matr_Commutator_Kperm {MultiStatM}R Documentation

Commutator for T-products of vectors

Description

Produces any permutation of kronecker products of vectors of any length. An option for sparse matrix is provided, by default a non-sparse matrix is produced. Using sparse matrices increases computation times, but far less memory is required.

Usage

matr_Commutator_Kperm(perm, dims, useSparse = FALSE)

Arguments

perm

vector indicating the permutation of the order in the Kronecker product,

dims

vector indicating the dimensions of the vectors, use dims <- d if all dimensions are equal

useSparse

T or F.

Value

A square permutation matrix of size prod(dims). If useSparse=TRUE an object of the class "dgCMatrix" is produced.

References

Holmquist B (1996) The d-variate vector Hermite polynomial of order. Linear Algebra and its Applications 237/238, 155-190.

Gy., Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021, 1.2.4 Commuting T-Products of Vectors.

See Also

Other Matrices and commutators: indx_Commutator_Kmn(), indx_Commutator_Kperm(), indx_Commutator_Mixing(), indx_Commutator_Moment(), indx_Elimination(), indx_Qplication(), indx_Symmetry(), indx_UnivMomCum(), matr_Commutator_Kmn(), matr_Commutator_Mixing(), matr_Commutator_Moment(), matr_Elimination(), matr_Qplication(), matr_Symmetry()

Examples

dims <- c(2,3,2)
perm  <-  c(1,3,2)
matr_Commutator_Kperm(perm,dims)
perm  <- c(3,1,4,2)
dims <- 4 # All vectors with dimension 4
# If all dimensions are equal, using dims <- d instead of
# dims <- c(d,d,d,d,d,d,d,d) will be much faster.
# For example, for perm <- c(2,4,6,1,3,8,5,7) and d <- 3
# matr_Commutator_Kperm(c(2,4,6,1,3,8,5,7),3)  ## requires 2.11 secs
# matr_Commutator_Kperm(c(2,4,6,1,3,8,5,7),c(3,3,3,3,3,3,3,3))  ## requires 1326.47 secs

[Package MultiStatM version 1.2.1 Index]