Profile with Cython complied function in ODE solvers

profile_cython.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import solve_ivp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fun(t, y):\n",
    "    mu = 50\n",
    "    return np.array([y[1], mu * (1 - y[0] ** 2) * y[1] - y[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def jac(t, y):\n",
    "    mu = 50\n",
    "    return np.array([\n",
    "        [0, 1],\n",
    "        [-2 * mu * y[0] * y[1] - 1, mu * (1 - y[0] ** 2)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "def fun_cython(double t, double[:] y, double [:] f):\n",
    "    cdef double mu = 50\n",
    "    f[0] = y[1]\n",
    "    f[1] = mu * (1 - y[0] * y[0]) * y[1] - y[0]\n",
    "    return f.base.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f_cython = np.empty(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y0 = [2, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    }
   ],
   "source": [
    "stats = %prun -r -q solve_ivp(fun, [0, 1000], y0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         2168754 function calls in 3.306 seconds\n",
      "\n",
      "   Ordered by: internal time\n",
      "   List reduced from 42 to 20 due to restriction <20>\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "    34082    0.941    0.000    2.321    0.000 rk.py:15(rk_step)\n",
      "    27354    0.452    0.000    3.097    0.000 rk.py:104(_step_impl)\n",
      "   204494    0.434    0.000    0.745    0.000 <ipython-input-4-54601b8d6733>:1(fun)\n",
      "   470432    0.346    0.000    0.346    0.000 {built-in method numpy.core.multiarray.array}\n",
      "   272659    0.241    0.000    0.241    0.000 {built-in method numpy.core.multiarray.dot}\n",
      "   204494    0.147    0.000    1.043    0.000 base.py:11(fun_wrapped)\n",
      "   238581    0.146    0.000    0.176    0.000 numeric.py:414(asarray)\n",
      "   204494    0.132    0.000    1.175    0.000 base.py:124(fun)\n",
      "    34085    0.125    0.000    0.246    0.000 linalg.py:1976(norm)\n",
      "    27354    0.055    0.000    3.152    0.000 base.py:147(step)\n",
      "        1    0.052    0.052    3.306    3.306 ivp.py:153(solve_ivp)\n",
      "    34085    0.047    0.000    0.293    0.000 common.py:38(norm)\n",
      "    27355    0.043    0.000    0.071    0.000 shape_base.py:61(atleast_2d)\n",
      "    34085    0.034    0.000    0.034    0.000 {method 'ravel' of 'numpy.ndarray' objects}\n",
      "    34083    0.020    0.000    0.020    0.000 {built-in method builtins.max}\n",
      "    27356    0.015    0.000    0.018    0.000 numeric.py:484(asanyarray)\n",
      "    34085    0.013    0.000    0.019    0.000 linalg.py:111(isComplexType)\n",
      "    68170    0.013    0.000    0.013    0.000 {built-in method builtins.issubclass}\n",
      "    27355    0.010    0.000    0.010    0.000 {built-in method builtins.min}\n",
      "    82063    0.010    0.000    0.010    0.000 {method 'append' of 'list' objects}\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pstats.Stats at 0x108c71860>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.print_stats(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    }
   ],
   "source": [
    "stats = %prun -r -q solve_ivp(lambda t, y: fun_cython(t, y, f_cython), [0, 1000], y0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         2168166 function calls in 3.815 seconds\n",
      "\n",
      "   Ordered by: internal time\n",
      "   List reduced from 43 to 20 due to restriction <20>\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "    34072    1.226    0.000    2.663    0.000 rk.py:15(rk_step)\n",
      "   204434    0.685    0.000    0.685    0.000 {_cython_magic_da45c9fac9fe52f051fb8b16785cf918.fun_cython}\n",
      "    27350    0.543    0.000    3.570    0.000 rk.py:104(_step_impl)\n",
      "   272579    0.256    0.000    0.256    0.000 {built-in method numpy.core.multiarray.dot}\n",
      "   238511    0.165    0.000    0.199    0.000 numeric.py:414(asarray)\n",
      "   204434    0.159    0.000    1.084    0.000 base.py:11(fun_wrapped)\n",
      "    34075    0.139    0.000    0.277    0.000 linalg.py:1976(norm)\n",
      "   204434    0.139    0.000    1.223    0.000 base.py:124(fun)\n",
      "        1    0.076    0.076    3.815    3.815 ivp.py:153(solve_ivp)\n",
      "   204434    0.070    0.000    0.755    0.000 <string>:1(<lambda>)\n",
      "    27350    0.067    0.000    3.637    0.000 base.py:147(step)\n",
      "    34075    0.056    0.000    0.333    0.000 common.py:38(norm)\n",
      "    27351    0.044    0.000    0.071    0.000 shape_base.py:61(atleast_2d)\n",
      "    34075    0.040    0.000    0.040    0.000 {method 'ravel' of 'numpy.ndarray' objects}\n",
      "   265864    0.039    0.000    0.039    0.000 {built-in method numpy.core.multiarray.array}\n",
      "    34073    0.021    0.000    0.021    0.000 {built-in method builtins.max}\n",
      "    27352    0.015    0.000    0.018    0.000 numeric.py:484(asanyarray)\n",
      "    34075    0.014    0.000    0.019    0.000 linalg.py:111(isComplexType)\n",
      "    68150    0.014    0.000    0.014    0.000 {built-in method builtins.issubclass}\n",
      "    27351    0.010    0.000    0.010    0.000 {built-in method builtins.min}\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pstats.Stats at 0x108c2b9e8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.print_stats(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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