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

clear
x=-2:0.01:2;
y1=exp(1./(1+x.^2))+0.1*sin(20*x);

plot(x,y1)
hold on
grid on

    y=inline('exp(1./(1+x.^2))+0.1*sin(20*x)');
lok_max=[];

for i=1:8
%     temp_x=-1.98;
    temp_x=(floor(100*((4*rand)-2)))/100;

    temp_y=y(temp_x);
    t=temp_x;

    if y(t+0.01) > y(t-0.01)
        direction = 2;                          % right
    elseif y(t+0.01) < y(t-0.01)
        direction = 1;                          % left
    else
        direction = 0;                          % flat
    end

    if direction ==2
        while y(t+0.01) > y(t)
            t=t+0.01;
            if t==x(end)
                break;
            end
            x_lokal_max=t;
            y_lokal_max=y(x_lokal_max);
            plot(x_lokal_max,y_lokal_max,'r*')
            pause(0.1)
        end
    end

    if direction ==1
        while y(t-0.01) > y(t)
            t=t-0.01;
            if t==x(1)
                break;
            end
            x_lokal_max=t;
            y_lokal_max=y(x_lokal_max);
            plot(x_lokal_max,y_lokal_max,'r*')
            pause(0.1)
        end
    end

    lok_max=[lok_max; t y(t)];
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,'gs','MarkerFaceColor','g', 'MarkerSize',12)