+function H = trigonometric_hessian1(x)
+ ##
+ ## The Hessian of the Trigonometric function. See trigonometric1.m
+ ## for more information. Not my implementation. Too ugly to
+ ## recreate.
+ ##
+ n = length(x);
+ H = zeros(n,n);
+
+ cos_sum = sum(cos(x));
+
+ for i = 1 : n
+ H(i,i) = sin ( x(i) );
+ end
+
+ s = 0;
+ for j = 1 : n
+ th = cos ( x(j) );
+ t = ( n + j ) - H(j,j) - cos_sum - j * th;
+ s = s + t;
+ for k = 1 : j-1
+ H(j,k) = 2 * ( sin ( x(k) ) * ( ( n + j + k ) * H(j,j) - th ) ...
+ - H(j,j) * cos ( x(k) ) );
+ end
+ H(j,j) = ( j * ( j + 2 ) + n ) * H(j,j)^2 + th * ...
+ ( th - ( 2 * j + 2 ) * H(j,j) ) + t * ( j * th + H(j,j) );
+ end
+
+ for j = 1 : n
+ H(j,j) = 2 * ( H(j,j) + cos ( x(j) ) * s );
+ end
+
+ for i = 1 : n
+ H(i,i+1:n) = H(i+1:n,i);
+ end
+
+end