Source code for tensorly.tt_tensor

"""
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
from scipy.optimize import brentq
import warnings

def _validate_tt_tensor(tt_tensor):
    factors = tt_tensor
    n_factors = len(factors)

    if isinstance(tt_tensor, TTTensor):
        # it's already been validated at creation
        return tt_tensor.shape, tt_tensor.rank
    elif isinstance(tt_tensor, (float, int)): #0-order tensor
        return 0, 0

    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)


[docs]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/Matrix-Product-State format into the corresponding full tensor Parameters ---------- factors : list of 3D-arrays TT factors (TT-cores) Returns ------- output_tensor : ndarray tensor whose TT/MPS decomposition was given by 'factors' """ if isinstance(factors, (float, int)): #0-order tensor return 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)
[docs]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)
[docs]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', constant_rank=False, 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 constant_rank : bool, default is False * if True, the *same* rank will be chosen for each modes * if False (default), the rank of each mode will be proportional to the corresponding tensor_shape *used only if rank == 'same' or 0 < rank <= 1* 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 constant_rank: # Choose the *same* rank for each mode n_param_tensor = np.prod(tensor_shape)*rank order = len(tensor_shape) if order == 2: rank = (1, n_param_tensor / (tensor_shape[0] + tensor_shape[1]), 1) warnings.warn(f'Determining the tt-rank for the trivial case of a matrix (order 2 tensor) of shape {tensor_shape}, not a higher-order tensor.') # R_k I_k R_{k+1} = R^2 I_k a = np.sum(tensor_shape[1:-1]) # Border rank of 1, R_0 = R_N = 1 # First and last factor of size I_0 R and I_N R 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, ) elif isinstance(rank, float): # Choose a rank proportional to the size of each mode # The method is similar to the above one for constant_rank == True order = len(tensor_shape) avg_dim = [(tensor_shape[i]+tensor_shape[i+1])/2 for i in range(order - 1)] if len(avg_dim) > 1: a = sum(avg_dim[i-1]*tensor_shape[i]*avg_dim[i] for i in range(1, order - 1)) else: warnings.warn(f'Determining the tt-rank for the trivial case of a matrix (order 2 tensor) of shape {tensor_shape}, not a higher-order tensor.') a = avg_dim[0]**2*tensor_shape[0] b = tensor_shape[0]*avg_dim[0] + tensor_shape[-1]*avg_dim[-1] c = -np.prod(tensor_shape)*rank delta = np.sqrt(b**2 - 4*a*c) # We get the non-negative solution fraction_param = (- b + delta)/(2*a) rank = tuple([max(int(rounding_fun(d*fraction_param)), 1) for d in avg_dim]) rank = (1, ) + rank + (1, ) else: # Check user input for potential 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)