Why does numpy.apply_along_axis seem to be slower than Python loop?

Question

I'm confused about when numpy's numpy.apply_along_axis() function will outperform a simple Python loop. For example, consider the case of a matrix with many rows, and you wish to compute the sum of each row:

x = np.ones([100000, 3])
sums1 = np.array([np.sum(x[i,:]) for i in range(x.shape[0])])
sums2 = np.apply_along_axis(np.sum, 1, x)

Here I am even using a built-in numpy function, np.sum, and yet calculating sums1 (Python loop) takes less than 400ms while calculating sums2 (apply_along_axis) takes over 2000ms (NumPy 1.6.1 on Windows). By further way of comparison, R's rowMeans function can often do this in less than 20ms (I'm pretty sure it's calling C code) while the similar R function apply() can do it in about 600ms.

Answer 1

np.sum take an axis parameter, so you could compute the sum simply using

sums3 = np.sum(x, axis=1)

This is much faster than the 2 methods you posed.

$ python -m timeit -n 1 -r 1 -s "import numpy as np;x=np.ones([100000,3])" "np.apply_along_axis(np.sum, 1, x)"
1 loops, best of 1: 3.21 sec per loop

$ python -m timeit -n 1 -r 1 -s "import numpy as np;x=np.ones([100000,3])" "np.array([np.sum(x[i,:]) for i in range(x.shape[0])])"
1 loops, best of 1: 712 msec per loop

$ python -m timeit -n 1 -r 1 -s "import numpy as np;x=np.ones([100000,3])" "np.sum(x, axis=1)"
1 loops, best of 1: 1.81 msec per loop

(As for why apply_along_axis is slower — I don't know, probably because the function is written in pure Python and is much more generic and thus less optimization opportunity than the array version.)