Plotting the objective function

The below shown objective function has to be plotted and while doing so its going in infinite recursion.

The functions m and b are external functions defined in different function files.

function P1=f(x0)
M=5;
x0=[5,8];
% x0=[12,13];
M2=m(M,x0(1));
M3=m(M2,x0(2));
M4=m(M3,(x0(1)+x0(2))); 

beta1=b(M,(x0(1)));
beta2=b(M2,(x0(2)));
beta3=b(M3,((x0(1)+x0(2))));

s1=sin(beta1);
s2=sin(beta2);
s3=sin(beta3);

t1n=(13.824)*((M2*M3*M)^2)*((s1*s2*s3)^2);
t1d=(((0.4)*(M3^2)*(s3^2))+2)*(((0.4)*(M2^2)*(s2^2))+2)*(((0.4)*(M^2)*(s1^2))+2);
t1=(t1n/t1d)^(3.5);

t2n=13.824;
t2d=((2.8*(M3^2)*(s3^2))-0.4)*((2.8*(M2^2)*(s2^2))-0.4)*((2.8*(M^2)*(s1^2))-0.4);
t2=(t2n/t2d)^(2.5);
    
P1=(t1*t2);
P= P1*(-1);
%  surf(
% fplot(x0,f)

end

[Torsten]

In the function f you supplied, I don't see a reason for an infinite recursion.

So we cannot give advice.

[Vivek]

elow shown is my objective function and related m and b function files are external function files.

function P1=f(x0)
M=5;
%x0=[5,8];
% x0=[12,13];
M2=m(M,x0(1));
M3=m(M2,x0(2));
M4=m(M3,(x0(1)+x0(2))); 
beta1=b(M,(x0(1)));
beta2=b(M2,(x0(2)));
beta3=b(M3,((x0(1)+x0(2))));
s1=sin(beta1);
s2=sin(beta2);
s3=sin(beta3);
t1n=(13.824)*((M2*M3*M)^2)*((s1*s2*s3)^2);
t1d=(((0.4)*(M3^2)*(s3^2))+2)*(((0.4)*(M2^2)*(s2^2))+2)*(((0.4)*(M^2)*(s1^2))+2);
t1=(t1n/t1d)^(3.5);
t2n=13.824;
t2d=((2.8*(M3^2)*(s3^2))-0.4)*((2.8*(M2^2)*(s2^2))-0.4)*((2.8*(M^2)*(s1^2))-0.4);
t2=(t2n/t2d)^(2.5);
    
P1=(t1*t2);
P= P1*(-1);
%  surf(
% fplot(x0,f)
end
%-----------------------------------------------------------------------
%-----------------------------------------------------------------------
%This is the separate script file 
x0=[x1,x2];
% Lower bounds
lb=[1,5];
% Upper Bounds
ub=[40,38];
nonlcon=@area
% 
rng default     
 x1   = linspace(1,100,55);
 x2   = linspace(1,100,55);
 [X, Y]  = meshgrid(x1, x2);
 Z      = f(x0);
 %contour(X, Y, Z)
 surfc(X, Y, Z)
 xlabel('x_1'), ylabel('x_2'), zlabel('f(x_1, x_2)')
% opts = optimoptions('fmincon','PlotFcn',["optimplotx","optimplotfunccount","optimplotfvalconstr","optimplotfval"],'Display','iter');
% opts1 = optimoptions(opts,'MaxIterations',100); % Recommended
% [x,fval,exitflag,output]= fmincon(@f,x0,[],[],[],[],lb,ub,[],opts1);
options=optimoptions('ga','ConstraintTolerance',1e-8,'Display','iter');
[x,fval,exitflag,output,population,scores]=ga(@f,2,[],[],[],[],lb,ub,nonlcon,[],options)

After using the above code it is showing the error as shown below.

Ig it is taking single value of x0

Error using surfc
The surface Z must contain more than one row or column.
Error in z (line 18)
surfc(X, Y, Z)

@Torsten

[Torsten]

Z   = arrayfun(@(x,y) f([x,y]),X,Y);

instead of

Z   = f(x0);

And my guess is that you mean

P1= P1*(-1);

instead of

P= P1*(-1);

at the end of function f.

[Vivek]

But the objective function is f(x0) and it is scripted in different file and the function has to be returned while plotting.

The below graph is returned by using Z = arrayfun(@(x,y) f([x,y]),X,Y);

[Torsten]

Your objective function accepts a vector with two elements [x y].

x1   = linspace(1,100,55);
x2   = linspace(1,100,55);
[X, Y]  = meshgrid(x1, x2);
Z      = arrayfun(@(x,y) f([x,y]),X,Y);

This code passes all tuples (x1(i),y1(j)) to your function f, evaluates f at these points and saves the result in Z(i,j).

If the subsequent command

surfc(X, Y, Z)

gives you a surface with constant z value, your function f does not seem to behave properly.

Answer 1

[Sarthak]

Hi,

It looks like the function ‘f(x0)’ is not recursively calling itself, but it might be stuck in an infinite loop due to some other reason. One possible reason could be that the external functions ‘m’ and ‘b’ are calling back the ‘f(x0)’ function, which can lead to an infinite recursion. Another reason could be that the values of ‘M’, ‘x0(1)’, and ‘x0(2)’ are not changing during the execution, leading to a loop that never terminates.

To debug this issue, you can try printing the values of the variables ‘M’, ‘x0(1)’, and ‘x0(2)’ at different points in the function to see if they are changing as expected. You can also try commenting out parts of the code to see which part is causing the infinite loop.

Once you have identified the issue, you can modify the code accordingly to fix the problem.