Last week I installed Julien Salort's Octave 3.4.0 for Mac OSX 10.6. It
seemed to work perfectly until I tried some heavy duty computation. Now
I see that Julien's Octave 3.4.0 compilation has the slow norm2 problem
that afflicted versions of Octave prior to version 2.9.15 (Oct 2007). I
don't know whether this is an Octave 3.4.0 problem per se or a problem
with Julien's Mac compilation of Octave 3.4.0.
I have compared the speed of the instructions "norm(x)" and
"sqrt(sum(x .* x))" on Thomas Treichl's Octave.app (3.2.3) and Julien
Salort's Octave.app (3.4.0). These versions of octave can be found at
http://sourceforge.net/projects/octave/files/Octave%20MacOSX%20Binary/
2011-03-27 binary of Octave 3.4.0 (2011-03-27)
2009-10-03 binary of Octave 3.2.3 (2010-11-23)
Here is a summary of the results I observed.
1. Octave 3.4.0 is a bit slower than Octave 3.2.3 on sqrt(sum(x .* x)).
2. On Octave 3.2.3, norm(x) is a bit faster than sqrt(sum(x .* x)). This
is as it should be since NRM2 is a BLAS.
3. On Octave 3.4.0, sqrt(sum(x .* x)) is four times as fast as norm(x).
This is not as it should be for the reason cited in 2.
4. norm(x) on Octave 3.2.3 is nine times as fast as norm(x) on Octave
3.4.0.
My test script and my results appear below.
Regards,
Vic
The test script. The two different shebang lines placed at the top
test the two different versions of octave.
#!/usr/local/bin/octave323
# norm2test.m
#!/usr/local/bin/octave323
#!/usr/local/bin/octave340
ntests = 20; n = 1e6; x = rand(n, 1);
test1 = zeros(ntests, 1); test2 = zeros(ntests, 1);
for i = 1 : ntests
tic;
norm(x);
test1(i) = toc;
endfor
for i = 1 : ntests
tic;
sqrt(sum(x .* x));
test2(i) = toc;
endfor
printf ("norm2 speed test - octave %s\n", version);
printf ("%40s\n","ellapsed times");
printf ("%30s%10s\n", "mean", "stdv");
printf ("%-20s", "norm(x)");
printf ("%10.2e", mean(test1));
printf ("%10.2e", std(test1));
printf ("\n");
printf ("%-20s", "sqrt(sum(x .* x))");
printf ("%10.2e", mean(test2));
printf ("%10.2e", std(test2));
printf ("\n");
The output.
---
GNU Octave, version 3.2.3
Copyright (C) 2009 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. For details, type `warranty'.
Octave was configured for "i386-apple-darwin8.11.1".
Additional information about Octave is available at http://www.octave.org.
Please contribute if you find this software useful.
For more information, visit http://www.octave.org/help-wanted.html
Report bugs to<address@hidden> (but first, please read
http://www.octave.org/bugs.html to learn how to write a helpful report).
For information about changes from previous versions, type `news'.
norm2 speed test - octave 3.2.3
ellapsed times
mean stdv
norm(x) 7.06e-03 2.62e-05
sqrt(sum(x .* x)) 1.06e-02 1.98e-03
---
GNU Octave, version 3.4.0
Copyright (C) 2011 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. For details, type `warranty'.
Octave was configured for "i386-apple-darwin10.6.0".
Additional information about Octave is available at http://www.octave.org.
Please contribute if you find this software useful.
For more information, visit http://www.octave.org/help-wanted.html
Read http://www.octave.org/bugs.html to learn how to submit bug reports.
For information about changes from previous versions, type `news'.
norm2 speed test - octave 3.4.0
ellapsed times
mean stdv
norm(x) 6.48e-02 3.78e-04
sqrt(sum(x .* x)) 1.46e-02 1.21e-04
---