https://github.com/tensorly/tensorly
Tip revision: 6b5a5fe85b64da3ca5e4c383c8f7b7b475fdfb48 authored by Jean Kossaifi on 15 October 2020, 18:31:27 UTC
Update website + API fix
Update website + API fix
Tip revision: 6b5a5fe
tt_tensor.py
"""
Core operations on tensors in Tensor-Train (TT) format, also known as Matrix-Product-State (MPS)
"""
import tensorly as tl
from ._factorized_tensor import FactorizedTensor
from .utils import DefineDeprecated
import numpy as np
def _validate_tt_tensor(tt_tensor):
factors = tt_tensor
n_factors = len(factors)
if n_factors < 2:
raise ValueError('A Tensor-Train (MPS) tensor should be composed of at least two factors and a core.'
'However, {} factor was given.'.format(n_factors))
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('TT expresses a tensor as third order factors (tt-cores).\n'
'However, tl.ndim(factors[{}]) = {}'.format(
index, tl.ndim(factor)))
# Consecutive factors should have matching ranks
if index and 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'
'However, tl.shape(factor[{}])[2] == {} but'
' tl.shape(factor[{}])[0] == {} '.format(
index - 1, tl.shape(factors[index - 1])[2], index, current_rank))
# Check for boundary conditions
if (index == 0) and current_rank != 1:
raise ValueError('Boundary conditions dictate factor[0].shape[0] == 1.'
'However, got factor[0].shape[0] = {}.'.format(
current_rank))
if (index == n_factors - 1) and next_rank != 1:
raise ValueError('Boundary conditions dictate factor[-1].shape[2] == 1.'
'However, got factor[{}].shape[2] = {}.'.format(
n_factors, next_rank))
shape.append(current_shape)
rank.append(current_rank)
# Add last rank (boundary condition)
rank.append(next_rank)
return tuple(shape), tuple(rank)
def tt_to_tensor(factors):
"""Returns the full tensor whose TT decomposition is given by 'factors'
Re-assembles 'factors', which represent a tensor in TT/TT format
into the corresponding full tensor
Parameters
----------
factors: list of 3D-arrays
TT factors (known as core in TT terminology)
Returns
-------
output_tensor: ndarray
tensor whose TT/TT decomposition was given by 'factors'
"""
full_shape = [f.shape[1] for f in factors]
full_tensor = tl.reshape(factors[0], (full_shape[0], -1))
for factor in factors[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))
return tl.reshape(full_tensor, full_shape)
def tt_to_unfolded(factors, mode):
"""Returns the unfolding matrix of a tensor given in TT (or Tensor-Train) format
Reassembles a full tensor from 'factors' and returns its unfolding matrix
with mode given by 'mode'
Parameters
----------
factors: list of 3D-arrays
TT 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(tt_to_tensor(factors), mode)
def tt_to_vec(factors):
"""Returns the tensor defined by its TT format ('factors') into
its vectorized format
Parameters
----------
factors: list of 3D-arrays
TT factors
Returns
-------
1-D array
vectorized format of tensor defined by 'factors'
"""
return tl.tensor_to_vec(tt_to_tensor(factors))
def _tt_n_param(tensor_shape, rank):
"""Number of parameters of a MPS 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 MPS decomposition
Returns
-------
n_params : int
Number of parameters of a MPS 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_tt_rank(tensor_shape, rank='same', rounding='round'):
"""Returns the rank of a TT Decomposition
Parameters
----------
tensor_shape : tupe
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)
if isinstance(rank, float) and (0 < rank <= 1):
n_param_tensor = np.prod(tensor_shape)*rank
order = len(tensor_shape)
# Border rank of 1, R_0 = R_N = 1
# First and last factor of size I_0 R and I_N R
a = np.sum(tensor_shape[1:-1])
# R_k I_k R_{k+1} = R^2 I_k
b = np.sum(tensor_shape[0] + tensor_shape[-1])
# We want the number of params of decomp (=sum of params of factors)
# To be equal to c = \prod_k I_k
c = -n_param_tensor
delta = np.sqrt(b**2 - 4*a*c)
# We get the non-negative solution
solution = int(rounding_fun((- b + delta)/(2*a)))
rank = rank=(1, ) + (solution, )*(order-1) + (1, )
else:
# Check user input for errors
n_dim = len(tensor_shape)
if isinstance(rank, int):
rank = [1] + [rank] * (n_dim-1) + [1]
elif n_dim+1 != len(rank):
message = 'Provided incorrect number of ranks. Should verify len(rank) == tl.ndim(tensor)+1, but len(rank) = {} while tl.ndim(tensor) + 1 = {}'.format(
len(rank), n_dim + 1)
raise(ValueError(message))
# Initialization
if rank[0] != 1:
message = 'Provided rank[0] == {} but boundaring conditions dictatate rank[0] == rank[-1] == 1: setting rank[0] to 1.'.format(rank[0])
raise ValueError(message)
if rank[-1] != 1:
message = 'Provided rank[-1] == {} but boundaring conditions dictatate rank[0] == rank[-1] == 1: setting rank[-1] to 1.'.format(rank[0])
raise ValueError(message)
return list(rank)
class TTTensor(FactorizedTensor):
def __init__(self, factors, inplace=False):
super().__init__()
# Will raise an error if invalid
shape, rank = _validate_tt_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 = 'factors list : rank-{} matrix-product-state tensor of shape {} '.format(
self.rank, self.shape)
return message
def to_tensor(self):
return tt_to_tensor(self)
def to_unfolding(self, mode):
return tt_to_unfolded(self, mode)
def to_vec(self):
return tt_to_vec(self)
mps_to_tensor = DefineDeprecated(deprecated_name='mps_to_tensor', use_instead=tt_to_tensor)
mps_to_unfolded = DefineDeprecated(deprecated_name='mps_to_unfolded', use_instead=tt_to_unfolded)
mps_to_vec = DefineDeprecated(deprecated_name='mps_to_vec', use_instead=tt_to_vec)
_validate_mps_tensor = DefineDeprecated(deprecated_name='_validate_mps_tensor', use_instead=_validate_tt_tensor)