Source code for pyCP_APR.torch_cp.ktensor_Torch

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
ktensor_Torch.py contains the K_TENSOR class for KRUSKAL tensor M object representation.

References
========================================
[1] General software, latest release: Brett W. Bader, Tamara G. Kolda and others, Tensor Toolbox for MATLAB, Version 3.2.1, www.tensortoolbox.org, April 5, 2021.\n
[2] Dense tensors: B. W. Bader and T. G. Kolda, Algorithm 862: MATLAB Tensor Classes for Fast Algorithm Prototyping, ACM Trans. Mathematical Software, 32(4):635-653, 2006, http://dx.doi.org/10.1145/1186785.1186794.\n
[3] Sparse, Kruskal, and Tucker tensors: B. W. Bader and T. G. Kolda, Efficient MATLAB Computations with Sparse and Factored Tensors, SIAM J. Scientific Computing, 30(1):205-231, 2007, http://dx.doi.org/10.1137/060676489.\n
[4] Chi, E.C. and Kolda, T.G., 2012. On tensors, sparsity, and nonnegative factorizations. SIAM Journal on Matrix Analysis and Applications, 33(4), pp.1272-1299.

@author: Maksim Ekin Eren
"""
from math import sqrt
import sys
import torch as tr


[docs]class K_TENSOR(): def __init__(self, Rank, Size, Minit='random', random_state=42, device='cpu', dtype='torch.DoubleTensor'): """ Initilize the K_TENSOR class.\n Creates the object representation of M.\n If initial M is not passed, by default, creates M from uniform distribution. Parameters ---------- Rank : int Tensor rank, i.e. number of components in M. Size : list Shape of the tensor. Minit : string or dictionary of latent factors Initial value of latent factors.\n If Minit = 'random', initial factors are chosen randomly from uniform distribution between 0 and 1.\n Else, pass dictionary where the key is the mode number and value is array size d x r where d is the number of elements on the dimension and r is the rank.\n The default is "random". random_state : int, optional Random seed for initial M. The default is 42. device : string, optional Torch device to be used. 'cpu' to use PyTorch with CPU. 'gpu' to use cuda:0 The default is cpu. dtype : string, optional Type to be used in torch tensors. Default is torch.cuda.DoubleTensor. """ self.Factors = dict() self.device = device self.dtype = dtype self.Weights = tr.ones(Rank).to(self.device) self.Rank = Rank self.Dimensions = len(Size) self.Type = 'ktensor' if Minit == 'random': tr.random.manual_seed(random_state) for d in range(self.Dimensions): if self.dtype == 'torch.FloatTensor': self.Factors[str(d)] = tr.FloatTensor(Size[d], Rank).uniform_(0, 1).to(self.device) else: self.Factors[str(d)] = tr.DoubleTensor(Size[d], Rank).uniform_(0, 1).to(self.device) # if initial Factors are passed else: for d in range(self.Dimensions): self.Factors[str(d)] = Minit[str(d)].to(self.device)
[docs] def innerprod(self, X): """ This function takes the inner product of tensor X and KRUSKAL tensor M. Parameters ---------- X : class Original tensor. sptensor_Torch.SP_TENSOR. Returns ------- res : array inner product of tensor X and KRUSKAL tensor M. """ # if there are no nonzero terms in X. if len(X.Values) == 0: res = 0 vecs = dict() res = 0 for r in range(self.Rank): for d in range(self.Dimensions): vecs[str(d)] = self.Factors[str(d)][:, r] res = res + self.Weights[r] * X.ttv(vecs) return res
[docs] def deep_copy_factors(self): """ Creates a deep copy of the latent factors in M. Returns ------- factors : dict Copy of the latent factors of M. """ # create a copy of the current factors Factors_ = dict() for d in range(self.Dimensions): Factors_[str(d)] = tr.copy(self.Factors[str(d)]) return Factors_
[docs] def norm(self): """ This function takes the Frobenius norm of a KRUSKAL tensor M. Returns ------- nrm : float Frobenius norm of M. """ weightsMatrix = tr.ones([self.Rank, self.Rank]).to(self.device) * self.Weights coefMatrix = weightsMatrix * weightsMatrix.T for d in range(self.Dimensions): tmp = tr.matmul(self.Factors[str(d)].T, self.Factors[str(d)]) coefMatrix = tr.mul(coefMatrix, tmp) nrm = sqrt(tr.abs(tr.sum(coefMatrix[:]))) return nrm
[docs] def redistribute(self, mode): """ This function distributes the weights to a specified dimension or mode.\n Parameters ---------- mode : int Dimension number. """ for r in range(self.Rank): self.Factors[str(mode)][:, r] *= self.Weights[r] self.Weights[r] = 1
[docs] def arrange(self, p=[]): """ This function arranges the components of KRUSKAL tensor M. Parameters ---------- p : list, optional permutation. The default is []. """ # Just rearrange and return if second argument is a permutation if len(p) > 0: self.Weights = self.Weights[p] for d in range(self.Dimensions): self.Factors[str(d)] = self.Factors[str(d)][:, p]
[docs] def normalize(self, M, normtype=1, N=-1, mode=-1): """ This function normalizes the columns of the factor matrices. Parameters ---------- M : object KRUSKAL tensor M class. ktensor_Torch.K_TENSOR. normtype : int, optional Determines the type of normalization. The default is 1. N : int, optional Factor matrix number. The default is -1. mode : int, optional Dimension number. The default is -1. Returns ------- M : object Normalized KRUSKAL tensor M class. ktensor_Torch.K_TENSOR. """ # If the target dimension is given if mode != -1: for r in range(M.Rank): tmp = tr.norm(M.Factors[str(mode)][:, r], normtype) if tmp > 0: M.Factors[str(mode)][:, r] /= tmp M.Weights[r] *= tmp return M # Normalize each of the component and weights for r in range(M.Rank): for d in range(M.Dimensions): tmp = tr.norm(M.Factors[str(d)][:, r], normtype) if tmp > 0: M.Factors[str(d)][:, r] /= tmp M.Weights[r] *= tmp negative_components = tr.where(M.Weights < 0) M.Factors[str(0)][:, [t.to('cpu').numpy() for t in negative_components]] *= -1 M.Weights[negative_components] *= -1 # Absorb the weight into one factor if N == 0: sys.exit("Reached to a location that has not been imlemented yet.") elif N > 0: M.Factors[str(N - 1)] = tr.matmul(M.Factors[str(N - 1)], tr.diag(M.Weights).to(self.device)) Lambdas = tr.ones(M.Rank) elif N == -2: if M.Rank > 1: p = tr.argsort(-M.Weights) M.arrange(p) return M