moon10hd <- function(xx)
{
##########################################################################
#
# MOON (2010) HIGH-DIMENSIONALITY 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, ..., x20)
#
##########################################################################
coefflin <- c(-2.08, 2.11, 0.76, -0.57, -0.72, -0.47, 0.39, 1.40, -0.09, -0.70, -1.27, -1.03, 1.07, 2.23, 2.46, -1.31, -2.94, 2.63, 0.07, 2.44)
sumdeg1 <- sum(coefflin*xx)
coeffs <- matrix(0, 20, 20)
coeffs[,1] <- c(1.42, 2.18, 0.58, -1.21, -7.15, -1.29, -0.19, -2.75, -1.16, -1.09, 0.89, -0.16, 4.43, 1.65, -1.25, -1.35, 1.15, -19.71, 23.72, 1.42)
coeffs[,2] <- c( 0, -1.70, 0.84, 1.20, -2.35, -0.16, -0.19, -5.93, -1.15, 1.89, -3.47, -0.07, -0.60, -1.09, -3.23, 0.44, 1.24, 2.13, -0.71, 1.64)
coeffs[,3] <- c( 0, 0, 1.00, -0.49, 1.74, 1.29, -0.35, -4.73, 3.27, 1.87, 1.42, -0.96, -0.91, 2.06, 2.89, 0.25, 1.97, 3.04, 2.00, 1.64)
coeffs[,4] <- c( 0, 0, 0, -3.23, 2.75, -1.40, 0.24, -0.70, -0.17, -3.38, -1.87, -0.17, 1.56, 2.40, -1.70, 0.32, 2.11, -0.20, 1.39, -2.01)
coeffs[,5] <- c( 0, 0, 0, 0, -1.10, 2.34, -3.90, -0.80, 0.13, -3.97, 1.99, 0.45, 1.77, -0.50, 1.86, 0.02, -2.08, -1.78, 1.76, 1.30)
coeffs[,6] <- c( 0, 0, 0, 0, 0, 0.21, -0.03, -0.37, -1.27, 2.78, 1.37, -2.75, -3.15, 1.86, 0.12, -0.74, 1.06, -3.76, -0.43, 1.25)
coeffs[,7] <- c( 0, 0, 0, 0, 0, 0, -4.16, 0.26, -0.30, -2.69, -2.56, 28.99, -2.13, 1.36, 1.45, 3.09, -1.73, -1.66, -3.94, -2.56)
coeffs[,8] <- c( 0, 0, 0, 0, 0, 0, 0, -1.00, 0.77, 1.09, -1.15, -1.09, -2.74, 1.59, 1.41, 0.48, 2.16, 0.34, 4.17, 0.73)
coeffs[,9] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 3.06, 2.46, 5.80, -5.15, -2.05, 3.17, 3.40, -0.49, -6.71, -0.74, 2.78, -0.41)
coeffs[,10] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.34, 2.36, -1.77, -3.16, 1.89, 2.20, -0.71, -3.78, 0.98, 1.40, -0.59)
coeffs[,11] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.17, -2.45, 6.04, 3.22, 0.19, -0.03, -2.65, -1.02, -1.96, -2.66)
coeffs[,12] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.52, 1.36, -0.59, -1.05, -0.84, -1.30, 0.42, 1.86, -0.32)
coeffs[,13] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.42, -0.50, 0.21, -0.18, 3.04, -0.53, -0.12, 0.09)
coeffs[,14] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.13, -2.42, -3.93, -2.30, 0.40, 0.81, -1.10)
coeffs[,15] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.26, 5.31, 1.66, -3.10, 3.37, 4.32)
coeffs[,16] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.26, 0.00, -0.77, -3.90, -1.08)
coeffs[,17] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.62, -1.06, -0.86, 0.44)
coeffs[,18] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.35, -1.99, 1.50)
coeffs[,19] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13.34, 1.34)
coeffs[,20] <- c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.38)
xxmat <- matrix(rep(xx,times=20), 20, 20, byrow=TRUE)
factors <- rowSums(coeffs*xxmat*t(xxmat))
sumdeg2 <- sum(sum(factors))
y <- sumdeg1 + sumdeg2
return(y)
}