rTensor-package: Tools for tensor analysis and decomposition
In rTensor: Tools for Tensor Analysis and Decomposition

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This package is centered around the Tensor-class, which defines a S4 class for tensors of arbitrary number of modes. A vignette and/or a possible paper will be included in a future release of this package.

This page will summarize the full functionality of this package. Note that since all the methods associated with S4 class Tensor-class are documented there, we will not duplicate it here.

The remaining functions can be split into two groups: the first is a set of tensor decompositions, and the second is a set of helper functions that are useful in tensor manipulation.

rTensor implements the following tensor decompositions:

cp: Canonical Polyadic (CP) decomposition
tucker: General Tucker decomposition
mpca: Multilinear Principal Component Analysis; note that for 3-Tensors this is also known as Generalized Low Rank Approximation of Matrices(GLRAM)
hosvd: (Truncated-)Higher-order singular value decomposition
t_svd: Tensor singular value decomposition; 3-Tensors only; also note that there is an asociated reconstruction function t_svd_reconstruct
pvd: Population value decomposition of images; 3-Tensors only

rTensor also provides a set functions for tensors multiplication:

ttm: Tensor times matrix, aka m-mode product
ttl: Tensor times list (of matrices)
t_mult: Tensor product based on block circulant unfolding; only implemented for a pair of 3-Tensors

...as well as for matrices:

hadamard_list: Computes the Hadamard (element-wise) product of a list of matrices
kronecker_list: Computes the Kronecker product of a list of matrices
khatri_rao: Computes the Khatri-Rao product of two matrices
khatri_rao_list: Computes the Khatri-Rao product of a list of matrices
fold: General folding of a matrix into a tensor
k_fold: Inverse operation for k_unfold
unmatvec: Inverse operation for matvec