, d))\n", " Q = np.vstack((np.hstack((a, b)), np.hstack((c, d))))\n", "\n", " PTP = P.T.dot(P)\n", " QTQ = Q.T.dot(Q)\n", "\n", " v[i] = np.trace(PTP @ PTP @ PTP @ PTP)\n", " w[i] = np.trace(QTQ @ QTQ @ QTQ @ QTQ)\n", " return (np.std(v)/np.mean(v), np.std(w)/np.mean(w))" ] }, { "cell_type": "code", "execution_count": 393, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def randmatstat_alt(t):\n", " n = 5\n", " v = np.zeros(t)\n", " w = np.zeros(t)\n", "\n", " for i in range(1,t):\n", " a, b, c, d = np.random.randn(4, n, n)\n", " P = np.hstack((a, b, c, d))\n", " Q = np.vstack((np.hstack((a, b)), np.hstack((c, d))))\n", "\n", " P1 = P.T @ P\n", " P2 = P1 @ P1\n", " P4 = P2 @ P2\n", "\n", " Q1 = Q.T @ Q\n", " Q2 = Q1 @ Q1\n", " Q4 = Q2 @ Q2\n", " \n", " v[i] = np.trace(P4)\n", " w[i] = np.trace(Q4)\n", "\n", " return (np.std(v)/np.mean(v), np.std(w)/np.mean(w))" ] }, { "cell_type": "code", "execution_count": 394, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 loops, best of 3: 131 ms per loop\n" ] } ], "source": [ "%timeit randmatstat_alt(1000)" ] }, { "cell_type": "code", "execution_count": 396, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "randmatstat: 1.0\n", "randmatstat_alt: 2.1\n" ] } ], "source": [ "report([randmatstat, randmatstat_alt], 1000)" ] }, { "cell_type": "code", "execution_count": 458, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.72398346943567571, 0.7713214961017032)\n", "(0.72398346943567571, 0.7713214961017032)\n" ] } ], "source": [ "for f in randmatstat, randmatstat_alt:\n", " np.random.seed(123)\n", " print(f(1000))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rand_mat_mul\n", "----" ] }, { "cell_type": "code", "execution_count": 289, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def randmatmul(n):\n", " A = np.random.rand(n,n)\n", " B = np.random.rand(n,n)\n", " return np.dot(A,B)" ] }, { "cell_type": "code", "execution_count": 290, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 loops, best of 3: 81 ms per loop\n" ] } ], "source": [ "%timeit randmatmul(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparison\n", "----\n", "\n", "These benchmarks don't mean very much - they were constructed by the Julia team presumably to show off Julia's strengths, and are used here just to illustrate basic Python optimization techniques. In some case (quicksort, mandel, pi_sum), this gives dramatic performance improvements but in other cases (parse_int, rand_mat_stat) there is less improvement. For fib, the speed depends on the algorithm used for calculation, and whether caching is enabled in the recursive case. The final test rand_mat_mul basically depends on the linear algebra library installed (blas, mkl, atlas) and is not really a comparison across languages.\n", "\n", "Julia certainly does look promising, and we might include mix in some Julia code in future courses." ] }, { "cell_type": "code", "execution_count": 459, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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