from math import prod
from . import backend as tl
[docs]
def tensor_to_vec(tensor):
"""Vectorises a tensor
Parameters
----------
tensor : ndarray
tensor of shape ``(i_1, ..., i_n)``
Returns
-------
1D-array
vectorised tensor of shape ``(i_1 * i_2 * ... * i_n)``
"""
return tl.reshape(tensor, (-1,))
[docs]
def vec_to_tensor(vec, shape):
"""Folds a vectorised tensor back into a tensor of shape `shape`
Parameters
----------
vec : 1D-array
vectorised tensor of shape ``(i_1 * i_2 * ... * i_n)``
shape : tuple
shape of the ful tensor
Returns
-------
ndarray
tensor of shape `shape` = ``(i_1, ..., i_n)``
"""
return tl.reshape(vec, shape)
[docs]
def unfold(tensor, mode):
"""Returns the mode-`mode` unfolding of `tensor` with modes starting at `0`.
Parameters
----------
tensor : ndarray
mode : int, default is 0
indexing starts at 0, therefore mode is in ``range(0, tensor.ndim)``
Returns
-------
ndarray
unfolded_tensor of shape ``(tensor.shape[mode], -1)``
"""
return tl.reshape(tl.moveaxis(tensor, mode, 0), (tensor.shape[mode], -1))
[docs]
def fold(unfolded_tensor, mode, shape):
"""Refolds the mode-`mode` unfolding into a tensor of shape `shape`
In other words, refolds the n-mode unfolded tensor
into the original tensor of the specified shape.
Parameters
----------
unfolded_tensor : ndarray
unfolded tensor of shape ``(shape[mode], -1)``
mode : int
the mode of the unfolding
shape : tuple
shape of the original tensor before unfolding
Returns
-------
ndarray
folded_tensor of shape `shape`
"""
full_shape = list(shape)
mode_dim = full_shape.pop(mode)
full_shape.insert(0, mode_dim)
return tl.moveaxis(tl.reshape(unfolded_tensor, full_shape), 0, mode)
[docs]
def partial_unfold(tensor, mode=0, skip_begin=1, skip_end=0, ravel_tensors=False):
"""Partially unfolds a tensor while ignoring the specified number of dimensions at the beginning and the end.
For instance, if the first dimension of the tensor is the number of samples, to unfold each sample,
set skip_begin=1.
This would, for each i in ``range(tensor.shape[0])``, unfold ``tensor[i, ...]``.
Parameters
----------
tensor : ndarray
tensor of shape n_samples x n_1 x n_2 x ... x n_i
mode : int
indexing starts at 0, therefore mode is in range(0, tensor.ndim)
skip_begin : int, optional
number of dimensions to leave untouched at the beginning
skip_end : int, optional
number of dimensions to leave untouched at the end
ravel_tensors : bool, optional
if True, the unfolded tensors are also flattened
Returns
-------
ndarray
partially unfolded tensor
"""
if ravel_tensors:
new_shape = [-1]
else:
new_shape = [tensor.shape[mode + skip_begin], -1]
if skip_begin:
new_shape = [tensor.shape[i] for i in range(skip_begin)] + new_shape
if skip_end:
new_shape += [tensor.shape[-i] for i in range(1, 1 + skip_end)]
return tl.reshape(tl.moveaxis(tensor, mode + skip_begin, skip_begin), new_shape)
[docs]
def partial_fold(unfolded, mode, shape, skip_begin=1, skip_end=0):
"""Re-folds a partially unfolded tensor
Parameters
----------
unfolded : ndarray
a partially unfolded tensor
mode : int
indexing starts at 0, therefore mode is in range(0, tensor.ndim)
shape : tuple
the shape of the original full tensor (including skipped dimensions)
skip_begin : int, optional, default is 1
number of dimensions to leave untouched at the beginning
skip_end : int, optional
number of dimensions to leave untouched at the end
Returns
-------
ndarray
partially re-folded tensor
"""
transposed_shape = list(shape)
mode_dim = transposed_shape.pop(skip_begin + mode)
transposed_shape.insert(skip_begin, mode_dim)
return tl.moveaxis(
tl.reshape(unfolded, transposed_shape), skip_begin, skip_begin + mode
)
[docs]
def partial_tensor_to_vec(tensor, skip_begin=1, skip_end=0):
"""Partially vectorises a tensor
Partially vectorises a tensor while ignoring the specified dimension at the beginning and the end
Parameters
----------
tensor : ndarray
tensor to partially vectorise
skip_begin : int, optional, default is 1
number of dimensions to leave untouched at the beginning
skip_end : int, optional
number of dimensions to leave untouched at the end
Returns
-------
ndarray
partially vectorised tensor with the `skip_begin` first and `skip_end` last dimensions untouched
"""
return partial_unfold(
tensor, mode=0, skip_begin=skip_begin, skip_end=skip_end, ravel_tensors=True
)
[docs]
def partial_vec_to_tensor(matrix, shape, skip_begin=1, skip_end=0):
"""Refolds a partially vectorised tensor into a full one
Parameters
----------
matrix : ndarray
a partially vectorised tensor
shape : tuple
the shape of the original full tensor (including skipped dimensions)
skip_begin : int, optional, default is 1
number of dimensions to leave untouched at the beginning
skip_end : int, optional
number of dimensions to leave untouched at the end
Returns
-------
ndarray
full tensor
"""
return partial_fold(
matrix, mode=0, shape=shape, skip_begin=skip_begin, skip_end=skip_end
)
def matricize(tensor, row_modes, column_modes=None):
"""Matricizes the given tensor
Parameters
----------
tensor : tl.tensor
row_modes : tuple[int]
modes to use as row of the matrix (in the desired order)
column_modes : tuple[int], default is None
modes to use as column of the matrix, in the desired order
if None, the modes not in `row_modes` will be used in ascending order
Returns
-------
matrix : tl.tensor of size (prod(tensor.shape[i] for i in row_modes), -1)
"""
try:
row_indices = list(row_modes)
except TypeError:
row_indices = [row_modes]
if column_modes is None:
column_indices = [i for i in range(tl.ndim(tensor)) if i not in row_indices]
else:
try:
column_indices = list(column_modes)
except TypeError:
column_indices = [column_modes]
if sorted(column_indices + row_indices) != list(range(tl.ndim(tensor))):
msg = (
"If you provide both column and row modes for the matricization"
" then column_modes + row_modes must contain all the modes of the tensor."
f" Yet, got row_modes={row_modes} and column_modes={column_modes}."
)
raise ValueError(msg)
row_size = prod(tl.shape(tensor)[i] for i in row_indices)
column_size = prod(tl.shape(tensor)[i] for i in column_indices)
return tl.reshape(
tl.transpose(tensor, row_indices + column_indices), (row_size, column_size)
)