Broadcasting 2D array to 4D array in numpy-CodePudding

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?

CodePudding user response：

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)

CodePudding user response：

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 operating on two arrays, NumPy compares their shapes element-wise. It starts with the trailing (i.e. rightmost) dimensions and works its way left.).
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))