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Annotation of OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd, Revision 1.8

1.8     ! takayama    1: % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.so3nc.Rd,v 1.7 2019/11/16 11:03:44 takayama Exp $
1.4       takayama    2: \name{hgm.ncso3}
                      3: \alias{hgm.ncso3}
1.1       takayama    4: %- Also NEED an '\alias' for EACH other topic documented here.
                      5: \title{
1.4       takayama    6:     The function hgm.ncso3 evaluates the normalization constant for the Fisher
1.1       takayama    7:   distribution on SO(3).
                      8: }
                      9: \description{
1.4       takayama   10:     The function hgm.ncso3 evaluates the normalization constant for the Fisher
1.1       takayama   11:   distribution on SO(3).
                     12: }
                     13: \usage{
1.7       takayama   14: hgm.ncso3(a,b,c,t0=0.0,q=1,deg=0,log=0)
1.1       takayama   15: }
                     16: %- maybe also 'usage' for other objects documented here.
                     17: \arguments{
1.5       takayama   18:   \item{a}{See the description of c.}
                     19:   \item{b}{See the description of c.}
1.2       takayama   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:   }
1.7       takayama   38:   \item{log}{
                     39:      If it is 1, then the function returns the log of the normalizing constant.
                     40:   }
1.1       takayama   41: }
                     42: \details{
1.2       takayama   43:   The normalization constant c(Theta)
                     44:   of the Fisher distribution on SO(3) is defined  by
                     45:   integral( exp(trace( transpose(Theta) X)) )
                     46:   where X is the integration variable and runs over S0(3) and
                     47:   Theta is a 3 x 3 matrix parameter.
                     48:   A general HGM algorithm to evaluate the normalization constant
1.1       takayama   49:   is given in the reference below.
1.2       takayama   50:   We use the Corollary 1 and the series expansion in 3.2 for the evaluation.
1.1       takayama   51: %  \code{\link[RCurl]{postForm}}.
                     52: }
                     53: \value{
1.7       takayama   54: 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.
1.1       takayama   55: }
                     56: \references{
                     57: Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
                     58: Properties and applications of Fisher distribution on the rotation group,
1.4       takayama   59: Journal of Multivariate Analysis, 116 (2013), 440--455,
1.8     ! takayama   60: \doi{10.1016/j.jmva.2013.01.010}
1.1       takayama   61: }
                     62: \author{
                     63: Nobuki Takayama
                     64: }
1.6       takayama   65: %\note{
                     66: %%%  ~~further notes~~
                     67: %}
1.1       takayama   68:
                     69: %% ~Make other sections like Warning with \section{Warning }{....} ~
                     70:
1.6       takayama   71: %\seealso{
                     72: %%%\code{\link{oxm.matrix_r2tfb}}
                     73: %}
1.1       takayama   74: \examples{
                     75: ## =====================================================
                     76: ## Example 1. Computing normalization constant of the Fisher distribution on SO(3)
                     77: ## =====================================================
1.7       takayama   78: hgm.ncso3(1,2,3)[1]
1.2       takayama   79:
                     80: ## =====================================================
                     81: ## Example 2. Asteroid data in the paper
                     82: ## =====================================================
1.7       takayama   83: hgm.ncso3(19.6,0.831,-0.671)[1]
1.1       takayama   84: }
                     85: % Add one or more standard keywords, see file 'KEYWORDS' in the
                     86: % R documentation directory.
                     87: \keyword{ Normalization constant }
                     88: \keyword{ Holonomic gradient method }
1.2       takayama   89: \keyword{ HGM }
                     90: \keyword{ Fisher distribution on SO(3)}
1.1       takayama   91: