##### https://github.com/tensorly/tensorly

tr_tensor.py

```
"""
Core operations on tensors in Tensor Ring (TR) format
"""
import warnings
import numpy as np
import tensorly as tl
from ._factorized_tensor import FactorizedTensor
def tr_to_tensor(factors):
"""Returns the full tensor whose TR decomposition is given by 'factors'
Re-assembles 'factors', which represent a tensor in TR format
into the corresponding full tensor
Parameters
----------
factors : list of 3D-arrays
TR factors (TR-cores)
Returns
-------
output_tensor : ndarray
tensor whose TR decomposition was given by 'factors'
"""
full_shape = [f.shape[1] for f in factors]
full_tensor = tl.reshape(factors[0], (-1, factors[0].shape[2]))
for factor in factors[1:-1]:
rank_prev, _, rank_next = factor.shape
factor = tl.reshape(factor, (rank_prev, -1))
full_tensor = tl.dot(full_tensor, factor)
full_tensor = tl.reshape(full_tensor, (-1, rank_next))
full_tensor = tl.reshape(
full_tensor, (factors[-1].shape[2], -1, factors[-1].shape[0])
)
full_tensor = tl.moveaxis(full_tensor, 0, -1)
full_tensor = tl.reshape(
full_tensor, (-1, factors[-1].shape[0] * factors[-1].shape[2])
)
factor = tl.moveaxis(factors[-1], -1, 1)
factor = tl.reshape(factor, (-1, full_shape[-1]))
full_tensor = tl.dot(full_tensor, factor)
return tl.reshape(full_tensor, full_shape)
def tr_to_unfolded(factors, mode):
"""Returns the unfolding matrix of a tensor given in TR format
Reassembles a full tensor from 'factors' and returns its unfolding matrix
with mode given by 'mode'
Parameters
----------
factors: list of 3D-arrays
TR factors
mode: int
unfolding matrix to be computed along this mode
Returns
-------
2-D array
unfolding matrix at mode given by 'mode'
"""
return tl.unfold(tr_to_tensor(factors), mode)
def tr_to_vec(factors):
"""Returns the tensor defined by its TR format ('factors') into
its vectorized format
Parameters
----------
factors: list of 3D-arrays
TR factors
Returns
-------
1-D array
vectorized format of tensor defined by 'factors'
"""
return tl.tensor_to_vec(tr_to_tensor(factors))
def _validate_tr_tensor(tr_tensor):
factors = tr_tensor
n_factors = len(factors)
if n_factors < 2:
raise ValueError(
"A Tensor Ring tensor should be composed of at least two factors."
f"However, {n_factors} factor was given."
)
rank = []
shape = []
for index, factor in enumerate(factors):
current_rank, current_shape, next_rank = tl.shape(factor)
# Check that factors are third order tensors
if not tl.ndim(factor) == 3:
raise ValueError(
"TR expresses a tensor as third order factors (tr-cores).\n"
f"However, tl.ndim(factors[{index}]) = {tl.ndim(factor)}"
)
# Consecutive factors should have matching ranks
if tl.shape(factors[index - 1])[2] != current_rank:
raise ValueError(
"Consecutive factors should have matching ranks\n"
" -- e.g. tl.shape(factors[0])[2]) == tl.shape(factors[1])[0])\n"
f"However, tl.shape(factor[{index-1}])[2] == {tl.shape(factors[index-1])[2]} but"
f" tl.shape(factor[{index}])[0] == {current_rank}"
)
shape.append(current_shape)
rank.append(current_rank)
# Add last rank (boundary condition)
rank.append(next_rank)
return tuple(shape), tuple(rank)
def _tr_n_param(tensor_shape, rank):
"""Number of parameters of a TR decomposition for a given `rank` and full `tensor_shape`.
Parameters
----------
tensor_shape : int tuple
shape of the full tensor to decompose (or approximate)
rank : tuple
rank of the TR decomposition
Returns
-------
n_params : int
Number of parameters of a TR decomposition of rank `rank` of a full tensor of shape `tensor_shape`
"""
factor_params = []
for i, s in enumerate(tensor_shape):
factor_params.append(rank[i] * s * rank[i + 1])
return np.sum(factor_params)
def validate_tr_rank(tensor_shape, rank="same", rounding="round"):
"""Returns the rank of a Tensor Ring Decomposition
Parameters
----------
tensor_shape : tuple
shape of the tensor to decompose
rank : {'same', float, tuple, int}, default is same
way to determine the rank, by default 'same'
if 'same': rank is computed to keep the number of parameters (at most) the same
if float, computes a rank so as to keep rank percent of the original number of parameters
if int or tuple, just returns rank
rounding : {'round', 'floor', 'ceil'}
Returns
-------
rank : int tuple
rank of the decomposition
"""
if rounding == "ceil":
rounding_fun = np.ceil
elif rounding == "floor":
rounding_fun = np.floor
elif rounding == "round":
rounding_fun = np.round
else:
raise ValueError(f"Rounding should be round, floor or ceil, but got {rounding}")
if rank == "same":
rank = float(1)
n_dim = len(tensor_shape)
if n_dim == 2:
warnings.warn(
"Determining the TR-rank for the trivial case of a matrix"
f" (order 2 tensor) of shape {tensor_shape}, not a higher-order tensor."
)
if isinstance(rank, float):
# Choose the *same* rank for each mode
n_param_tensor = np.prod(tensor_shape) * rank
# R_k I_k R_{k+1} = R^2 I_k
solution = int(rounding_fun(np.sqrt(n_param_tensor / np.sum(tensor_shape))))
rank = (solution,) * (n_dim + 1)
else:
# Check user input for potential errors
n_dim = len(tensor_shape)
if isinstance(rank, int):
rank = (rank,) * (n_dim + 1)
elif n_dim + 1 != len(rank):
message = (
"Provided incorrect number of ranks. "
"Should verify len(rank) == tl.ndim(tensor)+1, "
f"but len(rank) = {len(rank)} while tl.ndim(tensor)+1 = {n_dim + 1}"
)
raise ValueError(message)
# Check first and last rank
if rank[0] != rank[-1]:
message = (
f"Provided rank[0] == {rank[0]} and rank[-1] == {rank[-1]}"
" but boundaring conditions dictatate rank[0] == rank[-1]"
)
raise ValueError(message)
return list(rank)
class TRTensor(FactorizedTensor):
def __init__(self, factors):
super().__init__()
# Will raise an error if invalid
shape, rank = _validate_tr_tensor(factors)
self.shape = tuple(shape)
self.rank = tuple(rank)
self.factors = factors
def __getitem__(self, index):
return self.factors[index]
def __setitem__(self, index, value):
self.factors[index] = value
def __iter__(self):
for index in range(len(self)):
yield self[index]
def __len__(self):
return len(self.factors)
def __repr__(self):
message = (
f"factors list : rank-{self.rank} tensor ring tensor of shape {self.shape}"
)
return message
def to_tensor(self):
return tr_to_tensor(self)
def to_unfolding(self, mode):
return tr_to_unfolded(self, mode)
def to_vec(self):
return tr_to_vec(self)
```