# 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?

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Dan 2019 年 11 月 6 日
Commented: Dan 2019 年 11 月 7 日
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')

#### 4 件のコメント

Dan 2019 年 11 月 7 日
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 2019 年 11 月 7 日
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.
Dan 2019 年 11 月 7 日
okey, thank you!

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### 件の回答 (1)

Bjorn Gustavsson 2019 年 11 月 7 日
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

#### 1 件のコメント

Dan 2019 年 11 月 7 日
thank you!

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