No speed gains from Cython

Question

I am trying to define a function that contains an inner loop for simulating an integral.

The problem is speed. Evaluating the function once can take up to 30 seconds on my machine. Since my ultimate goal is to minimize this function, some extra speed would be nice.

As such, I have tried to get Cython to work, but I must be making a severe mistake (likely many of them!). Following the Cython documentation, I have tried to type my variables. After doing so, the code is just as slow as pure Python. This seems strange.

Here is my code:

import numpy as np 
cimport cython
cimport numpy as np
import minuit

data = np.genfromtxt('q6data.csv', usecols = np.arange(1, 24, 1), delimiter = ',')  

cdef int ns    = 1000                 # Number of simulation draws
cdef int K     = 5                    # Number of observed characteristics, including            constant
cdef int J     = len(data[:,1])       # Number of products, including outside
cdef double tol   = 0.0001            # Inner GMM loop tolerance
nu = np.random.normal(0, 1, (6, ns))  # ns random deviates

@cython.boundscheck(False)
@cython.wraparound(False)


def S(np.ndarray[double, ndim=1] delta, double s1, double s2, double s3, double s4,  double s5, double a):
    """Computes the simulated integrals, one for each good.
    Parameters: delta is an array of length J containing mean product specific utility levels
    Returns: Numpy array with length J."""
    cdef np.ndarray[double, ndim=2] mu_ij = np.dot((data[:,2:7]*np.array([s1, s2, s3, s4, s5])), nu[1:K+1,:])
    cdef np.ndarray[double, ndim=2] mu_y  = a * np.log(np.exp(data[:,21].reshape(J,1) +  data[:,22].reshape(J,1)*nu[0,:].reshape(1, ns)) - data[:,7].reshape(J,1))
    cdef np.ndarray[double, ndim=2] V = delta.reshape(J,1) + mu_ij + mu_y
    cdef np.ndarray[double, ndim=2] exp_vi = np.exp(V)
    cdef np.ndarray[double, ndim=2] P_i = (1.0 / np.sum(exp_vi[np.where(data[:,1] == 71)], 0)) * exp_vi[np.where(data[:,1] == 71)] 
    cdef int yrs = 19
    cdef int yr
    for yr in xrange(yrs):
        P_yr = (1.0 / np.sum(exp_vi[np.where(data[:,1]== (yr + 72))], 0)) *   exp_vi[np.where(data[:,1] == (yr + 72))]
        P_i  = np.concatenate((P_i, P_yr)) 
    cdef np.ndarray[double, ndim=1] S = np.zeros(dtype = "d", shape = J)
    cdef int j
    for j in xrange(ns):
        S += P_i[:,j]
    return (1.0 / ns) * S

def d_infty(np.ndarray[double, ndim=1] x, np.ndarray[double, ndim=1] y):
    """Sup norm."""
    return np.max(np.abs(x - y)) 

def T(np.ndarray[double, ndim=1] delta_exp, double s1, double s2, double s3, double s4,  double s5, double a):
    """The contraction operator.  This function takes the parameters and the exponential
    of the starting value of delta and returns the fixed point.""" 
    cdef int iter = 0
    cdef int maxiter = 200
    cdef int i
    for i in xrange(maxiter): 
        delta1_exp = delta_exp * (data[:, 8] / S(np.log(delta_exp), s1, s2, s3, s4, s5, a))                    
        print i
        if d_infty(delta_exp, delta1_exp) < tol:                                       
            break
        delta_exp = delta1_exp
    return np.log(delta1_exp)


def Q(double s1, double s2, double s3, double s4, double s5, double a):
    """GMM objective function."""  
    cdef np.ndarray[double, ndim=1] delta0_exp = np.exp(data[:,10])                                                     
    cdef np.ndarray[double, ndim=1] delta1 = T(delta0_exp, s1, s2, s3, s4, s5, a)
    delta1[np.where(data[:,10]==0)] = np.zeros(len(np.where(data[:,10]==0)))            
    cdef np.ndarray[double, ndim=1] xi =  delta1 - (np.dot(data[:,2:7],   np.linalg.lstsq(data[:,2:7], delta1)[0]))   
    cdef np.ndarray[double, ndim=2] g_J = xi.reshape(J,1) * data[:,11:21]
    cdef np.ndarray[double, ndim=1] G_J = (1.0 / J) * np.sum(g_J, 0) 
    return np.sqrt(np.dot(G_J, G_J))

I have profiled the code, and it seems to be the function S, the integral simulator, that is killing performance. Anyway, I would have expected at least some speed gains from typing my variables. Since it produced no gains, I am led to believe that I am making some fundamental mistakes.

Does anybody see a glaring error in the Cython code that could lead to this result?

Oh, and since I am very new to programming, there is surely a lot of bad style and things slowing the code down. If you have the time, feel free to set me straight on these points as well.

Answer 1

Cython can produce an html file to help with this:

cython -a MODULE.py

This shows each line of source code colored white through various shades of yellow. The darker the yellow color, the more dynamic Python behaviour is still being performed on that line. For each line that contains some yellow, you need to add more static typing declarations.

When I'm doing this, I like to split parts of my source code that I'm having trouble with onto many separate lines, one for each expression or operator, to get the most granular view.

Without this, it's easy to overlook some static type declarations of variables, function calls or operators. (e.g. the indexing operator x[y] is still a fully-dynamic Python operation unless you declare otherwise)