Source code for tensorly.tenalg.core_tenalg._kronecker

from ... import backend as T

# Author: Jean Kossaifi

# License: BSD 3 clause

[docs]def kronecker(matrices, skip_matrix=None, reverse=False): """Kronecker product of a list of matrices For more details, see [1]_ Parameters ---------- matrices : ndarray list skip_matrix : None or int, optional, default is None if not None, index of a matrix to skip reverse : bool, optional if True, the order of the matrices is reversed Returns ------- kronecker_product: matrix of shape ``(prod(n_rows), prod(n_columns)`` where ``prod(n_rows) = prod([m.shape[0] for m in matrices])`` and ``prod(n_columns) = prod([m.shape[1] for m in matrices])`` Notes ----- Mathematically: .. math:: \\text{If every matrix } U_k \\text{ is of size } (I_k \\times J_k),\\\\ \\text{Then } \\left(U_1 \\otimes \\cdots \\otimes U_n \\right) \\text{ is of size } (\\prod_{k=1}^n I_k \\times \\prod_{k=1}^n J_k) References ---------- .. [1] T.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications", SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009. """ if skip_matrix is not None: matrices = [matrices[i] for i in range(len(matrices)) if i != skip_matrix] if reverse: order = -1 else: order = 1 for i, matrix in enumerate(matrices[::order]): if not i: res = matrix else: res = T.kron(res, matrix) return res