levy <- function(xx)
{
  ##########################################################################
  #
  # LEVY 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(x1, x2, ..., xd)
  #
  ##########################################################################
  
  d <- length(xx)
  w <- 1 + (xx - 1)/4
	
  term1 <- (sin(pi*w[1]))^2 
  term3 <- (w[d]-1)^2 * (1+1*(sin(2*pi*w[d]))^2)
	
  wi <- w[1:(d-1)]
  sum <- sum((wi-1)^2 * (1+10*(sin(pi*wi+1))^2))
	
  y <- term1 + sum + term3
  return(y)
}