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