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\name{tensorSparse}
\alias{tensorSparse}
\title{
Tensor Product of Sparse Vectors, Matrices or Arrays
}
\description{
Compute the tensor product of two vectors, matrices or arrays
which may be sparse or non-sparse.
}
\usage{
tensorSparse(A, B, alongA = integer(0), alongB = integer(0))
}
\arguments{
\item{A,B}{
Vectors, matrices, three-dimensional arrays,
or objects of class \code{sparseVector}, \code{sparseMatrix}
or \code{sparse3Darray}.
}
\item{alongA}{
Integer vector specifying the dimensions of \code{A} to be collapsed.
}
\item{alongB}{
Integer vector specifying the dimensions of \code{B} to be collapsed.
}
}
\details{
This function is a generalisation, to sparse arrays, of the function
\code{\link[tensor]{tensor}} in the \pkg{tensor} package.
\code{tensorSparse} has the same syntax and interpretation
as \code{\link[tensor]{tensor}}.
For example, if \code{A} and \code{B} are matrices, then
\code{tensor(A,B,2,1)} is the matrix product \code{A \%*\% B}
while \code{tensor(A,B,2,2)} is \code{A \%*\% t(B)}.
This function \code{tensorSparse} handles
sparse vectors (class \code{"sparseVector"} in the \pkg{Matrix} package),
sparse matrices (class \code{"sparseMatrix"} in the \pkg{Matrix}
package) and sparse three-dimensional arrays (class
\code{"sparse3Darray"} in the \pkg{spatstat.sparse} package)
in addition to the usual vectors, matrices and arrays.
The result is a sparse object if at least one of \code{A} and \code{B}
is sparse. Otherwise, if neither \code{A} nor \code{B} is sparse, then the
result is computed using \code{\link[tensor]{tensor}}.
The main limitation is that the result cannot have more than 3
dimensions (because sparse arrays with more than 3 dimensions are not yet
supported).
}
\value{
Either a scalar, a vector, a matrix, an array,
a sparse vector (class \code{"sparseVector"} in the \pkg{Matrix} package),
a sparse matrix (class \code{"sparseMatrix"} in the \pkg{Matrix}
package) or a sparse three-dimensional array (class
\code{"sparse3Darray"} in the \pkg{spatstat.sparse} package).
}
\author{
\spatstatAuthors.
}
\seealso{
\code{\link{sparse3Darray}},
\code{\link{aperm.sparse3Darray}}
}
\examples{
M <- sparse3Darray(i=1:4, j=sample(1:4, replace=TRUE),
k=c(1,2,1,2), x=1:4, dims=c(5,5,2))
A <- tensorSparse(M, M, 1:2, 2:1)
}
\keyword{array}
\keyword{algebra}
\concept{sparse}
|
