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
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 ofobject
are 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)
# }