scipy.linalg.khatri_rao#

scipy.linalg.khatri_rao(a, b)[source]#

Khatri-rao product

A column-wise Kronecker product of two matrices

Parameters:
a(n, k) array_like

Input array

b(m, k) array_like

Input array

Returns:
c: (n*m, k) ndarray

Khatri-rao product of a and b.

See also

kron

Kronecker product

Notes

The mathematical definition of the Khatri-Rao product is:

\[(A_{ij} \bigotimes B_{ij})_{ij}\]

which is the Kronecker product of every column of A and B, e.g.:

c = np.vstack([np.kron(a[:, k], b[:, k]) for k in range(b.shape[1])]).T

Examples

>>> from scipy import linalg
>>> a = np.array([[1, 2, 3], [4, 5, 6]])
>>> b = np.array([[3, 4, 5], [6, 7, 8], [2, 3, 9]])
>>> linalg.khatri_rao(a, b)
array([[ 3,  8, 15],
       [ 6, 14, 24],
       [ 2,  6, 27],
       [12, 20, 30],
       [24, 35, 48],
       [ 8, 15, 54]])