isSymmetric
Test if a Matrix or other Object is Symmetric (Hermitian)
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 matrix
isSymmetric(object, tol = 100 * .Machine$double.eps,
tol1 = 8 * tol, …)Arguments
- object
any R object; a
matrixfor 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 ofobjectare allowed to differ for the symmetry check do usecheck.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
library(base)
# NOT RUN {
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)
# }