% Problem # 8 (Modified Trigonometric Polynomial or Lévy's Function # 2)
% Range of initial points: -10 <= x <= 10
% It has three global maximum: x={-7.08350640682890, -0.800321099691209,
% 5.48286420658132}
% f(x)=14.508007927195038
% Coded by: Ali R. Alroomi | Last Update: 25 Feb. 2015 | www.al-roomi.org
 
clear
clc
warning off
 
xmin=-10;
xmax=10;
R=100000; % steps resolution
x=xmin:(xmax-xmin)/R:xmax;
 
for i=1:length(x)
    
    for j=1:5
        fs(j)=j*cos((j+1)*x(i)+j);
    end
    
    f(i)=sum(fs);
    
end
 
plot(x,f,'r','LineWidth',2);grid;set(gca,'FontSize',12);
xlabel('x','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('f(x)','FontName','Times','FontSize',20,'FontAngle','italic');