www.pudn.com > starter.zip > rosenbrock.m, change:2011-01-04,size:1074b


function [f, df, ddf, dddf] = rosenbrock(x);

% rosenbrock.m This function returns the function value, partial derivatives
% and Hessian of the (general dimension) rosenbrock function, given by:
%
%       f(x) = sum_{i=1:D-1} 100*(x(i+1) - x(i)^2)^2 + (1-x(i))^2 
%
% where D is the dimension of x. The true minimum is 0 at x = (1 1 ... 1).
%
% Carl Edward Rasmussen, 2001-07-21.

D = length(x);
f = sum(100*(x(2:D)-x(1:D-1).^2).^2 + (1-x(1:D-1)).^2);

if nargout > 1
  df = zeros(D, 1);
  df(1:D-1) = - 400*x(1:D-1).*(x(2:D)-x(1:D-1).^2) - 2*(1-x(1:D-1));
  df(2:D) = df(2:D) + 200*(x(2:D)-x(1:D-1).^2);
end

if nargout > 2
  ddf = zeros(D,D);
  ddf(1:D-1,1:D-1) = diag(-400*x(2:D) + 1200*x(1:D-1).^2 + 2);
  ddf(2:D,2:D) = ddf(2:D,2:D) + 200*eye(D-1);
  ddf = ddf - diag(400*x(1:D-1),1) - diag(400*x(1:D-1),-1);
end

if nargout > 3
    dddf = zeros(D,D,D);
    for d = 1:D
       if d > 1
           dddf(d,d-1,d-1) = -400;
       end
       if d < D
          dddf(d,d+1,d) = -400;
          dddf(d,d,d+1) = -400;
          dddf(d,d,d) = 2400*x(d);
       end
    end
end