optimization/test_functions/trigonometric_gradient1.m

   1 function g = trigonometric_gradient1(x)
   2   ##
   3   ## The gradient of the trigonometric function. See trigonometric1.m
   4   ## for more information.
   5   ##
   6   n  = length(x);
   7   g  = zeros(n,1);
   8
   9   cos_sum = sum(cos(x));
  10
  11   for k = [ 1 : n ]
  12     f_k = n - cos_sum + k*(1 - cos(x(k))) - sin(x(k));
  13
  14     for j = [ 1 : n ]
  15       ## Add to the jth component of g the partial of f^2 with
  16       ## respect to x(j). The first term that we add here exists
  17       ## regardless of j.
  18       g(j) = g(j) + 2*f_k*sin(x(j));
  19
  20       if (j == k)
  21         ## But this term vanishes when j != k.
  22         g(j) = g(j) + 2*f_k*k*sin(x(k)) - 2*f_k*cos(x(k));
  23       end
  24     end
  25   end
  26
  27 end