version 1.1, 2013/02/23 07:00:21 |
version 1.2, 2013/03/01 05:27:08 |
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% $OpenXM$ |
% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.1 2013/02/23 07:00:21 takayama Exp $ |
\name{hgm.cwishart} |
\name{hgm.cwishart} |
\alias{hgm.cwishart} |
\alias{hgm.cwishart} |
%- Also NEED an '\alias' for EACH other topic documented here. |
%- Also NEED an '\alias' for EACH other topic documented here. |
Line 15 hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x) |
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Line 15 hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x) |
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} |
} |
%- maybe also 'usage' for other objects documented here. |
%- maybe also 'usage' for other objects documented here. |
\arguments{ |
\arguments{ |
\item{m}{} |
\item{m}{The dimension of the Wishart matrix.} |
\item{n}{} |
\item{n}{The degree of freedome (a parameter of the Wishart distribution)} |
\item{beta}{ |
\item{beta}{The eigenvalues of the inverse of the covariant matrix |
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(a parameter of the Wishart distribution) |
} |
} |
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\item{x0}{The point to evaluate the matrix hypergeometric series. x0>0} |
\item{approxdeg}{ |
\item{approxdeg}{ |
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Zonal polynomials upto the approxdeg are calculated to evaluate |
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values near the origin. A zonal polynomial is determined by a given |
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partition (k1,...,km). We call the sum k1+...+km the degree. |
} |
} |
\item{h}{ |
\item{h}{ |
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A (small) step size for the Runge-Kutta method. h>0. |
} |
} |
\item{dp}{ |
\item{dp}{ |
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Sampling interval of solutions by the Runge-Kutta method. |
} |
} |
\item{x}{} |
\item{x}{ |
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The first value of this function is the Prob(L1 < x) |
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where L1 is the first eigenvalue of the Wishart matrix. |
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} |
} |
} |
\details{ |
\details{ |
It is evaluated by the Koev-Edelman algorithm near the origin and |
It is evaluated by the Koev-Edelman algorithm when x is near the origin and |
and by the HGM when x is far from the origin. |
by the HGM when x is far from the origin. |
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We can obtain more accurate result when the variables h, x0 are smaller |
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and the approxdeg is more larger. |
% \code{\link[RCurl]{postForm}}. |
% \code{\link[RCurl]{postForm}}. |
} |
} |
\value{ |
\value{ |
The output is x, y[0], ..., y[0] is the value of the cumulative distribution |
The output is x, y[0], ..., y[2^m], |
function at x. y[1],... are some derivatives. |
y[0] is the value of the cumulative distribution |
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function P(L1 < x) at x. y[1],...,y[2^m] are some derivatives. |
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See the reference below. |
} |
} |
\references{ |
\references{ |
HNTT, |
H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura, |
\url{http://arxiv.org/abs/??}, |
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix |
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\url{http://arxiv.org/abs/1201.0472}, |
} |
} |
\author{ |
\author{ |
Nobuki Takayama |
Nobuki Takayama |