[SciPy-User] understanding machine precision

[josef.pktd at gmail.com]

On Tue, Dec 14, 2010 at 1:47 PM, Robert Kern <robert.kern at gmail.com> wrote:
> On Tue, Dec 14, 2010 at 12:42, Keith Goodman <kwgoodman at gmail.com> wrote:
>> On Tue, Dec 14, 2010 at 9:42 AM,  <josef.pktd at gmail.com> wrote:
>>> I thought that we get deterministic results, with identical machine
>>> precision errors, but I get (with some random a0, b0)
>>>
>>>>>> for i in range(5):
>>>        x = scipy.linalg.lstsq(a0,b0)[0]
>>>        x2 = scipy.linalg.lstsq(a0,b0)[0]
>>>        print np.max(np.abs(x-x2))
>>>
>>>
>>> 9.99200722163e-016
>>> 9.99200722163e-016
>>> 0.0
>>> 0.0
>>> 9.99200722163e-016
>>
>> I've started a couple of threads in the past on repeatability. Most of
>> the discussion ends up being about ATLAS. I suggest repeating the test
>> without ATLAS.

Is there a way to turn ATLAS off without recompiling?

>
> On OS X with numpy linked against the builtin Accelerate.framework
> (which is based off of ATLAS), I get the same result every time.

When I run the script on the commandline (with a new python each
time), I get the same results each time, but within the loop the
results still differ up to 1.55431223448e-015. On IDLE when I remain
in the same session, results differ with each run.

An explanation that ATLAS has some builtin state is enough for me, I
try not to rely on numerical precision in this range.

Josef

>
> --
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
>   -- Umberto Eco
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