Numpy: modify array elements at certain positions

Question

I have an array a:

array([[[[14, 59, 18, 92],
     [91, 38, 58, 23],
     [33, 52, 93, 68],
     [19, 21, 50, 77]],

    [[90, 37, 22, 55],
     [56, 54, 10, 16],
     [83, 20, 36,  3],
     [84, 87, 85, 81]]],

   [[[ 0, 45, 72,  5],
     [49, 46, 94, 53],
     [34, 51, 75,  8],
     [27, 79, 35, 15]],

    [[ 7, 86, 64, 31],
     [12, 70, 89, 62],
     [13, 63, 88, 25],
     [39, 11, 26,  6]]]])

I also have a mask b:

array([[[[ 0.,  0.,  0.,  1.],
     [ 1.,  0.,  0.,  0.],
     [ 0.,  1.,  1.,  0.],
     [ 0.,  0.,  0.,  0.]],

    [[ 0.,  0.,  0.,  0.],
     [ 1.,  0.,  1.,  0.],
     [ 0.,  0.,  0.,  0.],
     [ 0.,  1.,  1.,  0.]]],

   [[[ 0.,  0.,  0.,  0.],
     [ 1.,  0.,  1.,  0.],
     [ 0.,  0.,  1.,  0.],
     [ 0.,  1.,  0.,  0.]],

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

How can I modify those elements of the array a, which correspond to the ones in the mask b?

In particular, I have an array c:

array([[[[ 0,  1],
     [ 2,  3]],

    [[ 4,  5],
     [ 6,  7]]],

   [[[ 8,  9],
     [10, 11]],

    [[12, 13],
     [14, 15]]]])

How can I add c to a, so that only elements indicated by mask b will be added to?

(This is what I need to do to backpropagate errors through the max-pooling layer in a convolutional neural network)

Answer 1

That's quite easy if you interpret your b as boolean mask:

b_mask = b.astype(bool)
d = a.copy()
d[b_mask] = a[b_mask] + c.ravel()
d

giving me

array([[[[ 14,  59,  18,  92],
         [ 92,  38,  58,  23],
         [ 33,  54,  96,  68],
         [ 19,  21,  50,  77]],

        [[ 90,  37,  22,  55],
         [ 60,  54,  15,  16],
         [ 83,  20,  36,   3],
         [ 84,  93,  92,  81]]],


       [[[  0,  45,  72,   5],
         [ 57,  46, 103,  53],
         [ 34,  51,  85,   8],
         [ 27,  90,  35,  15]],

        [[  7,  98,  64,  31],
         [ 12,  70, 102,  62],
         [ 13,  77, 103,  25],
         [ 39,  11,  26,   6]]]])

or if you want it in-place:

b_mask = b.astype(bool)
a[b_mask] = a[b_mask] + c.ravel()