numpy vs Matlab speed - arctan and power

Question

In Python and Matlab, I wrote codes that generate a matrix and populates it with a function of indices. Execution time of Python code is about 20 times longer than the execution time of Matlab code. Two functions with same results are written in python, the bWay() is based on this answer

Here's the full Python code:

import numpy as np
from timeit import timeit

height = 1080
width = 1920
heightCm = 30
distanceCm = 70

centerY = height / 2 - 0.5;
centerX = width / 2 - 0.5;

constPart = height * heightCm / distanceCm

def aWay():
    M = np.empty([height, width], dtype=np.float64);
    for y in xrange(height):
        for x in xrange(width):
            M[y, x] = np.arctan(pow((pow((centerX - x), 2) + pow((centerY - y), 2)), 0.5) / constPart)

def bWay():
    M = np.frompyfunc(
        lambda y, x: np.arctan(pow((pow((centerX - x), 2) + pow((centerY - y), 2)), 0.5) / constPart), 2, 1## Heading ##
    ).outer(
        np.arange(height),
        np.arange(width),
    ).astype(np.float64)

and here's the full Matlab code:

height = 1080;
width = 1920;
heightCm = 30;
distanceCm = 70;

centerY = height / 2 + 0.5;
centerX = width / 2 + 0.5;

constPart = height * heightCm / distanceCm;
M = zeros(height, width);
for y = 1 : height
    for x = 1 : width
        M(y, x) = atan(((centerX - x)^2 + (centerY - y)^2)^0.5 / constPart);
    end
end

Python execution time measured with timeit.timeit:

aWay() - 6.34s
bWay() - 6.68s

Matlab execution time measured with tic toc:

0.373s

To narrow it down I measured arctan, squaring and looping times

Python:

>>> timeit('arctan(3)','from numpy import arctan', number = 1000000)
1.3365135641797679
>>> timeit('pow(3, 2)', number = 1000000)
0.11460829719908361
>>> timeit('power(3, 2)','from numpy import power', number = 1000000)
1.5427879383046275
>>> timeit('for x in xrange(10000000): pass', number = 1)
0.18364813832704385

Matlab:

tic
for i = 1 : 1000000
    atan(3);
end
toc
Elapsed time is 0.179802 seconds.
tic
for i = 1 : 1000000
    3^2;
end
toc
Elapsed time is 0.044160 seconds.
tic
for x = 1:10000000
end
toc
Elapsed time is 0.034853 seconds.

In all 3 cases, Python code execution time was multiple times longer.

Is there anything I could do to improve this python code performance?

numpy vs Matlab speed - arctan and power

2 Answers