Matrix (version 1.5-1)

symmpart: Symmetric Part and Skew(symmetric) Part of a Matrix

Description

symmpart(x) computes the symmetric part (x + t(x))/2 and skewpart(x) the skew symmetric part (x - t(x))/2 of a square matrix x, more efficiently for specific Matrix classes.

Note that x == symmpart(x) + skewpart(x) for all square matrices -- apart from extraneous NA values in the RHS.

Usage

symmpart(x)
skewpart(x)

Value

symmpart() returns a symmetric matrix, inheriting from

symmetricMatrix iff x inherited from

Matrix.

skewpart() returns a skew-symmetric matrix, typically of the same class as x (or the closest

“general” one, see generalMatrix).

Arguments

x

a square matrix; either “traditional” of class "matrix", or typically, inheriting from the Matrix class.

Details

These are generic functions with several methods for different matrix classes, use e.g., showMethods(symmpart) to see them.

If the row and column names differ, the result will use the column names unless they are (partly) NULL where the row names are non-NULL (see also the examples).

See Also

isSymmetric.

Examples

m <- Matrix(1:4, 2,2)
symmpart(m)
skewpart(m)

stopifnot(all(m == symmpart(m) + skewpart(m)))

dn <- dimnames(m) <- list(row = c("r1", "r2"), col = c("var.1", "var.2"))
stopifnot(all(m == symmpart(m) + skewpart(m)))
colnames(m) <- NULL
stopifnot(all(m == symmpart(m) + skewpart(m)))
dimnames(m) <- unname(dn)
stopifnot(all(m == symmpart(m) + skewpart(m)))


## investigate the current methods:
showMethods(skewpart, include = TRUE)