OPR-computation-related linear algebra problem

[Nikhil Bajaj]

New Code, based on what James put up (I just added some disp's so that the results would be more clear. disps are outside of tics and tocs. I did not find any bugs though had to change #'s to %'s.

clc
disp('Loading Data...')
tic
d = load('d.dat');
N = load('N.dat');
toc
Ns = sparse(N);
D = diag(Ns);
Ds = sparse(diag(D)); %This was a bug... maybe it still is!

% Reference Solution 
disp('Reference Solution:')
tic
output1 = Ns\d;
toc


% CG Solution
disp('CG Solution:');
tic
output2 = pcg(Ns,d);
toc

% Diagonal PCG Solution
disp('Diagonal PCG Solution:');
tic
output3 = pcg(Ns,d,[],[],Ds);
toc

% Reverse Cutthill-McKee re-ordering
disp('Re-ordering (Reverse Cutthill-McKee:');
tic
p = symrcm(Ns); % permutation array
Nr = Ns(p,p); % re-ordered problem
toc

% Re-ordered Solve
disp('Re-ordered Solution:');
tic
output4 = Nr\d; %answer is stored in a permuted matrix indexed by 'p'
toc

Output:

Loading Data...
Elapsed time is 3.033846 seconds.
Reference Solution:
Elapsed time is 0.014136 seconds.
CG Solution:
pcg stopped at iteration 20 without converging to the desired tolerance 1e-06
because the maximum number of iterations was reached.
The iterate returned (number 20) has relative residual 4.8e-05.
Elapsed time is 0.007545 seconds.
Diagonal PCG Solution:
pcg converged at iteration 17 to a solution with relative residual 8.9e-07.
Elapsed time is 0.009216 seconds.
Re-ordering (Reverse Cutthill-McKee:
Elapsed time is 0.004523 seconds.
Re-ordered Solution:
Elapsed time is 0.015021 seconds.

I didn't precondition earlier because I was being sloppy/lazy . Thanks for calling me out. And you're right, I should have used pcg. Thanks for the suggestion.