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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd between version 1.1 and 1.2

version 1.1, 2013/02/07 07:38:23 version 1.2, 2013/02/08 01:27:01
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 % $OpenXM$  % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.1 2013/02/07 07:38:23 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=0,deg=0)
 }  }
 %- maybe also 'usage' for other objects documented here.  %- maybe also 'usage' for other objects documented here.
 \arguments{  \arguments{
     \item{a}{}
     \item{b}{}
     \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}{    \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)
Line 32  hgm.so3nc(x,y,z,t0=0.0,q=0,deg=0)
   }    }
   \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)
     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.    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  
 %  \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}  
   
 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},
   to appear in Journal of Multivariate Analysis.
 }  }
 \author{  \author{
 Nobuki Takayama  Nobuki Takayama
Line 62  Nobuki Takayama
Line 73  Nobuki Takayama
 ## 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)
   
   ## =====================================================
   ## Example 2. Asteroid data in the paper
   ## =====================================================
   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 }
   \keyword{ HGM }
   \keyword{ Fisher distribution on SO(3)}
   
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