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Annotation of OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd, Revision 1.2

1.2     ! takayama    1: % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.1 2013/02/23 07:00:21 takayama Exp $
1.1       takayama    2: \name{hgm.cwishart}
                      3: \alias{hgm.cwishart}
                      4: %- Also NEED an '\alias' for EACH other topic documented here.
                      5: \title{
                      6:     The function hgm.cwishart evaluates the cumulative distribution function
                      7:   of random wishart matrix.
                      8: }
                      9: \description{
                     10:     The function hgm.cwishart evaluates the cumulative distribution function
                     11:   of random wishart matrix of size m times m.
                     12: }
                     13: \usage{
                     14: hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
                     15: }
                     16: %- maybe also 'usage' for other objects documented here.
                     17: \arguments{
1.2     ! takayama   18:   \item{m}{The dimension of the Wishart matrix.}
        !            19:   \item{n}{The degree of freedome (a parameter of the Wishart distribution)}
        !            20:   \item{beta}{The eigenvalues of the inverse of the covariant matrix
        !            21: (a parameter of the Wishart distribution)
1.1       takayama   22:   }
1.2     ! takayama   23:   \item{x0}{The point to evaluate the matrix hypergeometric series. x0>0}
1.1       takayama   24:   \item{approxdeg}{
1.2     ! takayama   25:     Zonal polynomials upto the approxdeg are calculated to evaluate
        !            26:    values near the origin. A zonal polynomial is determined by a given
        !            27:    partition (k1,...,km). We call the sum k1+...+km the degree.
1.1       takayama   28:   }
                     29:   \item{h}{
1.2     ! takayama   30:    A (small) step size for the Runge-Kutta method. h>0.
1.1       takayama   31:   }
                     32:   \item{dp}{
1.2     ! takayama   33:     Sampling interval of solutions by the Runge-Kutta method.
        !            34:   }
        !            35:   \item{x}{
        !            36:     The first value of this function is the Prob(L1 < x)
        !            37:     where L1 is the first eigenvalue of the Wishart matrix.
1.1       takayama   38:   }
                     39: }
                     40: \details{
1.2     ! takayama   41:   It is evaluated by the Koev-Edelman algorithm when x is near the origin and
        !            42:   by the HGM when x is far from the origin.
        !            43:   We can obtain more accurate result when the variables h, x0 are smaller
        !            44:   and the approxdeg is more larger.
1.1       takayama   45: %  \code{\link[RCurl]{postForm}}.
                     46: }
                     47: \value{
1.2     ! takayama   48: The output is x, y[0], ..., y[2^m],
        !            49: y[0] is the value of the cumulative distribution
        !            50: function P(L1 < x) at x.  y[1],...,y[2^m] are some derivatives.
        !            51: See the reference below.
1.1       takayama   52: }
                     53: \references{
1.2     ! takayama   54: H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura,
        !            55: Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
        !            56: \url{http://arxiv.org/abs/1201.0472},
1.1       takayama   57: }
                     58: \author{
                     59: Nobuki Takayama
                     60: }
                     61: \note{
                     62: %%  ~~further notes~~
                     63: }
                     64:
                     65: %% ~Make other sections like Warning with \section{Warning }{....} ~
                     66:
                     67: \seealso{
                     68: %%\code{\link{oxm.matrix_r2tfb}}
                     69: }
                     70: \examples{
                     71: ## =====================================================
                     72: ## Example 1. Computing normalization constant of the Fisher distribution on SO(3)
                     73: ## =====================================================
                     74: hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10)
                     75:
                     76: }
                     77: % Add one or more standard keywords, see file 'KEYWORDS' in the
                     78: % R documentation directory.
                     79: \keyword{ Cumulative distribution function of random wishart matrix }
                     80: \keyword{ Holonomic gradient method }
                     81: \keyword{ HGM }
                     82: