Source code for tensorly.decomposition._tt

import tensorly as tl
from ._base_decomposition import DecompositionMixin
from ..tt_tensor import validate_tt_rank, TTTensor
from ..tt_matrix import validate_tt_matrix_rank, TTMatrix
from ..utils import DefineDeprecated

[docs]def tensor_train(input_tensor, rank, verbose=False): """TT decomposition via recursive SVD Decomposes `input_tensor` into a sequence of order-3 tensors (factors) -- also known as Tensor-Train decomposition [1]_. Parameters ---------- input_tensor : tensorly.tensor rank : {int, int list} maximum allowable TT rank of the factors if int, then this is the same for all the factors if int list, then rank[k] is the rank of the kth factor verbose : boolean, optional level of verbosity Returns ------- factors : TT factors order-3 tensors of the TT decomposition References ---------- .. [1] Ivan V. Oseledets. "Tensor-train decomposition", SIAM J. Scientific Computing, 33(5):2295–2317, 2011. """ rank = validate_tt_rank(tl.shape(input_tensor), rank=rank) tensor_size = input_tensor.shape n_dim = len(tensor_size) unfolding = input_tensor factors = [None] * n_dim # Getting the TT factors up to n_dim - 1 for k in range(n_dim - 1): # Reshape the unfolding matrix of the remaining factors n_row = int(rank[k]*tensor_size[k]) unfolding = tl.reshape(unfolding, (n_row, -1)) # SVD of unfolding matrix (n_row, n_column) = unfolding.shape current_rank = min(n_row, n_column, rank[k+1]) U, S, V = tl.partial_svd(unfolding, current_rank) rank[k+1] = current_rank # Get kth TT factor factors[k] = tl.reshape(U, (rank[k], tensor_size[k], rank[k+1])) if(verbose is True): print("TT factor " + str(k) + " computed with shape " + str(factors[k].shape)) # Get new unfolding matrix for the remaining factors unfolding= tl.reshape(S, (-1, 1))*V # Getting the last factor (prev_rank, last_dim) = unfolding.shape factors[-1] = tl.reshape(unfolding, (prev_rank, last_dim, 1)) if(verbose is True): print("TT factor " + str(n_dim-1) + " computed with shape " + str(factors[n_dim-1].shape)) return TTTensor(factors)
[docs]def tensor_train_matrix(tensor, rank): """Decompose a tensor into a matrix in tt-format Parameters ---------- tensor : tensorized matrix if your input matrix is of size (4, 9) and your tensorized_shape (2, 2, 3, 3) then tensor should be tl.reshape(matrix, (2, 2, 3, 3)) rank : 'same', float or int tuple - if 'same' creates a decomposition with the same number of parameters as `tensor` - if float, creates a decomposition with `rank` x the number of parameters of `tensor` - otherwise, the actual rank to be used, e.g. (1, rank_2, ..., 1) of size tensor.ndim//2. Note that boundary conditions dictate that the first rank = last rank = 1. Returns ------- tt_matrix """ order = tl.ndim(tensor) n_input = order // 2 # (n_output = n_input) if tl.ndim(tensor) != n_input*2: msg = 'The tensor should have as many dimensions for inputs and outputs, i.e. order should be even ' msg += f'but got a tensor of order tl.ndim(tensor)={order} which is odd.' raise ValueError(msg) in_shape = tl.shape(tensor)[:n_input] out_shape = tl.shape(tensor)[n_input:] if n_input == 1: # A TTM with a single factor is just a matrix... return TTMatrix([tensor.reshape(1, in_shape[0], out_shape[0], 1)]) new_idx = list([idx for tuple_ in zip(range(n_input), range(n_input, 2*n_input)) for idx in tuple_]) new_shape = list([a*b for (a,b) in zip(in_shape, out_shape)]) tensor = tl.reshape(tl.transpose(tensor, new_idx), new_shape) factors = tensor_train(tensor, rank).factors for i in range(len(factors)): factors[i] = tl.reshape(factors[i], (factors[i].shape[0], in_shape[i], out_shape[i], -1)) return TTMatrix(factors)
[docs]class TensorTrain(DecompositionMixin): """TT decomposition via recursive SVD Decomposes `input_tensor` into a sequence of order-3 tensors (factors) -- also known as Tensor-Train decomposition [1]_. Parameters ---------- input_tensor : tensorly.tensor rank : {int, int list} maximum allowable TT rank of the factors if int, then this is the same for all the factors if int list, then rank[k] is the rank of the kth factor verbose : boolean, optional level of verbosity Returns ------- factors : TT factors order-3 tensors of the TT decomposition References ---------- .. [1] Ivan V. Oseledets. "Tensor-train decomposition", SIAM J. Scientific Computing, 33(5):2295–2317, 2011. """ def __init__(self, rank, verbose=False): self.rank = rank self.verbose = verbose def fit_transform(self, tensor): self.decomposition_ = tensor_train(tensor, rank=self.rank, verbose=self.verbose) return self.decomposition_
matrix_product_state = DefineDeprecated('matrix_product_state', tensor_train)