Source code for tensorly.tt_matrix

"""Module for matrices in the TT format"""

import tensorly as tl

# Note how tt_matrix_to_tensor is implemented in tenalg to allow for more efficient implementations
# (e.g. using the einsum backend)
from .tenalg import _tt_matrix_to_tensor as tt_matrix_to_tensor

from ._factorized_tensor import FactorizedTensor
import numpy as np


def validate_tt_matrix_rank(tensorized_shape, rank="same"):
    """Returns the rank of a TT-Matrix Decomposition

    Parameters
    ----------
    tensor_shape : tupe
        shape of the tensorized matrix 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
    """

    n_dim = len(tensorized_shape) // 2

    if n_dim * 2 != len(tensorized_shape):
        msg = (
            f"The order of the give tensorized shape is not a multiple of 2."
            "However, there should be as many dimensions for the left side (number of rows)"
            " as of the right side (number of columns). "
            " For instance, to convert a matrix of size (8, 9) to the TT-format, "
            " it can be tensorized to (2, 4, 3, 3) but NOT to (2, 2, 2, 3, 3)."
        )
        raise ValueError(msg)

    left_shape = tensorized_shape[:n_dim]
    right_shape = tensorized_shape[n_dim:]

    full_shape = tuple(i * o for i, o in zip(left_shape, right_shape))
    return tl.tt_tensor.validate_tt_rank(full_shape, rank)


def _tt_matrix_n_param(tensorized_shape, rank):
    """Number of parameters of a TT-Matrix decomposition for a given `rank` and full `tensor_shape`.

    Parameters
    ----------
    tensorized_shape : int tuple
        shape of the full tensorized matrix to decompose (or approximate)

    rank : tuple
        rank of the TT-Matrix decomposition

    Returns
    -------
    n_params : int
        Number of parameters of a TT-Matrix decomposition of rank `rank` of a full tensor of shape `tensor_shape`
    """
    n_dim = len(tensorized_shape) // 2

    if n_dim * 2 != len(tensorized_shape):
        msg = (
            f"The order of the give tensorized shape is not a multiple of 2."
            "However, there should be as many dimensions for the left side (number of rows)"
            " as of the right side (number of columns). "
            " For instance, to convert a matrix of size (8, 9) to the TT-format, "
            " it can be tensorized to (2, 4, 3, 3) but NOT to (2, 2, 2, 3, 3)."
        )
        raise ValueError(msg)

    left_shape = tensorized_shape[:n_dim]
    right_shape = tensorized_shape[n_dim:]

    factor_params = []
    for i, (ls, rs) in enumerate(zip(left_shape, right_shape)):
        factor_params.append(rank[i] * ls * rs * rank[i + 1])

    return np.sum(factor_params)


def tt_matrix_to_matrix(tt_matrix):
    """Reconstruct the original matrix that was tensorized and compressed in the TT-Matrix format

        Re-assembles 'factors', which represent a tensor in TT-Matrix format
        into the corresponding matrix

    Parameters
    ----------
    factors: list of 4D-arrays
              TT-Matrix factors (known as core) of shape (rank_k, left_dim_k, right_dim_k, rank_{k+1})

    Returns
    -------
    output_matrix: 2D-array
        matrix whose TT-Matrix decomposition was given by 'factors'
    """
    in_shape = tuple(c.shape[1] for c in tt_matrix)
    return tl.reshape(tt_matrix_to_tensor(tt_matrix), (np.prod(in_shape), -1))


[docs]def tt_matrix_to_unfolded(tt_matrix, mode): """Returns the unfolding matrix of a tensor given in TT-Matrix format Reassembles a full tensor from 'factors' and returns its unfolding matrix with mode given by 'mode' Parameters ---------- factors : list of 3D-arrays TT-Matrix 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_matrix_to_tensor(tt_matrix), mode)
[docs]def tt_matrix_to_vec(tt_matrix): """Returns the tensor defined by its TT-Matrix format ('factors') into its vectorized format Parameters ---------- factors : list of 3D-arrays TT factors Returns ------- 1-D array format of tensor defined by 'factors' """ return tl.tensor_to_vec(tt_matrix_to_tensor(tt_matrix))
def _validate_tt_matrix(tt_tensor): factors = tt_tensor n_factors = len(factors) if n_factors < 1: raise ValueError( "A Tensor-Train (MPS) tensor should be composed of at least one factor." "However, {} factor was given.".format(n_factors) ) rank = [] left_shape = [] right_shape = [] for index, factor in enumerate(factors): current_rank, current_left_shape, current_right_shape, next_rank = tl.shape( factor ) # Check that factors are third order tensors if not tl.ndim(factor) == 4: raise ValueError( "A TTMatrix expresses a tensor as fourth 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])[-1] != current_rank: raise ValueError( "Consecutive factors should have matching ranks\n" " -- e.g. tl.shape(factors[0])[-1]) == tl.shape(factors[1])[0])\n" "However, tl.shape(factor[{}])[-1] == {} but" " tl.shape(factor[{}])[0] == {} ".format( index - 1, tl.shape(factors[index - 1])[-1], 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) ) left_shape.append(current_left_shape) right_shape.append(current_right_shape) rank.append(current_rank) # Add last rank (boundary condition) rank.append(next_rank) return tuple(left_shape) + tuple(right_shape), tuple(rank) class TTMatrix(FactorizedTensor): def __init__(self, factors, inplace=False): super().__init__() # Will raise an error if invalid shape, rank = _validate_tt_matrix(factors) self.shape = tuple(shape) self.order = len(self.shape) // 2 self.left_shape = self.shape[: self.order] self.right_shape = self.shape[self.order :] 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} TT-Matrix of tensorized shape {self.shape}" f" corresponding to a matrix of size {np.prod(self.left_shape)} x {np.prod(self.right_shape)}" ) return message def to_tensor(self): return tt_matrix_to_tensor(self) def to_matrix(self): return tt_matrix_to_matrix(self) def to_unfolding(self, mode): return tt_matrix_to_unfolded(self, mode) def to_vec(self): return tt_matrix_to_vec(self)