scipy.linalg.

khatri_rao

scipy.linalg.khatri_rao(a, b)

Khatri-rao product

A column-wise Kronecker product of two matrices

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

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.

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

Try it in your browser!

>>> import numpy as np
>>> 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]])

Go BackOpen In Tab