# rvlb_sm: Sample from the vector 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 vector Langevin-Bingham on the Stiefel manifold.

## Usage

 1 rvlb_sm(num, mA, vc, vx) 

## Arguments

 num number of observations or sample size. mA the matrix A which is symmetric ip*ip matrix. vc the vector c with dimension ip. vx the vector x, the initial value.

## Details

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

f(X) \propto \mathrm{etr}\{ x' A x + c' x \}

where x satisfies x'x = 1, and A is a symmetric matrix.

## Value

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

## 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.

## Author(s)

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

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