langer <- function(xx, m=5, cvec, A)
{
  ##########################################################################
  #
  # LANGERMANN 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/
  #
  ##########################################################################
  #
  # INPUTS:
  #
  # xx   = c(x1, x2, ..., xd)
  # m    = constant (optional), with default value 5
  # cvec = m-dimensional vector (optional), with default value c(1, 2, 5, 2, 3)
  #        (when m=5)
  # A    = (mxd)-dimensional matrix (optional), with default value:
  #        [3  5]
  #        [5  2]
  #        [2  1]
  #        [1  4]
  #        [7  9]
  #        (when m=5 and d=2)
  #
  ##########################################################################
  
  d <- length(xx)
  
  if (missing(cvec)) {
    if (m == 5){
      cvec <- c(1,2,5,2,3)
    }
    else {
      stop('Value of the m-dimensional vector cvec is required.')
    }
  }
  
  if (missing(A)) {
    if (m==5 && d==2) {
      A <- matrix(c(3,5,5,2,2,1,1,4,7,9),5,2,byrow=TRUE)
    }
    else {
        stop('Value of the (mxd)-dimensional matrix A is required.')
    }
  }
  
  xxmat <- matrix(rep(xx,times=m), m, d, byrow=TRUE)    
  inner <- rowSums((xxmat-A[,1:d])^2)	
  outer <- sum(cvec * exp(-inner/pi) * cos(pi*inner))
	
  y <- outer
  return(y)
}