version 1.2, 2013/03/01 05:27:08 |
version 1.3, 2013/03/08 07:32:28 |
|
|
% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.1 2013/02/23 07:00:21 takayama Exp $ |
% $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} |
\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. |
|
|
of random wishart matrix of size m times m. |
of random wishart matrix of size m times m. |
} |
} |
\usage{ |
\usage{ |
hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x) |
hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,err) |
} |
} |
%- maybe also 'usage' for other objects documented here. |
%- maybe also 'usage' for other objects documented here. |
\arguments{ |
\arguments{ |
\item{m}{The dimension of the Wishart matrix.} |
\item{m}{The dimension of the Wishart matrix.} |
\item{n}{The degree of freedome (a parameter of the Wishart distribution)} |
\item{n}{The degree of freedome (a parameter of the Wishart distribution)} |
\item{beta}{The eigenvalues of the inverse of the covariant matrix |
\item{beta}{The eigenvalues of the inverse of the covariant matrix /2 |
(a parameter of the Wishart distribution) |
(a parameter of the Wishart distribution). |
|
The beta is equal to inverse(sigma)/2. |
} |
} |
\item{x0}{The point to evaluate the matrix hypergeometric series. x0>0} |
\item{x0}{The point to evaluate the matrix hypergeometric series. x0>0} |
\item{approxdeg}{ |
\item{approxdeg}{ |
Line 33 hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x) |
|
Line 34 hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x) |
|
Sampling interval of solutions by the Runge-Kutta method. |
Sampling interval of solutions by the Runge-Kutta method. |
} |
} |
\item{x}{ |
\item{x}{ |
The first value of this function is the Prob(L1 < x) |
The second value y[0] of this function is the Prob(L1 < x) |
where L1 is the first eigenvalue of the Wishart matrix. |
where L1 is the first eigenvalue of the Wishart matrix. |
} |
} |
|
\item{mode}{ |
|
When mode=c(1,0,0), it returns the evaluation |
|
of the matrix hypergeometric series and its derivatives at x0. |
|
When mode=c(1,1,(m^2+1)*p), intermediate values of P(L1 < x) with respect to |
|
p-steps of x are also returned. Sampling interval is controled by dp. |
|
} |
|
\item{method}{ |
|
rk4 is the default value. |
|
When method="a-rk4", the adaptive Runge-Kutta method is used. |
|
Steps are automatically adjusted by err. |
|
} |
|
\item{err}{ |
|
When err=c(e1,e2), e1 is the absolute error and e2 is the relative error. |
|
As long as NaN is not returned, it is recommended to set to |
|
err=c(0.0, 1e-10), because initial values are usually very small. |
|
} |
} |
} |
\details{ |
\details{ |
It is evaluated by the Koev-Edelman algorithm when x is near the origin and |
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. |
by the HGM when x is far from the origin. |
We can obtain more accurate result when the variables h, x0 are smaller |
We can obtain more accurate result when the variables h is smaller, |
|
x0 is relevant value (not very big, not very small), |
and the approxdeg is more larger. |
and the approxdeg is more larger. |
|
A heuristic method to set parameters x0, h, approxdeg properly |
|
is to make x larger and to check if the y[0] approaches to 1. |
% \code{\link[RCurl]{postForm}}. |
% \code{\link[RCurl]{postForm}}. |
} |
} |
\value{ |
\value{ |
The output is x, y[0], ..., y[2^m], |
The output is x, y[0], ..., y[2^m] in the default mode, |
y[0] is the value of the cumulative distribution |
y[0] is the value of the cumulative distribution |
function P(L1 < x) at x. y[1],...,y[2^m] are some derivatives. |
function P(L1 < x) at x. y[1],...,y[2^m] are some derivatives. |
See the reference below. |
See the reference below. |
|
|
} |
} |
\examples{ |
\examples{ |
## ===================================================== |
## ===================================================== |
## Example 1. Computing normalization constant of the Fisher distribution on SO(3) |
## Example 1. |
## ===================================================== |
## ===================================================== |
hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10) |
hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10) |
|
## ===================================================== |
|
## Example 2. |
|
## ===================================================== |
|
b<-hgm.cwishart(m=4,n=10,beta=c(1,2,3,4),x0=1,x=10,approxdeg=20,mode=c(1,1,(16+1)*100)); |
|
c<-matrix(b,ncol=16+1,byrow=1); |
|
#plot(c) |
} |
} |
% Add one or more standard keywords, see file 'KEYWORDS' in the |
% Add one or more standard keywords, see file 'KEYWORDS' in the |
% R documentation directory. |
% R documentation directory. |