How to calculate vektor distances fast in python

Question

I would like to calculate the vector between points as fast as possible. My Input array has a list of points in 3D. And looks like this

b = [[0,0,1],  #first point
     [1,0,2],  #second point
     ...    ]

I want to calculate a matrix with the vector as entry (m_ij = b_i - b_j) and it should look like this:

m = [[[0,0,0], [-1,0,-1],...],
     [[1,0,1], [0,0,0],...],
          ...             ]

How do I calculate this with built in functions of numpy and scipy without using any slow loops? I found pdist, but this uses a metric and I don't think it really fits my needs.

Answer 1

Use broadcasting:

m = b[:,None]-b[None]

Output:

array([[[ 0,  0,  0],
        [-1,  0, -1]],

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

Shapes:

b[:,None].shape
(2, 1, 3)

b[None].shape
(1, 2, 3)

m.shape
(2, 2, 3)