Thu 31 Mar 2011 03:48:47 PM UTC, original submission:
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.
The test script. The two different shebang lines placed at the top of
the file 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.
---
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
---
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
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