gaussian <- function(xx, u=rep(0.5, 1, length(xx)), a=rep(5, 1, length(xx)))
{
  ##########################################################################
  #
  # GAUSSIAN PEAK INTEGRAND FAMILY
  #
  # 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/
  #
  ##########################################################################
  #
  # INPUTS:
  #
  # xx = c(x1, x2, ..., xd)
  # u  = c(u1, u2, ..., ud) (optional), with default value
  #      c(0.5, 0.5, ..., 0.5)
  # a  = c(a1, a2, ..., ad) (optional), with default value c(5, 5, ..., 5)
  #
  ##########################################################################

  sum <- sum(a^2 * (xx-u)^2)
	
  y <- exp(-sum)
  return(y)
}