\HeaderA{pdLogChol}{General Positive-Definite Matrix}{pdLogChol}
\keyword{models}{pdLogChol}
\begin{Description}\relax
This function is a constructor for the \code{pdLogChol} class,
representing a general positive-definite matrix. If the matrix
associated with \code{object} is of dimension \eqn{n}{}, it is
represented by \eqn{n(n+1)/2}{n*(n+1)/2} unrestricted parameters,
using the log-Cholesky parametrization described in Pinheiro and
Bates (1996). When \code{value} is \code{numeric(0)}, an uninitialized
\code{pdMat} object, a one-sided
formula, or a vector of character strings, \code{object} is returned
as an uninitialized \code{pdLogChol} object (with just some of its
attributes and its class defined) and needs to have its coefficients
assigned later, generally using the \code{coef} or \code{matrix} replacement
functions. If \code{value} is an initialized \code{pdMat} object,
\code{object} will be constructed from
\code{as.matrix(value)}. Finally, if \code{value} is a numeric vector,
it is assumed to represent the unrestricted coefficients of the
matrix-logarithm parametrization of the underlying positive-definite
matrix.
\end{Description}
\begin{Usage}
\begin{verbatim}
pdLogChol(value, form, nam, data)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{value}] an optional initialization value, which can be any of the
following: a \code{pdMat} object, a positive-definite
matrix, a one-sided linear formula (with variables separated by
\code{+}), a vector of character strings, or a numeric
vector. Defaults to \code{numeric(0)}, corresponding to an
uninitialized object.
\item[\code{form}] an optional one-sided linear formula specifying the
row/column names for the matrix represented by \code{object}. Because
factors may be present in \code{form}, the formula needs to be
evaluated on a data.frame to resolve the names it defines. This
argument is ignored when \code{value} is a one-sided
formula. Defaults to \code{NULL}.
\item[\code{nam}] an optional vector of character strings specifying the
row/column names for the matrix represented by object. It must have 
length equal to the dimension of the underlying positive-definite
matrix and unreplicated elements. This argument is ignored when
\code{value} is a vector of character strings. Defaults to
\code{NULL}.
\item[\code{data}] an optional data frame in which to evaluate the variables
named in \code{value} and \code{form}. It is used to
obtain the levels for \code{factors}, which affect the
dimensions and the row/column names of the underlying matrix. If
\code{NULL}, no attempt is made to obtain information on 
\code{factors} appearing in the formulas. Defaults to the
parent frame from which the function was called.
\end{ldescription}
\end{Arguments}
\begin{Value}
a \code{pdLogChol} object representing a general positive-definite
matrix, also inheriting from class \code{pdMat}.
\end{Value}
\begin{Author}\relax
Jose Pinheiro \email{Jose.Pinheiro@pharma.novartis.com} and Douglas Bates \email{bates@stat.wisc.edu}
\end{Author}
\begin{References}\relax
Pinheiro, J.C. and Bates., D.M.  (1996) "Unconstrained
Parametrizations for Variance-Covariance Matrices", Statistics and
Computing, 6, 289-296.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models
in S and S-PLUS", Springer.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{as.matrix.pdMat}{as.matrix.pdMat}},
\code{\LinkA{coef.pdMat}{coef.pdMat}},
\code{\LinkA{pdClasses}{pdClasses}},
\code{\LinkA{matrix<\Rdash.pdMat}{matrix<.Rdash..pdMat}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
pd1 <- pdLogChol(diag(1:3), nam = c("A","B","C"))
pd1
\end{ExampleCode}
\end{Examples}

