\name{TimelessNormalParam}
\alias{TimelessNormalParam}
\alias{getmu}
\alias{getSigma}
\alias{getiSigma}
\alias{is.pd}
\title{Parameter for the TimelessNormalPM
}
\description{

  The \code{\link{TimelessNormalPM}} is a proficiency model for a single
  time point where the proficiency itself is considered multidimesional.
  The parameter consists of a mean vector (\code{mu}) and a covariance
  matrix (\code{Sigma}).
}
\usage{
TimelessNormalParam(mu=numeric(),Sigma=matrix(),is.pd=is.pdm(Sigma),
                   iSig=solve(Sigma))
getmu(param)
getmu(param) <- m
getSigma(param)
getSigma(param) <- S
getiSigma(param)
}
\arguments{
  \item{mu}{
    A mean vector for a multivate normal distribuiton.  This should have
    conformable dimensions with the \code{Sigma} argument.
  }
  \item{Sigma}{
    A square covariance matrix. The number of rows and columns should
    equal the length of \code{mu}.  Although \code{Sigma} should
    normally be positive definite, the various functions using this
    class should fail gracefully if that is not true.
  }
  \item{is.pd}{A logical value, whether or not \code{Sigma} is posivite
    definite. This could be the case if say, a Newton-type optimizer took
    a step outside of the legal values for a covariance matrix.  The
    default value runs the function \code{\link{is.pd}} to check, so
    this should be fine.}
  \item{iSig}{If supplied, this should be then inverse of \code{Sigma}
    (if Sigma is positive definite). Note that if \code{iSig} and not
    \code{Sigma} is not supplied, then \code{Sigma} will be calculated
    by inverting \code{iSig}.}
  \item{param}{
    A \code{TimelessNormalParam} object whose paramers are desired.
  }
  \item{m}{
    A mean vector for a multivate normal distribuiton.  This should have
    conformable dimensions with the \code{Sigma} argument.
  }
  \item{S}{
    A square covariance matrix. The number of rows and columns should
    equal the length of \code{mu}.  Although \code{Sigma} should
    normally be positive definite, the various functions using this
    class should fail gracefully if that is not true.
  }

}
\details{

  This class is the parameter object corresponding to the
  \code{\link{TimelessNormalPM}} object.  The slot \code{mu} contains
  the mean vector and the slot \code{Sigma} contains the covariance
  matrix.  Note that many routines use the precision matrix (inverse
  variance matrix) so this is cached as \code{iSig}.

  It is possible when using the various optimization algorithms and the
  \code{\link{pvec}()} function, that a covariance matrix will be
  modified in such a way that it is no longer positive definite.  The
  flag \code{is.pd} is used to test for this case.  Functions using this
  class should always test this flag before using the parameter object.

  The constructor function as well as the setter method
  \code{getSigma(param) <- S} (and the \code{pvec(param)} setter)
  automatically check the positive definite flag and calculate the
  inverse the matrix is positive definite.
  
  
}
\value{

  A \code{TimelessNormalParam} object with slots:
  \item{mu}{Mean vector}
  \item{Sigma}{Covariance matrix}.
  \item{is.pd}{A logical flag which indicates whether the covariance matrix
    is positive definite.}
  \item{iSig}{Precision (inverse covariance) matrix.  Note that if the
    covariance matrix is not positive definite, this may return
    \code{matrix(NA)}.}

  The functions \code{getmu}, \code{getSigma}, \code{is.pd} and
  \code{getiSigma} return the value of the corresponding slots.
}
\references{
%% ~put references to the literature/web site here ~
}
\author{Russell Almond}

\seealso{
  Superclass:
  \code{\link{ParameterObject}}
  
  Subclasses:
  \code{\link{TimeInvariantNormalParam}}
  
  Used By:
  \code{\link{TimelessNormalPM}}
}
\examples{

p1 <- TimelessNormalParam(mu=c(Mechanics=2,Fluencey=2),
          Sigma=matrix(c(.7,.3,.3,.7),2,2))
stopifnot(is.pd(p1))
getmu(p1)
getSigma(p1)
stopifnot(all(abs(getiSigma(p1)-solve(getSigma(p1))) < sqrt(.Machine$double.eps)))

pvec(p1)
pvec(p1)[2]<-3
stopifnot(all(abs(getmu(p1)-c(2,3)) < sqrt(.Machine$double.eps)))

## Setting off-diagonal element of covariance matrix
pvec(p1)[5]<-.5
stopifnot(all(abs(as.vector(getSigma(p1)) - c(.7,.5,.5,.7)) <
              sqrt(.Machine$double.eps)))

## Supplying precision matrix rather than covariance
p2 <- TimelessNormalParam(mu=c(Mechanics=2,Fluencey=3),
      iSig = getiSigma(p1))
stopifnot(all(abs(getSigma(p1)-getSigma(p2)) < sqrt(.Machine$double.eps)))

## Test of making a singular matrix.
pvec(p2)[5] <- pvec(p2)[4]
stopifnot(!is.pd(p2))
print("This next command should generate a singular matrix error.")
stopifnot(class(try(getiSigma(p2))=="try-error"))

}
\keyword{ class }