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% File src/library/base/man/isSymmetric.Rd
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% File src/library/base/man/isSymmetric.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{isSymmetric}
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\name{isSymmetric}
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\alias{isSymmetric}
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\alias{isSymmetric}
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\alias{isSymmetric.matrix}
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\alias{isSymmetric.matrix}
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\title{Test if a Matrix or other Object is Symmetric (Hermitian)}
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\title{Test if a Matrix or other Object is Symmetric (Hermitian)}
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\description{
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\description{
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Generic function to test if \code{object} is symmetric or not.
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Generic function to test if \code{object} is symmetric or not.
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Currently only a matrix method is implemented, where a
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Currently only a matrix method is implemented, where a
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\code{\link{complex}} matrix \code{Z} must be \dQuote{Hermitian} for
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\code{\link{complex}} matrix \code{Z} must be \dQuote{Hermitian} for
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\code{isSymmetric(Z)} to be true.
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\code{isSymmetric(Z)} to be true, and
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(since \R >= 4.5.0),
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\code{isSymmetric(Z, trans = "T")} checks for \dQuote{simple} symmetry.
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}
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}
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\usage{
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\usage{
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isSymmetric(object, \dots)
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isSymmetric(object, \dots)
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\method{isSymmetric}{matrix}(object, tol = 100 * .Machine$double.eps,
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\method{isSymmetric}{matrix}(object, tol = 100 * .Machine$double.eps,
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tol1 = 8 * tol, \dots)
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tol1 = 8 * tol, trans = "C", \dots)
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}
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}
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\arguments{
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\arguments{
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\item{object}{any \R object; a \code{\link{matrix}} for the matrix method.}
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\item{object}{any \R object; a \code{\link{matrix}} for the matrix method.}
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\item{tol}{numeric scalar >= 0. Smaller differences are not
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\item{tol}{numeric scalar >= 0. Smaller differences are not
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considered, see \code{\link{all.equal.numeric}}.}
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considered, see \code{\link{all.equal.numeric}}.}
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\item{tol1}{numeric scalar >= 0. \code{isSymmetric.matrix()}
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\item{tol1}{numeric scalar >= 0. \code{isSymmetric.matrix()}
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\sQuote{pre-tests} the first and last few rows for fast detection of
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\sQuote{pre-tests} the first and last few rows for fast detection of
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\sQuote{obviously} asymmetric cases with this tolerance. Setting it
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\sQuote{obviously} asymmetric cases with this tolerance. Setting it
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to length zero will skip the pre-tests.}
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to length zero will skip the pre-tests.}
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\item{trans}{a single \code{\link{character}}, only relevant for a
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\code{\link{complex}} matrix \code{Z}: if it is \code{"C"} (as by
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default), \code{Conj(t(Z))} must be the same as \code{Z} whereas
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otherwise (typically it is \code{"T"}) \code{t(Z)} must equal
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\code{Z}. The argument name is inherited from LAPACK.}
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\item{\dots}{further arguments passed to methods; the matrix method
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\item{\dots}{further arguments passed to methods; the matrix method
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passes these to \code{\link{all.equal}}. If the row and column
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passes these to \code{\link{all.equal}}. If the row and column
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names of \code{object} are allowed to differ for the symmetry check
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names of \code{object} are allowed to differ for the symmetry check
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do use \code{check.attributes = FALSE}!}
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do use \code{check.attributes = FALSE}!}
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}
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}
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D3
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D3
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isSymmetric(D3) # TRUE
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isSymmetric(D3) # TRUE
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isSymmetric(D3, tol = 0) # FALSE for zero-tolerance
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isSymmetric(D3, tol = 0) # FALSE for zero-tolerance
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## Complex Matrices - Hermitian or not
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## Complex Matrices - Hermitian or not
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Z <- sqrt(matrix(-1:2 + 0i, 2)); Z <- t(Conj(Z)) \%*\% Z
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z <- sqrt(matrix(-1:2 + 0i, 2)); Z <- t(Conj(z)) \%*\% z
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ZtZ <- t(z) \%*\% z
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Z
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Z ; ZtZ
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isSymmetric(Z) # TRUE
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isSymmetric(Z) # TRUE
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isSymmetric(Z + 1) # TRUE
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isSymmetric(Z + 1) # TRUE
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isSymmetric(Z + 1i) # FALSE -- a Hermitian matrix has a *real* diagonal
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isSymmetric(Z + 1i) # FALSE -- a Hermitian matrix has a *real* diagonal
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colnames(D3) <- c("X", "Y", "Z")
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colnames(D3) <- c("X", "Y", "Z")
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