OPR-computation-related linear algebra problem

[flameout]

Originally Posted by Ether

Just installed SciLab 5.4.1 with Intel Math Kernel Library 10.3 on a 7-year-old desktop PC:

Now that I have working SciLab code, I'll go ahead and re-do the tests (with additional instrumentation on the reading). This is on the same computer as before (dual-core, hyperthreaded Intel i5, Linux 3.7.6).

MATLAB R2012b:

>> tic ; N = dlmread('N.dat'); toc
Elapsed time is 3.074810 seconds.
>> tic ; d = dlmread('d.dat'); toc
Elapsed time is 0.006744 seconds.
>> tic ; r = N \ d; toc
Elapsed time is 0.323021 seconds.
>> tic ; dlmwrite('out.dat', r); toc
Elapsed time is 0.124947 seconds.

I noticed that the solve time was very different from my previous run. This may be due to dynamic frequency scaling -- the results in this post (for all software) is with the frequency locked at the highest setting, 2.501 Ghz. It may also be due to a disk read -- I had not loaded MATLAB prior to running the previous test; now it's definitely in the disk cache. The solve is now consistently taking the time reported above, about a third of a second.

GNU Octave 3.6.2:

octave:1> tic ; N = dlmread('N.dat'); toc
Elapsed time is 1.87042 seconds.
octave:2> tic ; d = dlmread('d.dat'); toc
Elapsed time is 0.00241804 seconds.
octave:3> tic ; r = N \ d; toc
Elapsed time is 0.528489 seconds.
octave:4> tic ; dlmwrite('out.dat', r); toc
Elapsed time is 0.00820613 seconds.

Octave seems more consistent. The solve time is higher than for MATLAB, but the I/O times are consistently better.

Scilab 5.3.3:

-->stacksize(70000000);
 
-->tic; N=read("N.dat", 2509, 2509); toc
 ans  =
 
    1.21  
 
-->tic; d=read("d.dat", 2509, 1); toc
 ans  =
 
    0.003  
 
-->tic; x=N\d; toc
 ans  =
 
    1.052  
 
-->tic; Ns=sparse(N); toc
 ans  =
 
    0.081  
 
-->tic(); xs = umfpack(Ns,'\',d); toc
 ans  =
 
    0.081

Scilab failed to read the provided d.dat out of the box (reporting an EOF before it was done reading 2509 rows). I was able to correct this by adding a single newline to the end of d.dat.

FreeMat 4.0:

--> tic ; N = dlmread('N.dat'); toc
ans =
    2.8630
--> tic ; d = dlmread('d.dat'); toc
ans =
    0.0080
--> tic ; r = N \ d; toc
ans =
    3.4270

FreeMat did not have a dlmwrite function, so I haven't reported the write times for it. The time it took to solve the equations was significantly slower than any of the other programs. This did not improve with subsequent runs.