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115 | from .. import backend as T
from ..base import unfold, fold
def mode_dot(tensor, matrix_or_vector, mode):
"""n-mode product of a tensor and a matrix or vector at the specified mode
Mathematically: :math:`\\text{tensor} \\times_{\\text{mode}} \\text{matrix or vector}`
Parameters
----------
tensor : ndarray
tensor of shape ``(i_1, ..., i_k, ..., i_N)``
matrix_or_vector : ndarray
1D or 2D array of shape ``(J, i_k)`` or ``(i_k, )``
matrix or vectors to which to n-mode multiply the tensor
mode : int
Returns
-------
ndarray
`mode`-mode product of `tensor` by `matrix_or_vector`
* of shape :math:`(i_1, ..., i_{k-1}, J, i_{k+1}, ..., i_N)` if matrix_or_vector is a matrix
* of shape :math:`(i_1, ..., i_{k-1}, i_{k+1}, ..., i_N)` if matrix_or_vector is a vector
See also
--------
multi_mode_dot : chaining several mode_dot in one call
"""
# the mode along which to fold might decrease if we take product with a vector
fold_mode = mode
new_shape = list(tensor.shape)
if T.ndim(matrix_or_vector) == 2: # Tensor times matrix
# Test for the validity of the operation
if matrix_or_vector.shape[1] != tensor.shape[mode]:
raise ValueError(
'shapes {0} and {1} not aligned in mode-{2} multiplication: {3} (mode {2}) != {4} (dim 1 of matrix)'.format(
tensor.shape, matrix_or_vector.shape, mode, tensor.shape[mode], matrix_or_vector.shape[1]
))
new_shape[mode] = matrix_or_vector.shape[0]
elif T.ndim(matrix_or_vector) == 1: # Tensor times vector
if matrix_or_vector.shape[0] != tensor.shape[mode]:
raise ValueError(
'shapes {0} and {1} not aligned for mode-{2} multiplication: {3} (mode {2}) != {4} (vector size)'.format(
tensor.shape, matrix_or_vector.shape, mode, tensor.shape[mode], matrix_or_vector.shape[0]
))
if len(new_shape) > 1:
new_shape.pop(mode)
fold_mode -= 1
else:
new_shape = [1]
else:
raise ValueError('Can only take n_mode_product with a vector or a matrix.'
'Provided array of dimension {} not in [1, 2].'.format(T.ndim(matrix_or_vector)))
res = T.dot(matrix_or_vector, unfold(tensor, mode))
return fold(res, fold_mode, new_shape)
def multi_mode_dot(tensor, matrix_or_vec_list, modes=None, skip=None, transpose=False):
"""n-mode product of a tensor and several matrices or vectors over several modes
Parameters
----------
tensor : ndarray
matrix_or_vec_list : list of matrices or vectors of lengh ``tensor.ndim``
skip : None or int, optional, default is None
if not None, index of a matrix to skip
Note that in any case, `modes`, if provided, should have a lengh of ``tensor.ndim``
modes : None or int list, optional, default is None
transpose : bool, optional, default is False
if True, the matrices or vectors in in the list are transposed
Returns
-------
ndarray
tensor times each matrix or vector in the list at mode `mode`
Notes
-----
If no modes are specified, just assumes there is one matrix or vector per mode and returns:
:math:`\\text{tensor }\\times_0 \\text{ matrix or vec list[0] }\\times_1 \\cdots \\times_n \\text{ matrix or vec list[n] }`
See also
--------
mode_dot
"""
if modes is None:
modes = range(len(matrix_or_vec_list))
decrement = 0 # If we multiply by a vector, we diminish the dimension of the tensor
res = tensor
for i, (matrix_or_vec, mode) in enumerate(zip(matrix_or_vec_list, modes)):
if (skip is not None) and (i == skip):
continue
if transpose:
res = mode_dot(res, T.transpose(matrix_or_vec), mode - decrement)
else:
res = mode_dot(res, matrix_or_vec, mode - decrement)
if T.ndim(matrix_or_vec) == 1:
decrement = 1
return res
|