from ... import backend as T
from ... import unfold, fold, vec_to_tensor
[docs]def mode_dot(tensor, matrix_or_vector, mode, transpose=False):
"""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
transpose : bool, default is False
If True, the matrix is transposed.
For complex tensors, the conjugate transpose is used.
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
dim = 0 if transpose else 1
if matrix_or_vector.shape[dim] != tensor.shape[mode]:
raise ValueError(
f"shapes {tensor.shape} and {matrix_or_vector.shape} not aligned in mode-{mode} multiplication: "
f"{tensor.shape[mode]} (mode {mode}) != {matrix_or_vector.shape[dim]} (dim 1 of matrix)"
)
if transpose:
matrix_or_vector = T.conj(T.transpose(matrix_or_vector))
new_shape[mode] = matrix_or_vector.shape[0]
vec = False
elif T.ndim(matrix_or_vector) == 1: # Tensor times vector
if matrix_or_vector.shape[0] != tensor.shape[mode]:
raise ValueError(
f"shapes {tensor.shape} and {matrix_or_vector.shape} not aligned for mode-{mode} multiplication: "
f"{tensor.shape[mode]} (mode {mode}) != {matrix_or_vector.shape[0]} (vector size)"
)
if len(new_shape) > 1:
new_shape.pop(mode)
else:
# Ideally this should be (), i.e. order-0 tensors
# MXNet currently doesn't support this though..
new_shape = []
vec = True
else:
raise ValueError(
"Can only take n_mode_product with a vector or a matrix."
f"Provided array of dimension {T.ndim(matrix_or_vector)} not in [1, 2]."
)
res = T.dot(matrix_or_vector, unfold(tensor, mode))
if vec: # We contracted with a vector, leading to a vector
return vec_to_tensor(res, shape=new_shape)
else: # tensor times vec: refold the unfolding
return fold(res, fold_mode, new_shape)
[docs]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 length ``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 length 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.
For complex tensors, the conjugate transpose is used.
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
# Order of mode dots doesn't matter for different modes
# Sorting by mode shouldn't change order for equal modes
factors_modes = sorted(zip(matrix_or_vec_list, modes), key=lambda x: x[1])
for i, (matrix_or_vec, mode) in enumerate(factors_modes):
if (skip is not None) and (i == skip):
continue
if transpose:
res = mode_dot(res, T.conj(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