Symmetric Part and Skew(symmetric) Part of a Matrix

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.

symmpart(x)
skewpart(x)

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).

Value

symmpart(x) returns a symmetric matrix, inheriting from symmetricMatrix or diagonalMatrix if x inherits from Matrix.

skewpart(x) returns a skew-symmetric matrix, inheriting from generalMatrix, symmetricMatrix or diagonalMatrix if x inherits from Matrix.

See also

isSymmetric.

Examples

m <- Matrix(1:4, 2,2)
symmpart(m)
#> 2 x 2 Matrix of class "dsyMatrix"
#>      [,1] [,2]
#> [1,]  1.0  2.5
#> [2,]  2.5  4.0
skewpart(m)
#> 2 x 2 Matrix of class "dgeMatrix"
#>      [,1] [,2]
#> [1,]  0.0  0.5
#> [2,] -0.5  0.0

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)
#> Function: skewpart (package Matrix)
#> x="CsparseMatrix"
#> function (x) 
#> .Call(R_sparse_skewpart, x)
#> 
#> 
#> x="RsparseMatrix"
#> function (x) 
#> .Call(R_sparse_skewpart, x)
#> 
#> 
#> x="TsparseMatrix"
#> function (x) 
#> .Call(R_sparse_skewpart, x)
#> 
#> 
#> x="denseMatrix"
#> function (x) 
#> .Call(R_dense_skewpart, x)
#> 
#> 
#> x="diagonalMatrix"
#> function (x) 
#> {
#>     kind <- .M.kind(x)
#>     r <- new(if (kind == "z") 
#>         "zdiMatrix"
#>     else "ddiMatrix")
#>     r@Dim <- d <- x@Dim
#>     r@Dimnames <- symDN(x@Dimnames)
#>     r@x <- if (kind == "z") {
#>         if (x@diag != "N") 
#>             complex(d[1L])
#>         else complex(real = 0, imaginary = Im(x@x))
#>     }
#>     else double(d[1L])
#>     r
#> }
#> 
#> 
#> x="indMatrix"
#> function (x) 
#> skewpart(.M2kind(x, "d"))
#> 
#> 
#> x="matrix"
#> function (x) 
#> symmetrizeDN(0.5 * (x - t(x)))
#> 
#> 
#>