# rmLB_sm: Sample from the matrix Langevin-Bingham on the Stiefel... In SMFilter: Filtering Algorithms for the State Space Models on the Stiefel Manifold

## Description

This function draws a sample from the matrix Langevin-Bingham on the Stiefel manifold.

## Usage

 1 rmLB_sm(num, mJ, mH, mC, mX, ir) 

## Arguments

 num number of observations or sample size. mJ symmetric ip*ip matrix mH symmetric ir*ir matrix mC ip*ir matrix mX ip*ir matrix, the initial value ir ir

## Details

The matrix Langevin-Bingham distribution on the Stiefel manifold has the density kernel:

f(X) \propto \mathrm{etr}\{ H X' J X + C' X \}

where X satisfies X'X = I_r, and H and J are symmetric matrices.

## Value

an array containing a sample of draws from the matrix Langevin-Bingham on the Stiefel manifold.

## Author(s)

Yukai Yang, yukai.yang@statistik.uu.se

#' @section References: Hoff, P. D. (2009) "Simulation of the Matrix Bingham<e2><80><94>von Mises<e2><80><94>Fisher Distribution, With Applications to Multivariate and Relational Data", Journal of Computational and Graphical Statistics, Vol. 18, pp. 438-456.

SMFilter documentation built on May 1, 2019, 8:01 p.m.