A strange dot product in Python

Question

So I have two matrices, one is I×H and the other I×I, where H = M*I. I would like to take the dot product of the first M rows of the first matrix with the first row of the second, the next M rows with the next row of the second, etc.

Does anyone know an easy way to do this in NumPy? I'm trying to avoid a loop.

Answer 1

import numpy as np

# just some examples
i = 5
m = 3
h = m * i
first = np.arange(h * i).reshape(h, i) # note dimension H×i, not I×H
second = np.arange(i * i).reshape(i, i)

# Let's compute the dot product of 
# every column of `first`
# with every column of `second` (i.e. every row of `second` transposed):
#
full_matrix_product = np.dot(first, second.transpose()) # no (explicit) loops,
                                                        # but does much more
                                                        # multiplications than
                                                        # we need in the end.

# Extract the specific dot products you want:
wanted_rows = np.arange(h)
wanted_columns = np.arange(m).repeat(i)
result = full_matrix_product[wanted_rows, wanted_columns].reshape(m, i)