CommutatorMatr: Commutator Matrix
In MultiStatM: Multivariate Statistical Methods

CommutatorMatr

R Documentation

Commutator Matrix

Description

This function generates various types of commutator matrices.

Usage

CommutatorMatr(Type, ...)

Arguments

`Type`	A string specifying the type of commutator matrix. Choices are "Kmn", "Kperm", "Mixing", or "Moment".
`...`	Additional arguments specific to the type of commutator matrix (see Details).

Details

The function CommutatorMatr supports the following types of commutator matrices:

Kmn

Description: Transforms vec(A) to vec(A^T), where A^T is the transpose of matrix A. An option for sparse matrix is provided. By default, a non-sparse matrix is produced. Using sparse matrices increases computation times but requires far less memory. Arguments:

m (integer): Number of rows of the first matrix.
n (integer): Number of columns of the first matrix.
useSparse (logical, optional): If TRUE, returns a sparse matrix. Default is FALSE.

Kperm

Description: Generates a commutation matrix for a specified permutation of matrix dimensions. An option for sparse matrix is provided. By default, a non-sparse matrix is produced. Using sparse matrices increases computation times but requires far less memory. Arguments:

perm (integer vector): The permutation vector.
dims (integer vector): The dimensions of the matrices involved.
useSparse (logical, optional): If TRUE, returns a sparse matrix. Default is FALSE.

Mixing

Description: Generates the Mixing commutation matrix used in linear algebra transformations involving tensor products. An option for sparse matrix is provided. By default, a non-sparse matrix is produced. Using sparse matrices increases computation times but requires far less memory. Arguments:

d1 (integer vector): Dimensions of the first set.
d2 (integer vector): Dimensions of the second set.
useSparse (logical, optional): If TRUE, returns a sparse matrix. Default is FALSE.

Moment

Description: Generates the Moment commutation matrix based on partitioning of moments. An option for sparse matrix is provided. By default, a non-sparse matrix is produced. Using sparse matrices increases computation times but requires far less memory. Arguments:

el_rm (integer vector): Elements of the partition.
d (integer): Dimension of the partition.
useSparse (logical, optional): If TRUE, returns a sparse matrix. Default is FALSE.

Value

Depending on the type:

Kmn: A commutation matrix of dimension mn \times mn. If useSparse=TRUE, an object of class "dgCMatrix" is produced.
Kperm: A square permutation matrix of size prod(dims). If useSparse=TRUE, an object of class "dgCMatrix" is produced.
Mixing: A square matrix of dimension prod(d1) * prod(d2). If useSparse=TRUE, an object of class "dgCMatrix" is produced.
Moment: A commutator matrix for moment formulae.

Examples

# Example for Kmn
CommutatorMatr("Kmn", m = 3, n = 2)

# Example for Kperm
dims <- c(2, 3, 2)
perm <- c(1, 3, 2)
CommutatorMatr("Kperm", perm = perm, dims = dims)

# Example for Mixing
d1 <- c(2, 3, 2)
d2 <- c(3, 2, 2)
CommutatorMatr("Mixing", d1 = d1, d2 = d2)

# Example for Moment
n <- 4
r <- 2
m <- 1
d <- 2
PTA <- PartitionTypeAll(n)
el_r <- PTA$eL_r[[r]][m,]
CommutatorMatr("Moment", el_r = el_r, d = d)

MultiStatM documentation built on Sept. 11, 2024, 6:01 p.m.