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%
% Copyright 2007-2018 by the individuals mentioned in the source code history
%
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License.
% You may obtain a copy of the License at
%
% http://www.apache.org/licenses/LICENSE-2.0
%
% Unless required by applicable law or agreed to in writing, software
% distributed under the License is distributed on an "AS IS" BASIS,
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
% See the License for the specific language governing permissions and
% limitations under the License.
\name{eigenvec}
\alias{eigenval}
\alias{eigenvec}
\alias{ieigenval}
\alias{ieigenvec}
\title{Eigenvector/Eigenvalue Decomposition}
\description{
\code{eigenval} computes the real parts of the eigenvalues of a square matrix.
\code{eigenvec} computes the real parts of the eigenvectors of a square matrix.
\code{ieigenval} computes the imaginary parts of the eigenvalues of a square matrix.
\code{ieigenvec} computes the imaginary parts of the eigenvectors of a square matrix.
\code{eigenval} and \code{ieigenval} return nx1 matrices containing the real or imaginary parts of the eigenvalues, sorted in decreasing order of the modulus of the complex eigenvalue. For eigenvalues without an imaginary part, this is equivalent to sorting in decreasing order of the absolute value of the eigenvalue. (See \code{\link{Mod}} for more info.)
\code{eigenvec} and \code{ieigenvec} return nxn matrices, where each column corresponds to an eigenvector. These are sorted in decreasing order of the modulus of their associated complex eigenvalue.
}
\usage{
eigenval(x)
eigenvec(x)
ieigenval(x)
ieigenvec(x)
}
\arguments{
\item{x}{the square matrix whose eigenvalues/vectors are to be calculated.}
}
\details{
Eigenvectors returned by \code{eigenvec} and \code{ieigenvec} are normalized to unit length.
}
\seealso{
\code{\link{eigen}}
}
\examples{
A <- mxMatrix(values = runif(25), nrow = 5, ncol = 5, name = 'A')
G <- mxMatrix(values = c(0, -1, 1, -1), nrow=2, ncol=2, name='G')
model <- mxModel(A, G, name = 'model')
mxEval(eigenvec(A), model)
mxEval(eigenvec(G), model)
mxEval(eigenval(A), model)
mxEval(eigenval(G), model)
mxEval(ieigenvec(A), model)
mxEval(ieigenvec(G), model)
mxEval(ieigenval(A), model)
mxEval(ieigenval(G), model)
}
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