R/is.positive.definite.R

In zoib: Bayesian Inference for Beta Regression and Zero-or-One Inflated Beta Regression

is.square.matrix <- function( x )
{
  ###
  ### determines if the given matrix is a square matrix
  ###
  ### arguments
  ### x = a matrix object
  ###
  if ( !is.matrix( x ) )
    stop( "argument x is not a matrix" )
  return( nrow(x) == ncol(x) )
}

is.symmetric.matrix <- function( x )
{
  ###
  ### this function determines if the matrix is symmetric
  ###
  ### argument
  ### x = a numeric matrix object
  ###
  if ( !is.matrix( x ) ) {
    stop( "argument x is not a matrix" )
  }
  if ( !is.numeric( x ) ) {
    stop( "argument x is not a numeric matrix" )
  }    
  if ( !is.square.matrix( x ) )
    stop( "argument x is not a square numeric matrix" )
  return( sum( x == t(x) ) == ( nrow(x) ^ 2 ) )
}

is.positive.definite <- function( x, tol=1e-8 )
{
  ###
  ### this function determines if the given real symmetric matrix is positive definite
  ###
  ### parameters
  ### x = a square numeric matrix object
  ### tol = tolerance level for zero
  ###
  if ( !is.square.matrix( x ) )
    stop( "argument x is not a square matrix" )
  if ( !is.symmetric.matrix( x ) )
    stop( "argument x is not a symmetric matrix" )
  if ( !is.numeric( x ) )
    stop( "argument x is not a numeric matrix" )
  eigenvalues <- eigen(x, only.values = TRUE)$values
  n <- nrow( x )
  for ( i in 1: n ) {
    if ( abs( eigenvalues[i] ) < tol ) {
      eigenvalues[i] <- 0
    }
  }    
  if ( any( eigenvalues <= 0 ) ) {
    return( FALSE )
  }
  return( TRUE )
}