# rbmf.matrix.gibbs: Gibbs Sampling for the Matrix-variate Bingham-von... In rstiefel: Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

## Description

Simulate a random orthonormal matrix from the Bingham distribution using Gibbs sampling.

## Usage

 `1` ```rbmf.matrix.gibbs(A, B, C, X) ```

## Arguments

 `A` a symmetric matrix. `B` a diagonal matrix with decreasing entries. `C` a matrix with the same dimension as X. `X` the current value of the random orthonormal matrix.

## Value

a new value of the matrix `X` obtained by Gibbs sampling.

## Note

This provides one Gibbs scan. The function should be used iteratively.

Peter Hoff

Hoff(2009)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```## The function is currently defined as function (A, B, C, X) { m <- dim(X)[1] R <- dim(X)[2] if (m > R) { for (r in sample(seq(1, R, length = R))) { N <- NullC(X[, -r]) An <- B[r, r] * t(N) %*% (A) %*% N cn <- t(N) %*% C[, r] X[, r] <- N %*% rbmf.vector.gibbs(An, cn, t(N) %*% X[, r]) } } if (m == R) { for (s in seq(1, R, length = R)) { r <- sort(sample(seq(1, R, length = R), 2)) N <- NullC(X[, -r]) An <- t(N) %*% A %*% N Cn <- t(N) %*% C[, r] X[, r] <- N %*% rbmf.O2(An, B[r, r], Cn) } } X } ```

rstiefel documentation built on June 12, 2018, 5:19 p.m.