hart3 <- function(xx)

{

  ##########################################################################

  #

  # HARTMANN 3-DIMENSIONAL 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, x3)

  #

  ##########################################################################

  alpha <- c(1.0, 1.2, 3.0, 3.2)

  A <- c(3.0, 10, 30,

         0.1, 10, 35,

         3.0, 10, 30,

         0.1, 10, 35)

  A <- matrix(A, 4, 3, byrow=TRUE)

  P <- 10^(-4) * c(3689, 1170, 2673,

                   4699, 4387, 7470,

                   1091, 8732, 5547,

                   381, 5743, 8828)

  P <- matrix(P, 4, 3, byrow=TRUE)

  xxmat <- matrix(rep(xx,times=4), 4, 3, byrow=TRUE)

  inner <- rowSums(A[,1:3]*(xxmat-P[,1:3])^2)

  outer <- sum(alpha * exp(-inner))

  y <- -outer

  return(y)

}