franke2d <- function(xx)
{
  ##########################################################################
  #
  # FRANKE'S 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)
  #
  ##########################################################################
  
  x1 <- xx[1]
  x2 <- xx[2]
  
  term1 <- 0.75 * exp(-(9*x1-2)^2/4 - (9*x2-2)^2/4)
  term2 <- 0.75 * exp(-(9*x1+1)^2/49 - (9*x2+1)/10)
  term3 <- 0.5 * exp(-(9*x1-7)^2/4 - (9*x2-3)^2/4)
  term4 <- -0.2 * exp(-(9*x1-4)^2 - (9*x2-7)^2)
  
  y <- term1 + term2 + term3 + term4
  return(y)
}