isSymmetric-methods: Test if a Matrix is Symmetric

In Matrix: Sparse and Dense Matrix Classes and Methods

Test if a Matrix is Symmetric

Description

Tests whether its argument is a symmetric square matrix, by default tolerating some numerical fuzz and requiring symmetric dimnames in addition to symmetry in the mathematical sense.

isSymmetric is a generic function in base, which has a method for traditional matrices of implicit class matrix. Documented here are methods in package Matrix for subclasses of virtual class Matrix.

Usage

## S4 method for signature 'denseMatrix'
isSymmetric(object, tol = 100 * .Machine$double.eps, tol1 = 8 * tol,
            trans = "C", checkDN = TRUE, ...)
## S4 method for signature 'CsparseMatrix'
isSymmetric(object, tol = 100 * .Machine$double.eps,
            trans = "C", checkDN = TRUE, ...)
## S4 method for signature 'RsparseMatrix'
isSymmetric(object, tol = 100 * .Machine$double.eps,
            trans = "C", checkDN = TRUE, ...)
## S4 method for signature 'TsparseMatrix'
isSymmetric(object, tol = 100 * .Machine$double.eps,
            trans = "C", checkDN = TRUE, ...)
## S4 method for signature 'diagonalMatrix'
isSymmetric(object, tol = 100 * .Machine$double.eps,
            trans = "C", checkDN = TRUE, ...)
## S4 method for signature 'indMatrix'
isSymmetric(object, checkDN = TRUE, ...)

Arguments

object	a Matrix.
tol, tol1	see isSymmetric.matrix.
trans	a character string, "C" or "T", indicating either the conjugate transpose or transpose, i.e., whether to test for Hermitian or symmetric object. It matters only in the complex case. The default is "C", for consistency with isSymmetric.matrix.
checkDN	a logical indicating whether symmetry of the Dimnames slot of object should be checked.
...	further arguments passed from or to other methods. Notably, for numeric or complex (but not integer, logical, or pattern) object, these are used to set a tolerance for asymmetry. See arguments tol, tol1, and ... of isSymmetric.matrix.

Details

The Dimnames slot of object, say dn, is considered to be symmetric if and only if

• dn[[1]] and dn[[2]] are identical or one is NULL; and

• ndn <- names(dn) is NULL or ndn[1] and ndn[2] are identical or one is the empty string "".

Hence list(a=nms, a=nms) is considered to be symmetric and so too are list(a=nms, NULL) and list(NULL, a=nms).

Note that this definition is looser than that employed by isSymmetric.matrix, which requires dn[1] and dn[2] to be identical, where dn is the dimnames attribute of a traditional matrix.

Value

A logical, either TRUE or FALSE (never NA).

See Also

forceSymmetric, symmpart, skewpart; virtual class symmetricMatrix and its subclasses.

Examples

isSymmetric(Diagonal(4)) # TRUE of course
M <- Matrix(c(1,2,2,1), 2,2)
isSymmetric(M) # TRUE (*and* of formal class "dsyMatrix")
isSymmetric(as(M, "generalMatrix")) # still symmetric, even if not "formally"
isSymmetric(triu(M)) # FALSE

## Look at implementations:
showMethods("isSymmetric", includeDefs = TRUE) # includes S3 generic from base

Matrix documentation built on Aug. 13, 2024, 3:01 p.m.