Simulation from a Matrix Fisher distribution on SO(3)

Description

It simulates random samples (rotation matrices) from a Matrix Fisher distribution with any given parameter matrix, F (3x3).

Usage

1

Arguments

n

the sample size.

F

An arbitrary 3x3 matrix.

Details

Firstly corresponding Bingham parameter A is determined for a given Matrix Fisher parameter F using John Kent (2013) algorithm and then Bingham samples for parameter A are generated using rbingham code. Finally convert Bingham samples to Matrix Fisher samples according to the Kent (2013) transformation.

Value

An array with simulated rotation matrices.

Author(s)

Anamul Sajib & Chris Fallaize

R implementation and documentation: Anamul Sajib <pmxahsa@nottingham.ac.uk> & Chris Fallaize

References

Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf

Examples

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F <- matrix( c(85, 11, 41, 78, 39, 60, 43, 64, 48), ncol = 3) / 10   ### An arbitrary F matrix
a <- rmatrixfisher(10, F)

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