function fprimeprime=testfunctionprimeprime(x,funnum)
% TESTFUNCTIONPRIMEPRIME - The second derivative of various test functions for optimization
% These are the second derivatives of the test functions that appear in Appendix I.
% Set funnum to the function you want to use.
% funnum=17 is the MOO function and is not plotted
%
% From the book: 
% Practical Genetic Algorithms 
% by Haupt & Haupt.
%
% Epage: 250 
%   
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% check inputs:
assert( prod(size(x))==length(x), 'input must be a vector (and not a matrix)' );

% make sure our input is a row vector
x = x(:)'; 

switch funnum
 case 1,
  assert( false, 'not yet implemented' );
  f = abs(x)+cos(x);   
 case 2,
  assert( false, 'not yet implemented' ); 
  f = abs(x)+sin(x); 
 case 3,
  assert( false, 'not yet implemented' ); 
  fprime = x(:,1).^2 + x(:,2).^2; 
 case 4,
  assert( false, 'not yet implemented' ); 
  fprime = 100*(x(:,2).^2 - x(:,1)).^2 + (1-x(:,1)).^2; 
 case 5,
  assert( false, 'not yet implemented' ); 
  fprime = sum( abs(x')-10*cos(sqrt(abs(10*x'))) )';
 case 6,
  assert( false, 'not yet implemented' ); 
  fprime = (x.^2 + x).*cos(x); 
 case 7,
  fprimeprime = zeros(2,2);
  fprimeprime(1,1) = 8*cos(4*x(1)) + 16*x(1)*sin(4*x(1));
  fprimeprime(1,2) = 0.;
  fprimeprime(2,1) = 0.;
  fprimeprime(2,2) = 4.4*cos(2*x(2)) - 4.4*x(2)*sin(2*x(2));
 case 8,
  assert( false, 'not yet implemented' ); 
  fprime = x(:,2).*sin(4*x(:,1))+1.1*x(:,2).*sin(2*x(:,2)); 
 case 9,
  assert( false, 'not yet implemented' ); 
  f(:,1) = x(:,1).^4 + 2*x(:,2).^4 + randn(length(x(:,1)),1); 
 case 10,
  fprimeprime = zeros(2,2);
  fprimeprime(1,1) = 2 + 40*(pi^2)*cos(2*pi*x(1));
  fprimeprime(1,2) = 0;
  fprimeprime(2,1) = 0;
  fprimeprime(2,2) = 2 + 40*(pi^2)*cos(2*pi*x(2));
 case 11,
  fprimeprime = zeros(2,2);
  fprimeprime(1,1) = 1/2000. + cos(x(1))*cos(x(2));
  fprimeprime(1,2) = -sin(x(1))*sin(x(2)); 
  fprimeprime(2,1) = fprimeprime(1,2);
  fprimeprime(2,2) = 1/2000. - cos(x(1))*cos(x(2));
 case 12,
  assert( false, 'not yet implemented' ); 
  f(:,1) = 0.5+(sin(sqrt(x(:,1).^2 + x(:,2).^2).^2)-0.5)./(1+0.1*(x(:,1).^2+x(:,2).^2));
 case 13, 
  assert( false, 'not yet implemented' ); 
  aa = x(:,1).^2 + x(:,2).^2; 
  bb = ((x(:,1)+0.5).^2 + x(:,2).^2).^0.1; 
  f(:,1) = aa.^0.25.*sin(30*bb).^2 + abs(x(:,1))+abs(x(:,2));
 case 14,
  assert( false, 'not yet implemented' ); 
  f(:,1) = besselj(0,x(:,1).^2+x(:,2).^2)+abs(1-x(:,1))/10+abs(1-x(:,2))/10; 
 case 15,
  assert( false, 'not yet implemented' ); 
  f(:,1) = -exp(0.2*sqrt((x(:,1)-1).^2+(x(:,2)-1).^2)+(cos(2*x(:,1))+sin(2*x(:,1)))); 
 case 16,
  assert( false, 'not yet implemented' ); 
  f(:,1) = -x(:,1).*sin(sqrt(abs(x(:,1)-(x(:,2)+9))))-(x(:,2)+9).*sin(sqrt(abs(x(:,2)+0.5*x(:,1)+9))); 
 case 17, 
  assert( false, 'not yet implemented' ); 
  x=x+1;
  f(:,1) = (x(:,1)+x(:,2).^2 + sqrt(x(:,3))+ 1.0./x(:,4))/8.5;
  f(:,2) = (1./x(:,1)+1./x(:,2)+x(:,3)+x(:,4))/6; 
 otherwise
  error( 'unknown function' ); 
end