How do I calculate all pairs of vector differences in numpy?

问题:

I know I can do np.subtract.outer(x, x). If x has shape (n,), then I end up with an array with shape (n, n). However, I have an x with shape (n, 3). I want to output something with shape (n, n, 3). How do I do this? Maybe np.einsum?

回答1:

You can use broadcasting after extending the dimensions with None/np.newaxis to form a 3D array version of x and subtracting the original 2D array version from it, like so -

x[:, np.newaxis, :] - x 

Sample run -

In [6]: x Out[6]:  array([[6, 5, 3],        [4, 3, 5],        [0, 6, 7],        [8, 4, 1]])  In [7]: x[:,None,:] - x Out[7]:  array([[[ 0,  0,  0],         [ 2,  2, -2],         [ 6, -1, -4],         [-2,  1,  2]],         [[-2, -2,  2],         [ 0,  0,  0],         [ 4, -3, -2],         [-4, -1,  4]],         [[-6,  1,  4],         [-4,  3,  2],         [ 0,  0,  0],         [-8,  2,  6]],         [[ 2, -1, -2],         [ 4,  1, -4],         [ 8, -2, -6],         [ 0,  0,  0]]]) 

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