Sum each row of a numpy array with all rows of second numpy array (python)

Question

I would like to know if there is any fast way to sum each row of a first array with all rows of a second array. In this case both arrays have the same number of colulmns. For instance if array1.shape = (n,c) and array2.shape = (m,c) , the resulting array would be an array3.shape = ((n*m), c)

Look at the example below:

array1 = np.array([[0, 1, 2],
                   [3, 4, 5],
                   [6, 7, 8]])

array2 = np.array([[0, 1, 2],
                   [3, 4, 5]])

The result would be:

array3 = np.array([[0,  2,  4],
                   [3,  5,  7]
                   [3,  5,  7]
                   [6,  8, 10]
                   [6,  8, 10]
                   [9, 11, 13]])

The only way I see I can do this is to repeat each row of one of the arrays the number of rows of the other array. For instance, by doing np.repeat(array1, len(array2), axis=0) and then sum this array with array2 . This is not very practical however if the number of rows is too big. The other way would be with a for loop but this is too slow.

Any other better way to do it..?

Thanks in advance.

Answer 1

Extend array1 to 3D so that it becomes broadcastable against 2D array2 and then perform broadcasted addition and a final reshape is needed for desired output -

In [30]: (array1[:,None,:] + array2).reshape(-1,array1.shape[1])
Out[30]: 
array([[ 0,  2,  4],
       [ 3,  5,  7],
       [ 3,  5,  7],
       [ 6,  8, 10],
       [ 6,  8, 10],
       [ 9, 11, 13]])

Answer 2

You could try the following inline code if you haven't already. This is the simplest and probably also the quickest on a single thread.

>>> import numpy as np
>>> array1 = np.array([[0, 1, 2],
...                    [3, 4, 5],
...                    [6, 7, 8]])
>>> 
>>> array2 = np.array([[0, 1, 2],
...                    [3, 4, 5]])
>>> array3 = np.array([i+j for i in array1 for j in array2])
>>> array3
array([[ 0,  2,  4],
       [ 3,  5,  7],
       [ 3,  5,  7],
       [ 6,  8, 10],
       [ 6,  8, 10],
       [ 9, 11, 13]])
>>> 

If you are looking for speed up by treading, you could consider using CUDA ormultithreading . This suggestion goes a bit out of scope of your question but gives you an idea of what can be done to speed up matrix operations.