在 numpy 中将 2D 数组广播到 4D 数组

Question

I have a 2D array x of shape (48, 7) , and a 4D array T of shape (48, 7, 48, 7) . When I multiply x * T , python broadcasts the dimensions, but not in the way I expected (actually, I don´t understand how it is broadcasting). The following loop would achieve what I want:

for i in range(48):
    for j in range(7):
        Tx[i, j, :, :] = x[i, j] * T[i, j, :, :]

Where Tx is an array of shape (48, 7, 48, 7) . My question is, is there a way to achieve the same result using broadcasting?

Answer 1

I found the solution,
Python broadcast from the rightmost dimmesion and works it's way to the left ( https://numpy.org/doc/stable/user/basics.broadcasting.html#:~:text=When%20operating%20on%20two%20arrays%2C%20NumPy%20compares%20their%20shapes%20element%2Dwise.%20It%20starts%20with%20the%20trailing%20(ie%20rightmost)%20dimensions%20and%20works%20its%20way%20left. ).
By transposing the first two dimmesions and the last two dimmensions:

T = np.transpose(T, (2,3,0,1))

Then it would broadcast the way I expected, after that the resulting array can be transposed again to recover the original shape.

Tx = x*T
Tx = np.transpose(Tx, (2,3,0,1))

I hope this helps someone else.

Answer 2

Broadcasting aligns trailing dimensions. In other words, x * Tx is doing this:

for i in range(48):
    for j in range(7):
        Tx[:, :, i, j] = x[i, j] * T[:, :, i, j]

To get the leading dimensions to line up, add unit dimensions to x :

Tx = x[..., None, None] * T

Alternatively, you can use np.einsum to specify the dimensions explicitly:

Tx = np.einsum('ij,ij...->ij...', x, T)