zhouetal11 <- function(xx)
{
  ##########################################################################
  #
  # ZHOUT ET AL. (2011) FUNCTION
  #
  # Authors: Sonja Surjanovic, Simon Fraser University
  #          Derek Bingham, Simon Fraser University
  # Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
  #
  # Copyright 2013. Derek Bingham, Simon Fraser University.
  #
  # THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
  # FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
  # derivative works, such modified software should be clearly marked.
  # Additionally, this program is free software; you can redistribute it 
  # and/or modify it under the terms of the GNU General Public License as 
  # published by the Free Software Foundation; version 2.0 of the License. 
  # Accordingly, this program is distributed in the hope that it will be 
  # useful, but WITHOUT ANY WARRANTY; without even the implied warranty 
  # of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
  # General Public License for more details.
  #
  # For function details and reference information, see:
  # http://www.sfu.ca/~ssurjano/
  #
  ##########################################################################
  #
  # INPUT:
  #
  # xx = c(x, z)
  #
  ##########################################################################
  
  x <- xx[1]
  z <- xx[2]
  
  sign <- 1
  
  if (z == 1)
  {
    c <- 6.8
  }
  else if (z == 2)
  {
    c <- 7
    sign <- -1
  }
  else if (z == 3)
  {
    c <- 7.2
  }
  
  y <- sign * cos(c*pi*x/2)
  return(y)
}