Sum of Squares - np.inner vs squaring first, then summing

Question

I was surprised that calling np.inner to compute a sum of squares was about 5x faster than calling np.sum on a pre-computed array of squares:

Any insights into this behavior? I'm actually interested in a very fast implementation of a sum of squares, so those thoughts are welcome, too.

Answer 1

To check in which modules np.inner and np.sum are implemented I type

>>> np.inner.__module__
'numpy.core.multiarray'
>>> np.sum.__module__
'numpy.core.fromnumeric'
>>> np.__file__
'/Users/uweschmitt/venv_so/lib/python3.5/site-packages/numpy/__init__.py'

If you inspect the actual files, you can see that numpy.core.multiarray is a pure C module whereas numpy.core.fromnumeric first does some checks and conversions in Python before a second Python function and then a pure C implementation for the actual summation is called.

I suspect that this overhead from the Python interpreter explains the observed timing differences.

To prove my assumption I run the timing with a larger array and get

In [8]: a = np.random.random(1000000)
In [9]: %timeit np.inner(a, a)
1000 loops, best of 3: 673 µs per loop
In [10]: %timeit np.sum(a)
1000 loops, best of 3: 584 µs per loop

Now run times are quite similar and change a little if you repeat the statements, sometimes np.sum wins, somtimes np.inner.

For the big array the actual work of np.sum is done in C and the constant time overhead from the Python interpreter is negligible.