to.matrix.tensor {tensorA}

The matrix corresponding to a tensor seen as a linear mapping of tensors.

Description

A tensor can be seen as a linear mapping of a tensor to a tensor. This function gives the corresponding matrix of the mapping.

Usage

to.matrix.tensor(X,i,j,by=NULL)

Arguments

X

The tensor

i

The image indices of the linear mapping

j

The domain indices of the linear mapping

by

the operation is done in parallel for these dimensions

Details

A tensor can be seen as a linear mapping of a tensor to a tensor. This function computes the corresponding matrix, mapping the entries of the domain tensor to the entries of the image tensor.

Value

if no by is given a matrix. Otherwise a tensor of level 2+length(dim(X))[by] giving matrices for each specification of the by dimensions.

Author(s)

K. Gerald van den Boogaart

See Also

to.tensor, solve.tensor, inv.tensor, svd.tensor

Examples

A <- reorder.tensor(to.tensor(1:30,c(a=2,b=3,c=5)),c("c","a","b"))

to.matrix.tensor(A,"a",c("b","c"))              # matrix(1:30,nrow=2)

to.matrix.tensor(A,c("a","b"),c("c"))           # matrix(1:30,nrow=6)

to.matrix.tensor(A,c("a","b"),by=c("c")) # structure(1:30,dim=c(6,1,5)))
to.matrix.tensor(A,c("a"),by=c("c"))     # structure(1:30,dim=c(2,3,5)))