How to rapidly create array of N 3x3 matrices from

Question

Assume that I have 9 arrays (A, B, C, .. J) of size N. I want to create a new array of N 3x3 matrices such that e.g.

matrices[i] = [[A[i], B[i], C[i]],
               [D[i], E[i], F[i]],
               [G[i], H[i], J[i]]]

A simple solution is to add each entry to the array matrices in a for-loop as:

for i in range(len(matrices)):
    matrices[i] = [[A[i], B[i], C[i]],
            [D[i], E[i], F[i]],
            [G[i], H[i], J[i]]]

Anybody got some tips on how this can be done in a faster, vectorized way avoiding the for-loop? If there exists some smart indexing operations or something.

Answer 1

One approach would be to stack those in columns with np.column_stack and reshape with np.reshape -

np.column_stack((A,B,C,D,E,F,G,H,J)).reshape(-1,3,3)

Concatenating with np.concatenate is known to be much faster, so using it with 2D transpose and reshaping -

np.concatenate((A,B,C,D,E,F,G,H,J)).reshape(9,-1).T.reshape(-1,3,3)

Another with np.concatenate, 3D transpose and reshaping -

np.concatenate((A,B,C,D,E,F,G,H,J)).reshape(3,3,-1).transpose(2,0,1)

Runtime tests -

In [59]: # Setup input arrays
    ...: N = 1000
    ...: A = np.random.randint(0,9,(N,))
    ...: B = np.random.randint(0,9,(N,))
    ...: C = np.random.randint(0,9,(N,))
    ...: D = np.random.randint(0,9,(N,))
    ...: E = np.random.randint(0,9,(N,))
    ...: F = np.random.randint(0,9,(N,))
    ...: G = np.random.randint(0,9,(N,))
    ...: H = np.random.randint(0,9,(N,))
    ...: J = np.random.randint(0,9,(N,))
    ...: 

In [60]: %timeit np.column_stack((A,B,C,D,E,F,G,H,J)).reshape(-1,3,3)
10000 loops, best of 3: 84.4 µs per loop

In [61]: %timeit np.concatenate((A,B,C,D,E,F,G,H,J)).reshape(9,-1).T.reshape(-1,3,3)
100000 loops, best of 3: 15.8 µs per loop

In [62]: %timeit np.concatenate((A,B,C,D,E,F,G,H,J)).reshape(3,3,-1).transpose(2,0,1)
100000 loops, best of 3: 14.8 µs per loop