tensorSparse {spatstat.sparse}

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

A, B

Vectors, matrices, three-dimensional arrays, or objects of class sparseVector, sparseMatrix or sparse3Darray.

alongA

Integer vector specifying the dimensions of A to be collapsed.

alongB

Integer vector specifying the dimensions of B to be collapsed.

Details

This function is a generalisation, to sparse arrays, of the function tensor in the tensor package.

tensorSparse has the same syntax and interpretation as tensor. For example, if A and B are matrices, then tensor(A,B,2,1) is the matrix product A %*% B while tensor(A,B,2,2) is A %*% t(B).

This function tensorSparse handles sparse vectors (class "sparseVector" in the Matrix package), sparse matrices (class "sparseMatrix" in the Matrix package) and sparse three-dimensional arrays (class "sparse3Darray" in the spatstat.sparse package) in addition to the usual vectors, matrices and arrays.

The result is a sparse object if at least one of A and B is sparse. Otherwise, if neither A nor B is sparse, then the result is computed using 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 "sparseVector" in the Matrix package), a sparse matrix (class "sparseMatrix" in the Matrix package) or a sparse three-dimensional array (class "sparse3Darray" in the spatstat.sparse package).

Author(s)

Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].

See Also

sparse3Darray, 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)