Question

I’m looking for a fast way of creating a new matrix A_{ij} from a given vector b_i and another
matrix C_{ij}. The components of the new matrix should have the form

A_{ij} = b_i * C_{ij}.

So far I am using dot(diag(b), C), but the dot product naturally has a lot of multiplications
with zero, which is quite inefficient. Is there a better way?

Answer 1

Use *, the element-wise product with the appropriate broadcasting:

>>> b = array([1,2,3])
>>> C = arange(9).reshape(3,3)
>>> dot(diag(b), C)
array([[ 0,  1,  2],
       [ 6,  8, 10],
       [18, 21, 24]])
>>> atleast_2d(b).T * C
array([[ 0,  1,  2],
       [ 6,  8, 10],
       [18, 21, 24]])

atleast_2d(b).T (or b.reshape(-1,1)) reshapes the vector b to a column vector.