optimization/test_functions/trigonometric_hessian1.m

   1 function H = trigonometric_hessian1(x)
   2   %
   3   % The Hessian of the Trigonometric function. See trigonometric1.m
   4   % for more information. Not my implementation. Too ugly to
   5   % recreate.
   6   %
   7   n  = length(x);
   8   H  = zeros(n,n);
   9
  10   cos_sum = sum(cos(x));
  11
  12   for i = 1 : n
  13     H(i,i) = sin ( x(i) );
  14   end
  15
  16   s = 0;
  17   for j = 1 : n
  18     th = cos ( x(j) );
  19     t = ( n + j ) - H(j,j) - cos_sum - j * th;
  20     s = s + t;
  21     for k = 1 : j-1
  22       H(j,k) = 2 * ( sin ( x(k) ) * ( ( n + j + k ) * H(j,j) - th ) ...
  23              - H(j,j) * cos ( x(k) ) );
  24     end
  25     H(j,j) = ( j * ( j + 2 ) + n ) * H(j,j)^2 + th * ...
  26              ( th - ( 2 * j + 2 ) * H(j,j) ) + t * ( j * th + H(j,j) );
  27   end
  28
  29   for j = 1 : n
  30     H(j,j) = 2 * ( H(j,j) + cos ( x(j) ) * s );
  31   end
  32
  33   for i = 1 : n
  34     H(i,i+1:n) = H(i+1:n,i);
  35   end
  36
  37 end