version 1.1, 2013/02/07 07:38:23 |
version 1.3, 2013/03/08 07:32:28 |
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% $OpenXM$ |
% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.2 2013/02/08 01:27:01 takayama Exp $ |
\name{hgm.so3nc} |
\name{hgm.so3nc} |
\alias{hgm.so3nc} |
\alias{hgm.so3nc} |
%- Also NEED an '\alias' for EACH other topic documented here. |
%- Also NEED an '\alias' for EACH other topic documented here. |
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distribution on SO(3). |
distribution on SO(3). |
} |
} |
\usage{ |
\usage{ |
hgm.so3nc(x,y,z,t0=0.0,q=0,deg=0) |
hgm.so3nc(a,b,c,t0=0.0,q=1,deg=0) |
} |
} |
%- maybe also 'usage' for other objects documented here. |
%- maybe also 'usage' for other objects documented here. |
\arguments{ |
\arguments{ |
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\item{a}{} |
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\item{b}{} |
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\item{c}{ |
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This function evaluates the normalization constant for the parameter |
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Theta=diag(theta_{ii}) of the Fisher distribution on SO(3). |
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The variables a,b,c stand for the parameters |
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theta_{11}, theta_{22}, theta_{33} respectively. |
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} |
\item{t0}{ |
\item{t0}{ |
It is the initial point to evaluate the series. If it is set to 0.0, |
It is the initial point to evaluate the series. If it is set to 0.0, |
a default value is used. |
a default value is used. |
Line 24 hgm.so3nc(x,y,z,t0=0.0,q=0,deg=0) |
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Line 32 hgm.so3nc(x,y,z,t0=0.0,q=0,deg=0) |
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} |
} |
\item{deg}{ |
\item{deg}{ |
It gives the approximation degree of the power series approximation |
It gives the approximation degree of the power series approximation |
of the normalization constant. |
of the normalization constant near the origin. |
If it is 0, a default value is used. |
If it is 0, a default value is used. |
} |
} |
} |
} |
\details{ |
\details{ |
A general algorithm to obtain the normalization constant |
The normalization constant c(Theta) |
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of the Fisher distribution on SO(3) is defined by |
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integral( exp(trace( transpose(Theta) X)) ) |
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where X is the integration variable and runs over S0(3) and |
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Theta is a 3 x 3 matrix parameter. |
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A general HGM algorithm to evaluate the normalization constant |
is given in the reference below. |
is given in the reference below. |
% please refer to \url{http://www.openxm.org.} |
We use the Corollary 1 and the series expansion in 3.2 for the evaluation. |
% The function utilizes \code{\link{oxm.matrix_r2tfb}} and |
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% \code{\link[RCurl]{postForm}}. |
% \code{\link[RCurl]{postForm}}. |
} |
} |
\value{ |
\value{ |
The output is double. |
The output is c(Theta). |
} |
} |
\references{ |
\references{ |
\url{http://arxiv.org/abs/1110.0721} |
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Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama, |
Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama, |
Properties and applications of Fisher distribution on the rotation group, |
Properties and applications of Fisher distribution on the rotation group, |
arxiv:1110.0721 |
\url{http://arxiv.org/abs/1110.0721}, |
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to appear in Journal of Multivariate Analysis. |
} |
} |
\author{ |
\author{ |
Nobuki Takayama |
Nobuki Takayama |
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## Example 1. Computing normalization constant of the Fisher distribution on SO(3) |
## Example 1. Computing normalization constant of the Fisher distribution on SO(3) |
## ===================================================== |
## ===================================================== |
hgm.so3nc(1,2,3) |
hgm.so3nc(1,2,3) |
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## ===================================================== |
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## Example 2. Asteroid data in the paper |
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## ===================================================== |
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hgm.so3nc(19.6,0.831,-0.671) |
} |
} |
% 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. |
\keyword{ Normalization constant } |
\keyword{ Normalization constant } |
\keyword{ Holonomic gradient method } |
\keyword{ Holonomic gradient method } |
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\keyword{ HGM } |
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\keyword{ Fisher distribution on SO(3)} |
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