How to product element-wise a 2-d numpy array into 3-d over the second dimension of the latter?

Question

I have a numpy matrix b = np.array([[1,0,1,0],[0,0,0,1]]) and I want to product it element-wise into a 3-dim array a = np.array([[[1,2,3,4], [5,6,7,8], [9,10,11,12]], [[13,14,15,16], [17,18,19,20], [21,22,23,24]]]) for each index on the second dimension. So, the result I expect should be as follows:

[[[1,0,3,0], [5,0,7,0], [9,0,11,0]], [[0,0,0,16], [0,0,0,20], [0,0,0,24]]]

Numpy does not broadcast if I do a * b . I was thinking of broadcasting b in its second dimension. I tried np.broadcast_to(b, (2,3,4)) but I got error. I tried (np.broadcast_to(b, (3,2,4)).reshape(2,3,4)) but the output is not as expected.

Answer 1

You need to reshape:

c = b.reshape(2,-1,4)*a

Answer 2

Use None/newaxis to added a new middle dimension ( reshape also does this):

In [36]: b.shape
Out[36]: (2, 4)
In [37]: a.shape
Out[37]: (2, 3, 4)
In [38]: b[:,None,:]*a
Out[38]: 
array([[[ 1,  0,  3,  0],
        [ 5,  0,  7,  0],
        [ 9,  0, 11,  0]],

       [[ 0,  0,  0, 16],
        [ 0,  0,  0, 20],
        [ 0,  0,  0, 24]]])

In [39]: b[:,None,:].shape
Out[39]: (2, 1, 4)

broadcast_to can't add that extra dimension automatically. It follows the same rules as b*a operations. It can add leading dimensions if needed, and scale size 1 dimensions. But for anything else, you have to be explicit.

In [41]: np.broadcast_to(b, (2,3,4))
Traceback (most recent call last):
  File "<ipython-input-41-3c3268de7ce1>", line 1, in <module>
    np.broadcast_to(b, (2,3,4))
  File "<__array_function__ internals>", line 5, in broadcast_to
  File "/usr/local/lib/python3.8/dist-packages/numpy/lib/stride_tricks.py", line 411, in broadcast_to
    return _broadcast_to(array, shape, subok=subok, readonly=True)
  File "/usr/local/lib/python3.8/dist-packages/numpy/lib/stride_tricks.py", line 348, in _broadcast_to
    it = np.nditer(
ValueError: operands could not be broadcast together with remapped shapes [original->remapped]: (2,4)  and requested shape (2,3,4)

In [42]: np.broadcast_to(b[:,None,:], (2,3,4))
Out[42]: 
array([[[1, 0, 1, 0],
        [1, 0, 1, 0],
        [1, 0, 1, 0]],

       [[0, 0, 0, 1],
        [0, 0, 0, 1],
        [0, 0, 0, 1]]])