% This program finds the maximum of the function.
% It finds the local maximums, and hopefully finds 
% the global maximum too.

clear

step_x=0.01;

% x=-2:0.01:2;
% y=exp(1./(1+x.^2))+0.1*sin(20*x);

x=-10:step_x:10;
y=(x-2).*cos(x);

plot(x,y)
hold on
grid on
y1=inline('(x-2).*cos(x)');
% y1=inline('exp(1./(1+x.^2))+0.1*sin(20*x)');
lok_max=[];
lok_min=[];

for i=x(2):step_x:x(end-1)
    if (y1(i)>y1(i-0.01)) && (y1(i)>y1(i+0.01))
        lok_max=[lok_max; i y1(i)];
        plot(i, y1(i),'rs','MarkerFaceColor','r')
        pause(0.05)
    elseif (y1(i)<y1(i-0.01)) && (y1(i)<y1(i+0.01))
        lok_min=[lok_min; i y1(i)];
        plot(i, y1(i),'gs','MarkerFaceColor','g')
        pause(0.05)
    end
end

global_max=max(lok_max(:,2));
[p q]=find(lok_max==global_max);
max_x=lok_max(p,1);
max_y=lok_max(p,2);
plot(max_x,max_y,'rs','MarkerFaceColor','r', 'MarkerSize',12)

global_min=min(lok_min(:,2));
[p q]=find(lok_min==global_min);
min_x=lok_min(p,1);
min_y=lok_min(p,2);
plot(min_x,min_y,'gs','MarkerFaceColor','g', 'MarkerSize',12)