% ModelErrorGraph.m
%
% Plots graphs of parameter optimization for simple two-parameter
% functions. Shows results for three parameter search algorithms:
% SimpleHillClimb, fminsearch, and fmincon.
%
% Programmed by John Kruschke, 1/28/03. Modified 1/26/2005.

% Initial parameter values 
parInit = [ 1.6 -1.6 ] ;

% Increment (a.k.a. step) size on each parameter 
parInc = [ 0.1 0.1 ] ;

% Lowest and highest parameter values allowed 
parLow = [ -4 -4 ] ;
parHigh = [ 4 4 ] ;

% The function that returns the model error is "modelError".

% Compute optimization from SimpleHillClimb.
disp('======================= SimpleHillClimb ===========================')
traj = SimpleHillClimb(@ModelError,parInit,parLow,parHigh,parInc) 
bestFitSimpleHillClimb = traj(size(traj,1),:)

% Compute optimization from another built-in MATLAB routine.
disp('======================= fminsearch ================================')
searchOptions = optimset('Display','iter');
[X,FVAL,exitflag,output] = fminsearch(@ModelError,parInit,searchOptions)
bestFitFMINSEARCH = [ X FVAL ] 

% Compute optimization from a built-in MATLAB routine.
disp('======================= fmincon ===================================')
searchOptions = optimset('Display','iter');
[X,FVAL,exitflag,output] = fmincon(@ModelError,parInit,[],[],[],[], ...
   parLow,parHigh,[],searchOptions)
bestFitFMINCON = [ X FVAL ] 

% Graph the results

% GridEvaluation evaluates the model error over an entire grid of points.
% This can be done for the simplistic two-parameter "model"  used here,
% but in general is not feasible.
[ X Y Z ] = GridEvaluation(@ModelError,parLow,parHigh,parInc) ;

figure(1)

subplot(1,2,1,'replace') ;
surfc(X,Y,Z) ;
hold on;
plot3(traj(:,1),traj(:,2),traj(:,3),'-m','LineWidth',3);
plot3(bestFitSimpleHillClimb(1), bestFitSimpleHillClimb(2), ...
   bestFitSimpleHillClimb(3),'om', 'MarkerFaceColor','m','MarkerSize',10);
plot3(bestFitFMINSEARCH(1),bestFitFMINSEARCH(2),bestFitFMINSEARCH(3), ...
   'sb', 'MarkerFaceColor','b','MarkerSize',10);
plot3(bestFitFMINCON(1),bestFitFMINCON(2),bestFitFMINCON(3),'dg', ...
    'MarkerFaceColor','g','MarkerSize',10);
hold off;
axis([ parLow(1) parHigh(1) parLow(2) parHigh(2) 0 16 ]) ;
axis square ;
title('Magenta = SimpleHillClimb, Blue = fminsearch, Green = fmincon') ;
xlabel('Param_1') ;
ylabel('Param_2') ;
zlabel('Error') ;

subplot(1,2,2,'replace') ;
hold on;
contour(X,Y,Z,20) ;
plot(traj(:,1),traj(:,2),'-m','LineWidth',3);
plot(bestFitSimpleHillClimb(1),bestFitSimpleHillClimb(2),'om', ...
    'MarkerFaceColor','m','MarkerSize',10);
plot(bestFitFMINSEARCH(1),bestFitFMINSEARCH(2),'sb', ...
    'MarkerFaceColor','b','MarkerSize',10);
plot(bestFitFMINCON(1),bestFitFMINCON(2),'dg', ...
    'MarkerFaceColor','g','MarkerSize',10);
hold off;
axis([  parLow(1) parHigh(1) parLow(2) parHigh(2) ]) ;
axis square ;
grid on;
xlabel('Param_1') ;
ylabel('Param_2') ;

%%%%%%%%%%%%%%% end of program %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%