# hgm.so3nc: The function hgm.ncso3 evaluates the normalization constant... In hgm: Holonomic Gradient Method and Gradient Descent

## Description

The function hgm.ncso3 evaluates the normalization constant for the Fisher distribution on SO(3).

## Usage

 `1` ```hgm.ncso3(a,b,c,t0=0.0,q=1,deg=0) ```

## Arguments

 `a` See the description of c. `b` See the description of c. `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. `t0` It is the initial point to evaluate the series. If it is set to 0.0, a default value is used. `q` If it is 1, then the program works in a quiet mode. `deg` It gives the approximation degree of the power series approximation of the normalization constant near the origin. If it is 0, a default value is used.

## Details

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. We use the Corollary 1 and the series expansion in 3.2 for the evaluation.

## Value

The output is c(Theta).

Nobuki Takayama

## References

Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama, Properties and applications of Fisher distribution on the rotation group, Journal of Multivariate Analysis, 116 (2013), 440–455, http://dx.doi.org/10.1016/j.jmva.2013.01.010

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## ===================================================== ## Example 1. Computing normalization constant of the Fisher distribution on SO(3) ## ===================================================== hgm.ncso3(1,2,3) ## ===================================================== ## Example 2. Asteroid data in the paper ## ===================================================== hgm.ncso3(19.6,0.831,-0.671) ```

hgm documentation built on May 30, 2017, 8:17 a.m.