% m23b.m - m23_fminunc again, with two changes: a harder function
%          (Rosenbrock), and a gradient supplied

  function m23b()
  x = [-3:.1:3]; y = x;
  [xx,yy] = meshgrid(x,y);
  ff = (1-xx).^2 + 100*(yy-xx.^2).^2;           % Rosenbrock function
  levels = 0:20:500;
  hold off, contour(xx,yy,ff,levels)            % contour plot
  colorbar, grid on, hold on
  LW = 'linewidth'; MS = 'markersize';
  plot(1,1,'.k',MS,30)                          % the solution
  x = input('initial x? ');
  y = input('initial y? ');
  xold = x; yold = y;
  opts = optimset('gradobj','on');             
  X = fminunc(@f,[x;y],opts)                    % minimisation

  function [f,g] = f(X)                         % compute function and gradient
    x = X(1), y = X(2)
    f = (1-x)^2 + 100*(y-x^2)^2;
    g = [-2*(1-x)-400*x*(y-x^2); 200*(y-x^2)];
    plot([xold x],[yold y],'-r',LW,1.2)         % plot line to current point
    plot(x,y,'.r',MS,15)                        % plot current point
    disp(' '), pause
    xold = x; yold = y;
  end

  end