[Pw_forum] Errors in parallel 3D FFT

[Iain Bethune]

I used an optimized FFTW3, but I just tried using FFTW (-D_FFTW) and got the
same results:

Total grid elements on this process:        16200
 Error < 1e-18:         9515
 Error < 1e-15:        14191
 Error < 1e-12:        14191
 Error < 1e-09:        14191
 Error < 1e-06:        14191
 Error < 1e-03:        14586
 Error < 1e+00:        16200
 Error >= 1e+0:            0

So most of the elements have small errors (which is as expected), but there
are a large number which have very large errors (>1e-06), and I don't
understand why this should happen.

Here is a typical sample of elements that don't agree after the G->R->G FFT
steps:

(  0.0000000000000000     ,  0.0000000000000000     )  ->
(-6.19446221078556020E-004,-1.74898798599905760E-004)
(  0.0000000000000000     ,  0.0000000000000000     )  ->  (
9.03523919712864205E-005, 9.20886154392430039E-004)
(  0.0000000000000000     ,  0.0000000000000000     )  ->  (
3.07966800915878281E-004, 1.44523973744239645E-004)
(  0.0000000000000000     ,  0.0000000000000000     )  ->
(-1.71711886309486506E-004, 3.97860015055829619E-004)
(  0.0000000000000000     ,  0.0000000000000000     )  ->
(-4.92121624328117836E-004,-5.62768457197758659E-004)
(  0.0000000000000000     ,  0.0000000000000000     )  ->  (
6.02880566549388744E-005,-2.14744832649235777E-004)

I don't think this can be put down to numerical error in the FFT?

- Iain

--

Iain Bethune
Applications Consultant, EPCC

Email: ibethune at epcc.ed.ac.uk
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> -----Original Message-----
> From: Lorenzo Paulatto [mailto:paulatto at sissa.it]
> Sent: 13 January 2010 16:34
> To: ibethune at epcc.ed.ac.uk; PWSCF Forum
> Subject: Re: [Pw_forum] Errors in parallel 3D FFT
> 
> On Wed, 13 Jan 2010 16:51:20 +0100, Iain Bethune
> <ibethune at staffmail.ed.ac.uk> wrote:
> > Any idea what might be causing this?
> 
> Hi Iain,
> are you using "vanilla" FFTW libraries or architecture optimized ones?
> (e.g. ACML, ESSL) Some high performance libraries can trade a little of
> accuracy for speed, and to be honest. I'm not even sure that perfect
> matching (whatever the definition of perfect) is guaranteed even with the
> standard open-source FFTW libraries.
> 
> best regards
> 
> --
> Lorenzo Paulatto
> 
> *** Note: my affiliation has changed! please send future
> correspondence to: <Lorenzo.Paulatto at impmc.upmc.fr> ***
> 
> post-doc @ IMPMC/UPMC - Université Paris 6
> phone: +33 (0)1 44 27 74 89
> www:   http://www-int.impmc.upmc.fr/~paulatto/
> 
> previously:
> phd student @ SISSA  &  DEMOCRITOS (Trieste)
> phone: +39 040 3787 511
> www:   http://people.sissa.it/~paulatto/