% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.2 2013/03/01 05:27:08 takayama Exp $
\name{hgm.cwishart}
\alias{hgm.cwishart}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{
    The function hgm.cwishart evaluates the cumulative distribution function
  of random wishart matrix.
}
\description{
    The function hgm.cwishart evaluates the cumulative distribution function
  of random wishart matrix of size m times m.
}
\usage{
hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{m}{The dimension of the Wishart matrix.}
  \item{n}{The degree of freedome (a parameter of the Wishart distribution)}
  \item{beta}{The eigenvalues of the inverse of the covariant matrix
(a parameter of the Wishart distribution)
  }
  \item{x0}{The point to evaluate the matrix hypergeometric series. x0>0}
  \item{approxdeg}{
    Zonal polynomials upto the approxdeg are calculated to evaluate
   values near the origin. A zonal polynomial is determined by a given
   partition (k1,...,km). We call the sum k1+...+km the degree.
  }
  \item{h}{
   A (small) step size for the Runge-Kutta method. h>0.
  }
  \item{dp}{
    Sampling interval of solutions by the Runge-Kutta method.
  }
  \item{x}{
    The first value of this function is the Prob(L1 < x)
    where L1 is the first eigenvalue of the Wishart matrix.
  }
}
\details{
  It is evaluated by the Koev-Edelman algorithm when x is near the origin and
  by the HGM when x is far from the origin.
  We can obtain more accurate result when the variables h, x0 are smaller
  and the approxdeg is more larger.
%  \code{\link[RCurl]{postForm}}.
}
\value{
The output is x, y[0], ..., y[2^m],  
y[0] is the value of the cumulative distribution
function P(L1 < x) at x.  y[1],...,y[2^m] are some derivatives.
See the reference below.
}
\references{
H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura,
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
\url{http://arxiv.org/abs/1201.0472},
}
\author{
Nobuki Takayama
}
\note{
%%  ~~further notes~~
}

%% ~Make other sections like Warning with \section{Warning }{....} ~

\seealso{
%%\code{\link{oxm.matrix_r2tfb}}
}
\examples{
## =====================================================
## Example 1. Computing normalization constant of the Fisher distribution on SO(3)
## =====================================================
hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10)

}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{ Cumulative distribution function of random wishart matrix }
\keyword{ Holonomic gradient method }
\keyword{ HGM }