R/NullC.R

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

#' Null Space of a Matrix
#' 
#' Given a matrix \code{M}, find a matrix \code{N} giving a basis for the null
#' space. This is a modified version of Null from the package MASS.
#' 
#' 
#' @param M input matrix.
#' @return an orthonormal matrix such that \code{t(N)\%*\%M} is a matrix of
#' zeros.
#' @note The MASS function \code{Null(matrix(0,4,2))} returns a 4*2 matrix,
#' whereas \code{NullC(matrix(0,4,2))} returns \code{diag(4)}.
#' @author Peter Hoff
#' @examples
#' 
#' NullC(matrix(0,4,2))
#' 
#' ## The function is currently defined as
#' function (M) 
#' {
#'     tmp <- qr(M)
#'     set <- if (tmp$rank == 0L) 
#'         1L:nrow(M)
#'     else -(1L:tmp$rank)
#'     qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
#'   }
#' 
#' @export NullC
NullC <-
function(M)
{
  #modified from package "MASS" 
  #MASS version : Null(matrix(0,4,2))  returns a 4*2 matrix
  #this version : NullC(matrix(0,4,2)) returns diag(4)

  tmp <- qr(M)
  set <- if (tmp$rank == 0L)
      1L:nrow(M)
  else -(1L:tmp$rank)
  qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
}