% 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)
% set(gcf,'Position',[50 50 450 350])
hold on
grid on

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

    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;
            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;
            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=[t y(t)];

NumberOfRestartsLeft=5;

while NumberOfRestartsLeft > 0
    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;
            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;
            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 y_lokal_max <= lok_max(2)
        NumberOfRestartsLeft = NumberOfRestartsLeft - 1;
    else
        lok_max=[t y(t)];
        NumberOfRestartsLeft = 5;
    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,'gs','MarkerFaceColor','g', 'MarkerSize',12)