SMFilter (version 1.0.3)

rmLB_sm: Sample from the matrix Langevin-Bingham on the Stiefel manifold.

Description

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

Usage

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

Value

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

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.