Are NumPy's math functions faster than Python's?

Question

I have a function defined by a combination of basic math functions (abs, cosh, sinh, exp, ...).

I was wondering if it makes a difference (in speed) to use, for example, numpy.abs() instead of abs()?

Octodecimo

Use timeit. – Soemba

There is no math.abs(). I guess you mean abs()? – Gagnon

@EOL yes sorry, i edited the question. thx – Octodecimo

Answer 1

Here are the timing results:

lebigot@weinberg ~ % python -m timeit 'abs(3.15)' 
10000000 loops, best of 3: 0.146 usec per loop

lebigot@weinberg ~ % python -m timeit -s 'from numpy import abs as nabs' 'nabs(3.15)'
100000 loops, best of 3: 3.92 usec per loop

numpy.abs() is slower than abs() because it also handles Numpy arrays: it contains additional code that provides this flexibility.

However, Numpy is fast on arrays:

lebigot@weinberg ~ % python -m timeit -s 'a = [3.15]*1000' '[abs(x) for x in a]'
10000 loops, best of 3: 186 usec per loop

lebigot@weinberg ~ % python -m timeit -s 'import numpy; a = numpy.empty(1000); a.fill(3.15)' 'numpy.abs(a)'
100000 loops, best of 3: 6.47 usec per loop

(PS: '[abs(x) for x in a]' is slower in Python 2.7 than the better map(abs, a), which is about 30 % faster—which is still much slower than NumPy.)

Thus, numpy.abs() does not take much more time for 1000 elements than for 1 single float!

Gagnon

would be nice to have the result of python -m timeit -s 'import numpy' -s 'a=numpy.array((1,)*1000)' 'numpy.abs(a)' to show how numpy can be fast with its array – Horan

@EOL: It appears that your timeit includes importing numpy, which alone takes a few seconds. Further, in your second example, I wonder if much of the time for Python's base "abs" function comes more from your list comprehension than from the "abs" function itself? – Chalaza

@tbhartman: Note the -s option given to timeit: the import numpy is actually only done once, during setup. It is not timed. As for the abs() example, replacing abs(x) with x shows that abs() uses half the total run time. In any case, the point remains the same: NumPy is really fast compared to pure (CPython-interpreted) Python. – Gagnon

Answer 2

You should use numpy function to deal with numpy's types and use regular python function to deal with regular python types.

Worst performance usually occurs when mixing python builtins with numpy, because of types conversion. Those type conversion have been optimized lately, but it's still often better to not use them. Of course, your mileage may vary, so use profiling tools to figure out.

Also consider the use of programs like cython or making a C module if you want to optimize further your program. Or consider not to use python when performances matters.

but, when your data has been put into a numpy array, then numpy can be really fast at computing bunch of data.

Horan

Answer 3

In fact, on numpy array

built in abs calls numpy's implementation via __abs__, see Why built-in functions like abs works on numpy array?

So, in theory there shouldn't be much performance difference.

import timeit
 
x = np.random.standard_normal(10000)
 
def pure_abs():
    return abs(x)
 
def numpy_abs():
    return np.abs(x)
 
n = 10000
 
t1 = timeit.timeit(pure_abs, number = n)
print('Pure Python abs:', t1)
t2 = timeit.timeit(numpy_abs, number = n)
print('Numpy abs:', t2)
Pure Python abs: 0.435754060745
Numpy abs: 0.426516056061

Liquorice