"""
Core operations on Kruskal tensors.
"""
from . import backend as T
from .base import fold, tensor_to_vec
from .tenalg import khatri_rao
# Author: Jean Kossaifi
# License: BSD 3 clause
def kruskal_to_tensor(factors, weights=None):
"""Turns the Khatri-product of matrices into a full tensor
``factor_matrices = [|U_1, ... U_n|]`` becomes
a tensor shape ``(U[1].shape[0], U[2].shape[0], ... U[-1].shape[0])``
Parameters
----------
factors : ndarray list
list of factor matrices, all with the same number of columns
i.e. for all matrix U in factor_matrices:
U has shape ``(s_i, R)``, where R is fixed and s_i varies with i
Returns
-------
ndarray
full tensor of shape ``(U[1].shape[0], ... U[-1].shape[0])``
Notes
-----
This version works by first computing the mode-0 unfolding of the tensor
and then refolding it.
There are other possible and equivalent alternate implementation, e.g.
summing over r and updating an outer product of vectors.
"""
shape = [T.shape(factor)[0] for factor in factors]
if weights is not None:
full_tensor = T.dot(factors[0]*weights, T.transpose(khatri_rao(factors[1:])))
else:
full_tensor = T.dot(factors[0], T.transpose(khatri_rao(factors[1:])))
return fold(full_tensor, 0, shape)
def kruskal_to_unfolded(factors, mode):
"""Turns the khatri-product of matrices into an unfolded tensor
turns ``factors = [|U_1, ... U_n|]`` into a mode-`mode`
unfolding of the tensor
Parameters
----------
factors : ndarray list
list of matrices, all with the same number of columns
ie for all u in factor_matrices:
u[i] has shape (s_u_i, R), where R is fixed
mode: int
mode of the desired unfolding
Returns
-------
ndarray
unfolded tensor of shape (tensor_shape[mode], -1)
Notes
-----
Writing factors = [U_1, ..., U_n], we exploit the fact that
``U_k = U[k].dot(khatri_rao(U_1, ..., U_k-1, U_k+1, ..., U_n))``
"""
return T.dot(factors[mode], T.transpose(khatri_rao(factors, skip_matrix=mode)))
def kruskal_to_vec(factors):
"""Turns the khatri-product of matrices into a vector
(the tensor ``factors = [|U_1, ... U_n|]``
is converted into a raveled mode-0 unfolding)
Parameters
----------
factors : ndarray list
list of matrices, all with the same number of columns
i.e.::
for u in U:
u[i].shape == (s_i, R)
where `R` is fixed while `s_i` can vary with `i`
Returns
-------
ndarray
vectorised tensor
"""
return tensor_to_vec(kruskal_to_tensor(factors))