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Annotation of OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd, Revision 1.3

1.3     ! takayama    1: % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.2 2013/02/08 01:27:01 takayama Exp $
1.1       takayama    2: \name{hgm.so3nc}
                      3: \alias{hgm.so3nc}
                      4: %- Also NEED an '\alias' for EACH other topic documented here.
                      5: \title{
                      6:     The function hgm.so3nc evaluates the normalization constant for the Fisher
                      7:   distribution on SO(3).
                      8: }
                      9: \description{
                     10:     The function hgm.so3nc evaluates the normalization constant for the Fisher
                     11:   distribution on SO(3).
                     12: }
                     13: \usage{
1.3     ! takayama   14: hgm.so3nc(a,b,c,t0=0.0,q=1,deg=0)
1.1       takayama   15: }
                     16: %- maybe also 'usage' for other objects documented here.
                     17: \arguments{
1.2       takayama   18:   \item{a}{}
                     19:   \item{b}{}
                     20:   \item{c}{
                     21:      This function evaluates the normalization constant for the parameter
                     22:      Theta=diag(theta_{ii}) of the Fisher distribution on SO(3).
                     23:      The variables a,b,c stand for the parameters
                     24:      theta_{11}, theta_{22}, theta_{33} respectively.
                     25:   }
1.1       takayama   26:   \item{t0}{
                     27:      It is the initial point to evaluate the series. If it is set to 0.0,
                     28:      a default value is used.
                     29:   }
                     30:   \item{q}{
                     31:      If it is 1, then the program works in a quiet mode.
                     32:   }
                     33:   \item{deg}{
                     34:      It gives the approximation degree of the power series approximation
1.2       takayama   35:      of the normalization constant near the origin.
1.1       takayama   36:      If it is 0, a default value is used.
                     37:   }
                     38: }
                     39: \details{
1.2       takayama   40:   The normalization constant c(Theta)
                     41:   of the Fisher distribution on SO(3) is defined  by
                     42:   integral( exp(trace( transpose(Theta) X)) )
                     43:   where X is the integration variable and runs over S0(3) and
                     44:   Theta is a 3 x 3 matrix parameter.
                     45:   A general HGM algorithm to evaluate the normalization constant
1.1       takayama   46:   is given in the reference below.
1.2       takayama   47:   We use the Corollary 1 and the series expansion in 3.2 for the evaluation.
1.1       takayama   48: %  \code{\link[RCurl]{postForm}}.
                     49: }
                     50: \value{
1.2       takayama   51: The output is c(Theta).
1.1       takayama   52: }
                     53: \references{
                     54: Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
                     55: Properties and applications of Fisher distribution on the rotation group,
1.2       takayama   56: \url{http://arxiv.org/abs/1110.0721},
                     57: to appear in Journal of Multivariate Analysis.
1.1       takayama   58: }
                     59: \author{
                     60: Nobuki Takayama
                     61: }
                     62: \note{
                     63: %%  ~~further notes~~
                     64: }
                     65:
                     66: %% ~Make other sections like Warning with \section{Warning }{....} ~
                     67:
                     68: \seealso{
                     69: %%\code{\link{oxm.matrix_r2tfb}}
                     70: }
                     71: \examples{
                     72: ## =====================================================
                     73: ## Example 1. Computing normalization constant of the Fisher distribution on SO(3)
                     74: ## =====================================================
                     75: hgm.so3nc(1,2,3)
1.2       takayama   76:
                     77: ## =====================================================
                     78: ## Example 2. Asteroid data in the paper
                     79: ## =====================================================
                     80: hgm.so3nc(19.6,0.831,-0.671)
1.1       takayama   81: }
                     82: % Add one or more standard keywords, see file 'KEYWORDS' in the
                     83: % R documentation directory.
                     84: \keyword{ Normalization constant }
                     85: \keyword{ Holonomic gradient method }
1.2       takayama   86: \keyword{ HGM }
                     87: \keyword{ Fisher distribution on SO(3)}
1.1       takayama   88: