creating small arrays in cython takes a humongous amount of time

Question

I was writing a new random number generator for numpy that produces random numbers according to an arbitrary distribution when I came across this really weird behavior:

Answer 1

Creating np.empty inside the Cython function has some overhead as you already saw. Here you will see an example about how to create the empty array and pass it to the Cython module in order to fill with the correct values:

n=10:

numpy.searchsorted: 1.30574745517
cython O(1): 3.28732016088
cython no array declaration 1.54710909596

n=100:

numpy.searchsorted: 4.15200545373
cython O(1): 13.7273431067
cython no array declaration 11.4186086744

As you already pointed out, the numpy version scales better since it is O(len(u)*long(len(a))) and this algorithm here is O(len(u)*len(a))...

I also tried to use Memoryview, basically changing np.ndarray[double, ndim=1] by double[:], but the first option was faster in this case.

The new .pyx file is:

from __future__ import division
import numpy as np
cimport numpy as np
cimport cython

@cython.boundscheck(False)
@cython.wraparound(False)
def JustLoop(np.ndarray[double, ndim=1] a, np.ndarray[double, ndim=1] u,
             np.ndarray[int, ndim=1] r):
    cdef int i,j
    for j in range(u.shape[0]):
        if u[j] < a[0]:
            r[j] = 0
            continue

        if u[j] > a[a.shape[0]-1]:
            r[j] = a.shape[0]-1
            continue

        for i in range(1, a.shape[0]):
            if u[j] >= a[i-1] and u[j] < a[i]:
                r[j] = i
                break

@cython.boundscheck(False)
@cython.wraparound(False)
def WithArray(np.ndarray[double, ndim=1] a, np.ndarray[double, ndim=1] u):
    cdef np.ndarray[np.int_t, ndim=1] r=np.empty(u.shape[0],dtype=int)
    cdef int i,j
    for j in range(u.shape[0]):
        if u[j] < a[0]:
            r[j] = 0
            continue

        if u[j] > a[a.shape[0]-1]:
            r[j] = a.shape[0]-1
            continue

        for i in range(1, a.shape[0]):
            if u[j] >= a[i-1] and u[j] < a[i]:
                r[j] = i
                break
    return r

The new .py file:

import numpy
import subprocess
import timeit

#Compile the cython modules before importing them
subprocess.call(['python', 'setup.py', 'build_ext', '--inplace'])
from test import *

sstr="""
import test
import numpy
u=numpy.random.random(10)
a=numpy.random.random(10)
a=numpy.cumsum(a)
a/=a[-1]
a.sort()
r = numpy.empty(u.shape[0], dtype=int)
"""

print "numpy.searchsorted:",timeit.timeit('numpy.searchsorted(a,u)',sstr)
print "cython O(1):",timeit.timeit('test.WithArray(a,u)',sstr)
print "cython no array declaration",timeit.timeit('test.JustLoop(a,u,r)',sstr)