% Mishra's # 7 or Factorial Fuction
% Range of initial points: -10 <= xj <= 10 , j=1,2,...,n
% For n=1:
% Global minima: x=1
% f(x)=0
% For n=2:
% Infinite number of global minimum: x1*x2=2 >> x1=2/x2
% f(x1,x2)=0
% In general, fmin=0 when the product is equal to the factorial
% Coded by: Ali R. Alroomi | Last Update: 04 June 2015 | www.al-roomi.org   
 
% Larger value of n (=>8) will make the problem very hard
 
clear
clc
warning off
 
x1min=-10;
x1max=10;
x2min=-10;
x2max=10;
R=1500; % steps resolution
x1=x1min:(x1max-x1min)/R:x1max;
x2=x2min:(x2max-x2min)/R:x2max;
 
% Compute factorial(n):
Fact1=factorial(1);
Fact2=factorial(2);
 
for j=1:length(x1)
    
    % For 1-dimensional plotting
    f1(j)=(x1(j)-Fact1)^2;
    
    % For 2-dimensional plotting
    for i=1:length(x2)
        Prod=x1(j)*x2(i);
        f(i)=(Prod-Fact2)^2;
    end
    
    fn_tot(j,:)=f;
 
end
 
figure(1)
plot(x1,f1);set(gca,'FontSize',12);
xlabel('x','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('f(x)','FontName','Times','FontSize',20,'FontAngle','italic');
title('2D View','FontName','Times','FontSize',24,'FontWeight','bold');
 
figure(2)
meshc(x1,x2,fn_tot);colorbar;set(gca,'FontSize',12);
xlabel('x_2','FontName','Times','FontSize',20,'FontAngle','italic');
set(get(gca,'xlabel'),'rotation',25,'VerticalAlignment','bottom');
ylabel('x_1','FontName','Times','FontSize',20,'FontAngle','italic');
set(get(gca,'ylabel'),'rotation',-25,'VerticalAlignment','bottom');
zlabel('f(X)','FontName','Times','FontSize',20,'FontAngle','italic');
title('3D View','FontName','Times','FontSize',24,'FontWeight','bold');
 
figure(3)
mesh(x1,x2,fn_tot);view(0,90);colorbar;set(gca,'FontSize',12);
xlabel('x_2','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('x_1','FontName','Times','FontSize',20,'FontAngle','italic');
zlabel('f(X)','FontName','Times','FontSize',20,'FontAngle','italic');
title('X-Y Plane View','FontName','Times','FontSize',24,'FontWeight','bold');
 
figure(4)
mesh(x1,x2,fn_tot);view(90,0);colorbar;set(gca,'FontSize',12);
xlabel('x_2','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('x_1','FontName','Times','FontSize',20,'FontAngle','italic');
zlabel('f(X)','FontName','Times','FontSize',20,'FontAngle','italic');
title('X-Z Plane View','FontName','Times','FontSize',24,'FontWeight','bold');
 
figure(5)
mesh(x1,x2,fn_tot);view(0,0);colorbar;set(gca,'FontSize',12);
xlabel('x_2','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('x_1','FontName','Times','FontSize',20,'FontAngle','italic');
zlabel('f(X)','FontName','Times','FontSize',20,'FontAngle','italic');
title('Y-Z Plane View','FontName','Times','FontSize',24,'FontWeight','bold');