[SciPy-User] understanding machine precision

[Francesc Alted]

A Wednesday 15 December 2010 13:36:44 josef.pktd at gmail.com escrigué:
> On Tue, Dec 14, 2010 at 2:59 PM, Bruce Southey <bsouthey at gmail.com> 
wrote:
> > On 12/14/2010 01:29 PM, Francesc Alted wrote:
> >> A Tuesday 14 December 2010 20:17:10 Nils Wagner escrigué:
> >>> Hi all,
> >>> 
> >>> I am using ATLAS
> >>> 
> >>> python -i try_deterministic.py
> >>> 
> >>> lstsq
> >>> 0.0
> >>> 0.0
> >>> 0.0
> >>> 0.0
> >>> 0.0
> >> 
> >> That's interesting.  Maybe Josef is using a threaded ATLAS?  I
> >> positively know that threading introduces variability in the order
> >> that the computations are done.  However, I'm not sure on why
> >> ATLAS has decided to use several threads for so small matrices
> >> ((100, 10)) :-/
> > 
> > Does this 'issue' occur with numpy's lstsq?
> 
> good question, I didn't think about it.
> 
> same problem and my numpy is from an official installer (1.4.0) and
> not compiled against the old ATLAS, that I'm still using.

With the slightly modified script that depends only on numpy, I'm having 
problems of reproducibility only with pinv:

C:\Users\francesc>python x:\try_deterministic_numpy.py
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Python version:    2.6.6 (r266:84297, Aug 24 2010, 18:46:32) [MSC v.1500 
32 bit (Intel)]
NumPy version:     1.5.0
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

lstsq
0.0
0.0
0.0
0.0
0.0

pinv
0.0
5.55111512313e-17
0.0
0.0
0.0

And, curiously enough, that pattern is always the same for every run.  
So, at least, the issue is more deterministic that we initially thought.

But, in the same machine, using Python 2.7, problem disappears 
completely:

C:\Users\francesc>python x:\try_deterministic_numpy.py
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Python version:    2.7 (r27:82525, Jul  4 2010, 09:01:59) [MSC v.1500 32 
bit (Intel)]
NumPy version:     1.5.0
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

lstsq
0.0
0.0
0.0
0.0
0.0

pinv
0.0
0.0
0.0
0.0
0.0

Well, at least we have narrowed the possibilities significantly: this 
seems to happen only (up to now) with Win32, Python 2.6 and NumPy 
(without ATLAS in the loop).  It is worth noting that the compilers used 
for Python 2.6 and 2.7 should be the same (MSVC 1500).  I think I 
installed NumPy from sourceforge repository, so the compiler used here 
should also be the same.

And also interesting is the fact that the 'lstsq' method is always 
reproducible on my machine.  However, Josef also reported non-
deterministic behaviour with 'lstsq' :-/

-- 
Francesc Alted
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