Hello, we have received a Matlab code in school and the assignment is to explain what it means. I wonder if anybody could take us through the code and explain it?

clear; close all; clc;
 
R = 7.8;
a = 5.5;
b = 11; 
 
N = 8;
h = 2*pi/N;
u = 0:h:2*pi;
 
X = zeros(3,N); X(:,1) = [0;0;0];    
F = @(u,X) [(R - a*cos(u))/(sqrt(b^2 + (R - a*cos(u)).^2)); R*cos(X(1)); R*sin(X(1))];
 
for n = 1:N
    F1 = F(u(n), X(:,n));
    F2 = F(u(n) + h/2, X(:,n) + (h/2)*F1);
    F3 = F(u(n) + h/2, X(:,n) + (h/2)*F2);
    F4 = F(u(n) + h, X(:,n) + h*F3);
    X(:, n+1) = X(:,n) + (h/6)*(F1 + 2*F2 + 2*F3 + F4);
end
i = 0;
 
 
while X(2,i+2)-X(2,i+1) > 0
    i = i +1;
end
 
p = i;
while X(3,p+2)-X(3,p+1) > 0
    p = p + 1;
end
 
Cvek = zeros(4,N);

for i = 1:i
    HL = [X(3,i+1); X(3,i); X(1,i+1); X(1,i)];
    VL = [1 X(2,i+1) X(2,i+1).^2 X(2,i+1).^3;1 X(2,i) X(2,i).^2 X(2,i).^3;0 1 2*X(2,i+1) 3*X(2,i+1).^2;0 1 2*X(2,i) 3*X(2,i).^2];
    C = flip(VL\HL);
    Cvek(:,i) = C;
end
 

for i = 1:(p-i)
    HL = [X(3,(p+2)-i); X(3,(p+1)-i); -asin(sin(X(1,(p+2)-i))); -asin(sin(X(1,(p+1)-i)))];
    VL = [1 X(2,(p+2)-i) X(2,(p+2)-i).^2 X(2,(p+2)-i).^3;1 X(2,(p+1)-i) X(2,(p+1)-i).^2 X(2,(p+1)-i).^3;0 1 2*X(2,(p+2)-i) 3*X(2,(p+2)-i).^2;0 1 2*X(2,(p+1)-i) 3*X(2,(p+1)-i).^2];
    C = flip(VL\HL);
    Cvek(:,(p+1-i)) = C;  
end
 

for i = 1:(N-p)
    HL = [X(3,(N+2)-i); X(3,(N+1)-i); -asin(sin(X(1,(N+2)-i))); asin(sin(X(1,(N+1)-i)))];
    VL = [1 X(2,(N+2)-i) X(2,(N+2)-i).^2 X(2,(N+2)-i).^3;1 X(2,(N+1)-i) X(2,(N+1)-i).^2 X(2,(N+1)-i).^3;0 1 2*X(2,(N+2)-i) 3*X(2,(N+2)-i).^2;0 1 2*X(2,(N+1)-i) 3*X(2,(N+1)-i).^2];
    C = flip(VL\HL);
    Cvek(:,(N+1-i)) = C;  
end
 
P1 = [0; 0];
P2 = [0; sqrt(b^2 + (R - a)^2)];
xvek = [P1(1) P2(1) X(2,end)];
yvek = [P1(2) P2(2) X(3,end)];
 
plot(X(2,:),X(3,:),'*-')
hold on
plot(xvek, yvek,'*-')
hold on
for j = 1:i
    H = poly2sym(Cvek(:,j));
    fplot(H, [X(2,j) X(2,j+1)], 'blue')  
end
hold on
for j = 1:(p-i)
    H = flip(poly2sym(Cvek(:,(p+1-j))));
    fplot(H, [X(2,(p+2-j)) X(2,(p+1-j))], 'blue')
end
hold on
for j = 1:(N-p)
    H = flip(poly2sym(Cvek(:,(N+1-j))));
    fplot(H, [X(2,(N+2-j)) X(2,(N+1-j))], 'blue')
end
grid on
hold on
title('Hermiteinterpoation - Kräfthatten')
hold on
legend('RK4','Linjen till spetsen', 'Hermiteinterpolation')
hold on
xlabel('Epsilon'); ylabel('Eta')

[Rik]

Appart from this code being written quite badly, do I understand you correctly? You want us to do your homework? If you want to make getting a usefull answer more likely, you should edit your question to show what you have done already and explain what exactly is your question.

[Dan]

I'm sorry for being inaccurate with the question.

The main question is how we can evaluate the accuracy of the results we get in this code?

[Rik]

Since the code does not have any comments, the variable names are not very descriptive, and you don't provide any context, your question is impossible to answer.

Have a read here and here. It will greatly improve your chances of getting an answer.

[Dan]

okey, thank you!

Answer 1

[Bjorn Gustavsson]

At the matlab command-line prompt type:

dpstop in nameiofscript

where nameiofscript is the name of the script-file. Then you run the script at the matlab command-line:

nameiofscript

This will now be a run in debug-mode, so you'll have a command-line prompt looking like this:

K>>

and you can step throught the script line-by-line by pushing the button in the editor saying something like "step". Between steps you can inspect or plot different variables as you see fit. Don't modify them on the commandline since that might/would modify the workings of the script. This will allow you to describe what the script does.

HTH

[Dan]

thank you!