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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd between version 1.1 and 1.8

version 1.1, 2013/02/07 07:38:23 version 1.8, 2022/04/07 00:56:44
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 % $OpenXM$  % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.7 2019/11/16 11:03:44 takayama Exp $
 \name{hgm.so3nc}  \name{hgm.ncso3}
 \alias{hgm.so3nc}  \alias{hgm.ncso3}
 %- Also NEED an '\alias' for EACH other topic documented here.  %- Also NEED an '\alias' for EACH other topic documented here.
 \title{  \title{
     The function hgm.so3nc evaluates the normalization constant for the Fisher      The function hgm.ncso3 evaluates the normalization constant for the Fisher
   distribution on SO(3).    distribution on SO(3).
 }  }
 \description{  \description{
     The function hgm.so3nc evaluates the normalization constant for the Fisher      The function hgm.ncso3 evaluates the normalization constant for the Fisher
   distribution on SO(3).    distribution on SO(3).
 }  }
 \usage{  \usage{
 hgm.so3nc(x,y,z,t0=0.0,q=0,deg=0)  hgm.ncso3(a,b,c,t0=0.0,q=1,deg=0,log=0)
 }  }
 %- maybe also 'usage' for other objects documented here.  %- maybe also 'usage' for other objects documented here.
 \arguments{  \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}{    \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.
   }    }
     \item{log}{
        If it is 1, then the function returns the log of the normalizing constant.
     }
 }  }
 \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 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{  \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  Journal of Multivariate Analysis, 116 (2013), 440--455,
   \doi{10.1016/j.jmva.2013.01.010}
 }  }
 \author{  \author{
 Nobuki Takayama  Nobuki Takayama
 }  }
 \note{  %\note{
 %%  ~~further notes~~  %%%  ~~further notes~~
 }  %}
   
 %% ~Make other sections like Warning with \section{Warning }{....} ~  %% ~Make other sections like Warning with \section{Warning }{....} ~
   
 \seealso{  %\seealso{
 %%\code{\link{oxm.matrix_r2tfb}}  %%%\code{\link{oxm.matrix_r2tfb}}
 }  %}
 \examples{  \examples{
 ## =====================================================  ## =====================================================
 ## 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.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  % 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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