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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{vech2full}
\alias{vech2full}
\title{Inverse Half-vectorization}
\description{
This function returns the symmetric matrix constructed from a half-vectorization.
}
\usage{
vech2full(x)
}
\arguments{
\item{x}{an input single column or single row matrix.}
}
\details{
The half-vectorization of an input matrix consists of the elements in the lower triangle of the matrix, including the elements along the diagonal of the matrix, as a column vector. The column vector is created by traversing the matrix in column-major order. The inverse half-vectorization takes a vector and reconstructs a symmetric matrix such that \code{vech2full(vech(x))} is identical to \code{x} if \code{x} is symmetric.
Note that very few vectors have the correct number of elements to construct a symmetric matrix. For example, vectors with 1, 3, 6, 10, and 15 elements can be used to make a symmetric matrix, but none of the other numbers between 1 and 15 can. An error is thrown if the number of elements in \code{x} cannot be used to make a symmetric matrix.
}
\seealso{
\code{\link{vechs2full}}, \code{\link{vech}}, \code{\link{vechs}}, \code{\link{rvectorize}}, \code{\link{cvectorize}}
}
\examples{
vech2full(1:10)
matrix(1:16, 4, 4)
vech(matrix(1:16, 4, 4))
vech2full(vech(matrix(1:16, 4, 4)))
}
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