How can I get the Secant method to repeat ?

Hi everyone , can anyone please show me why my script isn't repeating its calculation? It only calculates the root at theta = 20 and then the loop isn't repeating cheers

clear all 
clc

M2=5;
r=1.4;
theta_vec=20:0.1:42;

ciL=35;
cim1L=ciL-1;
fi=((2*cotd(ciL).*((M2.^2).*((sind(ciL)).^2)-1))./((M2.^2).*(r+cosd(2*ciL))+2))-tand(theta_vec);
 for n=1:length(theta_vec);
    theta=theta_vec(n);
    while abs(fi)>1.0e-6;
      fi=((2*cotd(ciL).*((M2.^2).*((sind(ciL)).^2)-1))./((M2.^2).*(r+cosd(2*ciL))+2))-tand(theta);
      fim1=((2*cotd(cim1L).*((M2.^2).*((sind(cim1L)).^2)-1))./((M2.^2).*(r+cosd(2*cim1L))+2))-tand(theta);
      cip1L=ciL-(ciL-cim1L)*fi(n)/(fi-fim1);
      cim1L=ciL;
      ciL=cip1L;
    end
 end

Answer 1

[Scott MacKenzie]

Your code is rather dense. However, I did observe the looping in your code. And... (drum roll please) ...

You've got a bug in your calculation! The for-loop executes 221 times, but the while-loop only executes 4 times and only in the 1st iteration of the for-loop. Have a look at the code I added below and the output produced. This should give you a strong hint on where to look and adjust to set things right. Welcome to debugging. :)

M2=5;
r=1.4;
theta_vec=20:0.1:42;
ciL=35;
cim1L=ciL-1;
fi=((2*cotd(ciL).*((M2.^2).*((sind(ciL)).^2)-1))./((M2.^2).*(r+cosd(2*ciL))+2))-tand(theta_vec);
z=1; % use z to see how many times the while loop executes
for n=1:length(theta_vec)
    % I first added a line below to output n.  This confirmed that the
    % for-loop executes 221 times.  Then, I commented out the line.
    % n
    theta=theta_vec(n);
    
    while abs(fi)>1.0e-6
        [n z] % output n and z
        z = z+1; % increment z so it increases with each execution of the while-loop
        fi=((2*cotd(ciL).*((M2.^2).*((sind(ciL)).^2)-1))./((M2.^2).*(r+cosd(2*ciL))+2))-tand(theta);
        fim1=((2*cotd(cim1L).*((M2.^2).*((sind(cim1L)).^2)-1))./((M2.^2).*(r+cosd(2*cim1L))+2))-tand(theta);
        cip1L=ciL-(ciL-cim1L)*fi(n)/(fi-fim1);
        cim1L=ciL;
        ciL=cip1L;
    end    
end

Output:

ans =

1 1

ans =

1 2

ans =

1 3

ans =

1 4

[Jan]

Thanks. A good answer.

[JiaJun Zeng]

Thanks so much ! I figured out!!