Elegant expression for row-wise dot product of two matrices

Question

I have two 2-d numpy arrays with the same dimensions, A and B, and am trying to calculate the row-wise dot product of them. I could do:

np.sum(A * B, axis=1)


        

Answer 1

Even though it is significantly slower for even moderate data sizes, I would use

np.diag(A.dot(B.T))

while you are developing the library and worry about optimizing it later when it will run in a production setting, or after the unit tests are written.

To most people who come upon your code, this will be more understandable than einsum, and also doesn't require you to break some best practices by embedding your calculation within a mini DSL string to serve as the argument to some function call.

I agree that computing the off-diagonal elements is worth avoiding for large cases. It would have to be really really large for me to care about that though, and the trade-off for paying the awful price of expressing the calculating in an embedded string in einsum is pretty severe.

Answer 2

This is a good application for numpy.einsum.

a = np.random.randint(0, 5, size=(6, 4))
b = np.random.randint(0, 5, size=(6, 4))

res1 = np.einsum('ij, ij->i', a, b)
res2 = np.sum(a*b, axis=1)

print(res1)
# [18  6 20  9 16 24]

print(np.allclose(res1, res2))
# True

einsum also tends to be a bit faster.

a = np.random.normal(size=(5000, 1000))
b = np.random.normal(size=(5000, 1000))

%timeit np.einsum('ij, ij->i', a, b)
# 100 loops, best of 3: 8.4 ms per loop

%timeit np.sum(a*b, axis=1)
# 10 loops, best of 3: 28.4 ms per loop

Answer 3

Even faster is inner1d from numpy.core.umath_tests:

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Code to reproduce the plot:

import numpy
from numpy.core.umath_tests import inner1d
import perfplot


perfplot.show(
        setup=lambda n: (numpy.random.rand(n, 3), numpy.random.rand(n, 3)),
        kernels=[
            lambda a: numpy.sum(a[0]*a[1], axis=1),
            lambda a: numpy.einsum('ij, ij->i', a[0], a[1]),
            lambda a: inner1d(a[0], a[1])
            ],
        labels=['sum', 'einsum', 'inner1d'],
        n_range=[2**k for k in range(20)],
        xlabel='len(a), len(b)',
        logx=True,
        logy=True
        )