What does this code say? (Linear Algebra related) (Poisson)

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Guile
Guile 2013-10-29
回答： sixwwwwww 2013-10-29
This is my first time using MATLab and I have no idea what this code is saying. Can anyone translate this for me? I have proficient skills in Java, but it's not helping me out here.
p = 10; n = 2.^(1:p)'; % grid sizes
err = zeros(p,1); % error for each n
for i = 1:p
h = 1/n(i); x = (1:n(i)-1)'*h;
A = (1/h^2)*(diag(2*ones(n(i)-1,1))-diag(ones(n(i)-2,1), 1) ...
-diag(ones(n(i)-2,1),-1));
f = exp(x); % right-hand side
v = A\f; % solve
u = -exp(x)+(exp(1)-1)*x+1; % exact soln
err(i) = max(abs(u-v)); % infinity-norm error
end
format short e
disp(' ')
disp(' h err err/h^2 ')
disp(' ----- ------- -----------')
disp(' ')
disp([1./n err err./(1./n.^2)])
I need a step by step explanation, if possible. For example, I have no idea what's going on with n on the first line. What does 2.^(1:p)' do? Like the period, the carrot, the parentheses, the colon, specifically? When it runs, it looks like this:
h err err/h^2
----- ------- -----------
5.0000e-01 4.3295e-03 1.7318e-02
2.5000e-01 1.0925e-03 1.7480e-02
1.2500e-01 2.7377e-04 1.7521e-02
6.2500e-02 6.8827e-05 1.7620e-02
3.1250e-02 1.7234e-05 1.7647e-02
1.5625e-02 4.3098e-06 1.7653e-02
7.8125e-03 1.0776e-06 1.7655e-02
3.9063e-03 2.6940e-07 1.7655e-02
1.9531e-03 6.7351e-08 1.7656e-02
9.7656e-04 1.6838e-08 1.7656e-02

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回答（1 个）

sixwwwwww
sixwwwwww 2013-10-29
Dear Guile, I placed references for all the things which maybe confusing for you. You can try to access those references to find out how the code works:
p = 10;
% References for below code line:
% for (:) http://www.mathworks.de/de/help/matlab/ref/colon.html
% for (') http://www.mathworks.de/de/help/matlab/ref/transpose.html
% for (.^) http://www.mathworks.de/de/help/matlab/ref/power.html
n = 2.^(1:p)';
% References for below code line:
% for (zeros) http://www.mathworks.de/de/help/matlab/ref/zeros.html
err = zeros(p,1); % error for each n
% References for below code line:
% for (for) http://www.mathworks.de/de/help/matlab/ref/for.html
for i = 1:p
h = 1 / n(i);
x = (1:n(i) - 1)' * h;
% References for below code line:
% for (diag) http://www.mathworks.de/de/help/matlab/ref/diag.html
% for (ones) http://www.mathworks.de/de/help/matlab/ref/ones.html
A = (1 / h^2) * (diag(2*ones(n(i)-1,1))-diag(ones(n(i)-2,1), 1)-diag(ones(n(i)-2,1),-1));
% References for below code line:
% for (exp) http://www.mathworks.de/de/help/matlab/ref/exp.html
f = exp(x);
v = A\f;
u = -exp(x)+(exp(1)-1)*x+1;
% References for below code line:
% for (max) http://www.mathworks.de/de/help/fixedpoint/ref/max.html
err(i) = max(abs(u-v));
end
% References for below code line:
% for (format) http://www.mathworks.de/de/help/matlab/ref/format.html
format short e
% References for below code line:
% for (disp) http://www.mathworks.de/de/help/matlab/ref/disp.html
disp(' ')
disp(' h err err/h^2 ')
disp(' ----- ------- -----------')
disp(' ')
% References for below code line:
% for (./) http://www.mathworks.de/de/help/matlab/ref/rdivide.html
disp([1./n err err./(1./n.^2)])
I hope it can help you somehow. Good luck!

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