File: [local] / OpenXM / src / R / r-packages / hgm / man / hgm.so3nc.Rd (download)
Revision 1.7, Sat Nov 16 11:03:44 2019 UTC (4 years, 10 months ago) by takayama
Branch: MAIN
Changes since 1.6: +8 -5
lines
R package for the new hgm.ncso3(log=1) in the previous commit.
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% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.7 2019/11/16 11:03:44 takayama Exp $
\name{hgm.ncso3}
\alias{hgm.ncso3}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{
The function hgm.ncso3 evaluates the normalization constant for the Fisher
distribution on SO(3).
}
\description{
The function hgm.ncso3 evaluates the normalization constant for the Fisher
distribution on SO(3).
}
\usage{
hgm.ncso3(a,b,c,t0=0.0,q=1,deg=0,log=0)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{a}{See the description of c.}
\item{b}{See the description of c.}
\item{c}{
This function evaluates the normalization constant for the parameter
Theta=diag(theta_{ii}) of the Fisher distribution on SO(3).
The variables a,b,c stand for the parameters
theta_{11}, theta_{22}, theta_{33} respectively.
}
\item{t0}{
It is the initial point to evaluate the series. If it is set to 0.0,
a default value is used.
}
\item{q}{
If it is 1, then the program works in a quiet mode.
}
\item{deg}{
It gives the approximation degree of the power series approximation
of the normalization constant near the origin.
If it is 0, a default value is used.
}
\item{log}{
If it is 1, then the function returns the log of the normalizing constant.
}
}
\details{
The normalization constant c(Theta)
of the Fisher distribution on SO(3) is defined by
integral( exp(trace( transpose(Theta) X)) )
where X is the integration variable and runs over S0(3) and
Theta is a 3 x 3 matrix parameter.
A general HGM algorithm to evaluate the normalization constant
is given in the reference below.
We use the Corollary 1 and the series expansion in 3.2 for the evaluation.
% \code{\link[RCurl]{postForm}}.
}
\value{
The output is an array of c(Theta) and its derivatives with respect to Theta_{11},Theta_{22},Theta_{33}. It is the vector C of the reference below. When log=1, the output is an array of log of them.
}
\references{
Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
Properties and applications of Fisher distribution on the rotation group,
Journal of Multivariate Analysis, 116 (2013), 440--455,
\url{http://dx.doi.org/10.1016/j.jmva.2013.01.010}
}
\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.ncso3(1,2,3)[1]
## =====================================================
## Example 2. Asteroid data in the paper
## =====================================================
hgm.ncso3(19.6,0.831,-0.671)[1]
}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{ Normalization constant }
\keyword{ Holonomic gradient method }
\keyword{ HGM }
\keyword{ Fisher distribution on SO(3)}