% m23c.m - m23b with a harder function!

  function m23()
  counter = 0; x = [-3:.1:3]; y = x;
  [xx,yy] = meshgrid(x,y);
  ff = (1-xx).^2 + 100*(yy+cos(pi*xx)).^2;      % modified 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,36)                          % 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
    counter = counter+1; x = X(1); y = X(2);
    f = (1-x)^2 + 100*(y+cos(pi*x))^2;
    g = [-2*(1-x)-200*pi*sin(pi*x)*(y+cos(pi*x)); 200*(y+cos(pi*x))];
    plot([xold x],[yold y],'-r',LW,2)           % plot line to current point
    plot(x,y,'.r',MS,30)                        % plot current point
    drawnow
    xold = x; yold = y;
  end

  end