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I would like to add two arrays with different dimensions by simply performing an identical addition along the first axis.

A non-vectorized solution:

x = np.array([[[1,2],[3,4],[5,6]],[[7,8],[9,0],[1,2]],[[3,4],[5,6],[7,8]],[[9,0],[1,2],[3,4]]]) #shape (4,3,2)

y = np.array([[1,2],[3,4],[5,6]]) #shape (3,2)



ans = np.empty(x.shape)

for i in range(x.shape[0]):

    ans[i] = x[i] + y



print(ans) #shape (4,3,2)

How can I make this broadcast appropriately?

Due to broadcasting [numpy-doc], you can simply use:

x + y

So here we calculate the element at index i,j,k as:

x_ijk+y_jk

this gives:

>>> x + y

array([[[ 2,  4],

        [ 6,  8],

        [10, 12]],



       [[ 8, 10],

        [12,  4],

        [ 6,  8]],



       [[ 4,  6],

        [ 8, 10],

        [12, 14]],



       [[10,  2],

        [ 4,  6],

        [ 8, 10]]])

>>> (x + y).shape

(4, 3, 2)

If you add two arrays together such that the first array has for example three dimensions, and the second two dimensions, and the last two dimensions of the first left array equal the dimensions of the right array, the the array on the right side is "broacasted". It means that it is treated as a three dimensional array, where each subarray equals the array on the right side.

You can als "introduce" extra dimensions for y at arbitrary positions like in this answer to "broadcast" a specific dimension.