Pairwise difference of vectors

Question

Say i have a matrix that is composed of N vectors as columns: matrix=[v_1, v_2, .. v_N] where v is from R^N. I want a new matrix that gives: for all (r in N, s in N) v(r)-v(s). For example if N=3, then i want a 3x3x3 and for a particular index i,j,k, it Represents the kth index of v(i)-v(j).

Answer 1

You can use broadcasting on a new dimension:

out = matrix[:,None]-matrix

Example:

matrix = np.arange(9).reshape(3,3)
out = matrix[:,None]-matrix

Output:

array([[[ 0,  0,  0],
        [-3, -3, -3],
        [-6, -6, -6]],

       [[ 3,  3,  3],
        [ 0,  0,  0],
        [-3, -3, -3]],

       [[ 6,  6,  6],
        [ 3,  3,  3],
        [ 0,  0,  0]]])