isSymmetric Test if a Matrix or other Object is Symmetric (Hermitian)

Description

Generic function to test if object is symmetric or not. Currently only a matrix method is implemented, where a complex matrix Z must be “Hermitian” for isSymmetric(Z) to be true.

Usage

isSymmetric(object, ...)
## S3 method for class 'matrix'
isSymmetric(object, tol = 100 * .Machine$double.eps,
            tol1 = 8 * tol, ...)

Arguments

object	any R object; a matrix for the matrix method.
tol	numeric scalar >= 0. Smaller differences are not considered, see all.equal.numeric.
tol1	numeric scalar >= 0. isSymmetric.matrix() ‘pre-tests’ the first and last few rows for fast detection of ‘obviously’ asymmetric cases with this tolerance. Setting it to length zero will skip the pre-tests.
...	further arguments passed to methods; the matrix method passes these to all.equal. If the row and column names of object are allowed to differ for the symmetry check do use check.attributes = FALSE!

Details

The matrix method is used inside eigen by default to test symmetry of matrices up to rounding error, using all.equal. It might not be appropriate in all situations.

Note that a matrix m is only symmetric if its rownames and colnames are identical. Consider using unname(m).

Value

logical indicating if object is symmetric or not.

See Also

eigen which calls isSymmetric when its symmetric argument is missing.

Examples

isSymmetric(D3 <- diag(3)) # -> TRUE

D3[2, 1] <- 1e-100
D3
isSymmetric(D3) # TRUE
isSymmetric(D3, tol = 0) # FALSE for zero-tolerance

## Complex Matrices - Hermitian or not
Z <- sqrt(matrix(-1:2 + 0i, 2)); Z <- t(Conj(Z)) %*% Z
Z
isSymmetric(Z)      # TRUE
isSymmetric(Z + 1)  # TRUE
isSymmetric(Z + 1i) # FALSE -- a Hermitian matrix has a *real* diagonal

colnames(D3) <- c("X", "Y", "Z")
isSymmetric(D3)                         # FALSE (as row and column names differ)
isSymmetric(D3, check.attributes=FALSE) # TRUE  (as names are not checked)