tensorA (version 0.36.2.1)

inv.tensor: Inversion of a tensor as linear mapping from tensors to tensors

Description

A tensor can be seen as a linear mapping of a tensor to a tensor. This function computes its (generalized-Moore-Penrose) inverse.

Usage

inv.tensor(X,i,...,allowSingular=FALSE,eps=1E-10,by=NULL)

Value

a tensor containing the inverse mapping. If allowSingular is given and the condition number of the matrix is bellow eps a generalized inverse is returned.

Arguments

X

The tensor to be decomposed

i

The image dimensions of the linear mapping

allowSingular

A boolean, indicating that a Moore-Penrose-Inverse should be computed rather than an error generated in case of a numerically singular mapping.

...

further arguments for generic use

eps

The limit for condition-number, to select an generalized inverse.

by

the operation is done in parallel for these dimensions

Author

K. Gerald van den Boogaart

Details

A tensor can be seen as a linear mapping of a tensor to a tensor.

inv.tensor

Computes the inverse of the mapping

See Also

to.tensor, solve.tensor, svd.tensor

Examples

# SVD
# inv.tensor
R1  <- matrix(rnorm(9),nrow=3)
R1i <- solve(R1)
R2 <- to.tensor(R1,c(a=3,b=3),what=1:2)
R2i <- to.tensor(R1i,c(b=3,a=3),what=1:2)

inv.tensor(R2,"a","b") - R2i
inv.tensor(R2,"a","b",allowSingular=TRUE) - R2i

inv.tensor(rep(R2,4,1,"K"),"a","b",by="K") - rep(R2i,4,1,"K")
inv.tensor(rep(R2,4,1,"K"),"a","b",by="K",allowSingular=TRUE) - rep(R2i,4,3,"K")