How to build a 3D matrix from 1D time series in numpy?

Suppose I have four (N,) vectors A, B, C, and D:

import numpy as np

N = 100

A = 1*np.ones(N)   # => array([1,1,1,...])
B = 2*np.ones(N)   # => array([2,2,2,...])
C = 3*np.ones(N)   # => array([3,3,3,...])
D = 4*np.ones(N)   # => array([4,4,4,...])

In my application, these are each an element of a matrix and the matrix varies over time (although in this example each is constant in time). I want a matrix with shape (N,2,2) such that I have a 2×2 matrix for each time step, like [[a,b],[c,d]], extended along axis 0. Is there a nicer way to stack these into that kind of shape than what I have below?

My solution:

A_ = np.reshape(A, (N,1,1))
B_ = np.reshape(B, (N,1,1))
C_ = np.reshape(C, (N,1,1))
D_ = np.reshape(D, (N,1,1))

AB = np.concatenate((A_, B_),axis=2)
CD = np.concatenate((C_, D_),axis=2)

ABCD = np.concatenate((AB,CD),axis=1)

This gives:

>>> ABCD
array([[[1., 2.],
        [3., 4.]],

       [[1., 2.],
        [3., 4.]],

       [[1., 2.],
        [3., 4.]],
...
...
       [[1., 2.],
        [3., 4.]],

       [[1., 2.],
        [3., 4.]]])

As desired. It’s just difficult to understand what it’s doing, so I’m wondering if there’s a better way.

>Solution :

Concatenate as a 3D intermediate with dstack, then you’ll be in the ideal order to perform a simple reshape:

np.dstack([A, B, C, D]).reshape(N, 2, 2)

Output:

array([[[1., 2.],
        [3., 4.]],

       [[1., 2.],
        [3., 4.]],

       [[1., 2.],
        [3., 4.]],

       ...,

       [[3., 4.],
        [3., 4.]]])

Intermediate:

np.dstack([A,B,C,D]).shape
# (1, 100, 4)