R/rbing.matrix.gibbs.R

In pdhoff/rstiefel: Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

#' Gibbs Sampling for the Matrix-variate Bingham Distribution
#' 
#' Simulate a random orthonormal matrix from the Bingham distribution using
#' Gibbs sampling.
#' 
#' 
#' @param A a symmetric matrix.
#' @param B a diagonal matrix with decreasing entries.
#' @param X the current value of the random orthonormal matrix.
#' @return a new value of the matrix \code{X} obtained by Gibbs sampling.
#' @note This provides one Gibbs scan. The function should be used iteratively.
#' @author Peter Hoff
#' @references Hoff(2009)
#' @examples
#' 
#' Z<-matrix(rnorm(10*5),10,5) ; A<-t(Z)%*%Z
#' B<-diag(sort(rexp(5),decreasing=TRUE))
#' U<-rbing.Op(A,B)
#' U<-rbing.matrix.gibbs(A,B,U)
#' 
#' ## The function is currently defined as
#' function (A, B, 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
#'             X[, r] <- N %*% rbing.vector.gibbs(An, 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
#'             X[, r] <- N %*% rbing.Op(An, B[r, r])
#'         }
#'     }
#'     X
#'   }
#' 
#' @export rbing.matrix.gibbs
rbing.matrix.gibbs <-
function(A,B,X)
{
  #simulate from the matrix bmf distribution as described in Hoff(2009) 
  #this is one Gibbs step, and must be used iteratively

  ### assumes B is a diagonal matrix with *decreasing* entries 
  
  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 
      X[,r]<-N%*%rbing.vector.gibbs(An,t(N)%*%X[,r])
    }
  }

  #If m=R then the fc of one vector given all the others is 
  #just +-1 times the vector in the null space. In this case, 
  #the matrix needs to be updated at least two columns at a 
  #time. 
  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
      #X[,r]<-N%*%rbing.O2(An,B[r,r]) 
      X[,r]<-N%*%rbing.Op(An,B[r,r]) 
    }
  }
  X
}