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\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)))



}
