scipy.linalg.block_diag

scipy.linalg.block_diag(*arrs)

Create a block diagonal matrix from provided arrays.

Given the inputs A, B and C, the output will have these arrays arranged on the diagonal:

[[A, 0, 0],
 [0, B, 0],
 [0, 0, C]]

Parameters:

A, B, C, … : array_like, up to 2-D

Input arrays. A 1-D array or array_like sequence of length n is treated as a 2-D array with shape (1,n).

Returns:

D : ndarray

Array with A, B, C, … on the diagonal. D has the same dtype as A.

Notes

If all the input arrays are square, the output is known as a block diagonal matrix.

Empty sequences (i.e., array-likes of zero size) will not be ignored. Noteworthy, both [] and [[]] are treated as matrices with shape (1,0).

Examples

>>> from scipy.linalg import block_diag
>>> A = [[1, 0],
...      [0, 1]]
>>> B = [[3, 4, 5],
...      [6, 7, 8]]
>>> C = [[7]]
>>> P = np.zeros((2, 0), dtype='int32')
>>> block_diag(A, B, C)
array([[1, 0, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 0],
       [0, 0, 3, 4, 5, 0],
       [0, 0, 6, 7, 8, 0],
       [0, 0, 0, 0, 0, 7]])
>>> block_diag(A, P, B, C)
array([[1, 0, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0],
       [0, 0, 3, 4, 5, 0],
       [0, 0, 6, 7, 8, 0],
       [0, 0, 0, 0, 0, 7]])
>>> block_diag(1.0, [2, 3], [[4, 5], [6, 7]])
array([[ 1.,  0.,  0.,  0.,  0.],
       [ 0.,  2.,  3.,  0.,  0.],
       [ 0.,  0.,  0.,  4.,  5.],
       [ 0.,  0.,  0.,  6.,  7.]])