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]
vec = False
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)
else:
new_shape = [1]
vec = True
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))
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)
def unimodality_prox(tensor):
"""
This function projects each column of the input array on the set of arrays so that
x[1] <= x[2] <= x[j] >= x[j+1]... >= x[n]
is satisfied columnwise.
Parameters
----------
tensor : ndarray
Returns
-------
ndarray
A tensor of which columns' distribution are unimodal.
References
----------
.. [1]: Bro, R., & Sidiropoulos, N. D. (1998). Least squares algorithms under
unimodality and non‐negativity constraints. Journal of Chemometrics:
A Journal of the Chemometrics Society, 12(4), 223-247.
"""
if tl.ndim(tensor) == 1:
tensor = tl.vec_to_tensor(tensor, [tl.shape(tensor)[0], 1])
elif tl.ndim(tensor) > 2:
raise ValueError(
"Unimodality prox doesn't support an input which has more than 2 dimensions."
)
tensor_unimodal = tl.copy(tensor)
monotone_increasing = tl.tensor(monotonicity_prox(tensor),
**tl.context(tensor))
monotone_decreasing = tl.tensor(monotonicity_prox(tensor, decreasing=True),
**tl.context(tensor))
# Next line finds mutual peak points
values = tl.tensor(
tl.to_numpy((tensor - monotone_decreasing >= 0)) * tl.to_numpy(
(tensor - monotone_increasing >= 0)), **tl.context(tensor))
sum_inc = tl.where(values == 1,
tl.cumsum(tl.abs(tensor - monotone_increasing), axis=0),
tl.tensor(0, **tl.context(tensor)))
sum_inc = tl.where(values == 1,
sum_inc - tl.abs(tensor - monotone_increasing),
tl.tensor(0, **tl.context(tensor)))
sum_dec = tl.where(
tl.flip(values, axis=0) == 1,
tl.cumsum(tl.abs(
tl.flip(tensor, axis=0) - tl.flip(monotone_decreasing, axis=0)),
axis=0), tl.tensor(0, **tl.context(tensor)))
sum_dec = tl.where(
tl.flip(values, axis=0) == 1, sum_dec -
tl.abs(tl.flip(tensor, axis=0) - tl.flip(monotone_decreasing, axis=0)),
tl.tensor(0, **tl.context(tensor)))
difference = tl.where(values == 1, sum_inc + tl.flip(sum_dec, axis=0),
tl.max(sum_inc + tl.flip(sum_dec, axis=0)))
min_indice = tl.argmin(tl.tensor(difference), axis=0)
for i in range(len(min_indice)):
tensor_unimodal = tl.index_update(
tensor_unimodal, tl.index[:int(min_indice[i]), i],
monotone_increasing[:int(min_indice[i]), i])
tensor_unimodal = tl.index_update(
tensor_unimodal, tl.index[int(min_indice[i] + 1):, i],
monotone_decreasing[int(min_indice[i] + 1):, i])
return tensor_unimodal