Stack vertically 5 2D-arrays in diagonal to build a whole 2d-array

Question

l have 5 adjacency matrices (nump arrays) : A, B, C, D, E. each of dimension [20,20].

Given A, B, C, D, E, l would like to build F which stacks the 5 adjacency matrices. Since we have 5 2D arrays of [20,20] then F is of dimension [20*5,20*5] as follow :

F=np.zeros((100,100))

    F=[
       [A,0,0,0,...,0],
       [0,...,B,...,0],
       [0,...,..,C,0],
       [0,.........D,..,0],
       [0,...........,E],
    ]

such that :

 A is indexed at F[0][:20]
 B is indexed at F[1][20:40]
 C is indexed at F[2][40:60]
 D is indexed at F[3][60:80]
 E is indexed at F[4][80:100]

What is the efficient numpy way to do that for larage number of adjacency matrices ?. Let's, we have n adjacency matrices to stack in a diagonal of new 2D array of [n*20,n*20]

Answer 1

You could use scipy.sparse.block_diag:

>>> AtoE = np.add.outer(np.arange(5, 10), np.zeros((3, 3), int))
>>> scipy.sparse.block_diag(AtoE).A
array([[5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9]], dtype=int64)

Sparse storage may be a good idea, anyway.

Alternatively, here is a more direct method in case you definitely want to use dense arrays:

>>> A = AtoE[0]
>>> N, N = A.shape
>>> k = len(AtoE)
>>> out = np.zeros((k, N, k, N), A.dtype)
>>> np.einsum('ijik->ijk', out)[...] = AtoE
>>> out.reshape(k*N, k*N)
array([[5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9]])