Re: Convergence on different systems -- December 02, 2006 - 16:03

Convergence when using Newton optimisation in relax (or in any
application) should be quite fast.  The Newton algorithm has what is
known as quadratic convergence - the fastest type of convergence.  In
comparison steepest descent has linear convergence and the BFGS
algorithm has super-linear convergence.  For more details see, for
example, Nocedal, J. and S. J. Wright: 1999, Numerical Optimization,
Springer Series in Operations Research, New York: Springer-Verlag.
Because of the quadratic convergence, tiny parameter differences will
most likely never occur and hence the convergence tests for identical
values won't be an issue.  These tests for identical values will not
increase the amount of CPU time required relative to approximate value
tests where a small tolerance is added.

The only problem is if you continually change CPU architectures,
operating systems, etc., during the running of the 'full_analysis.py'
script.  It should be fine though if the same diffusion tensor is
optimised on the same machine.

Cheers,

Edward


On 12/2/06, Sebastien Morin <sebastien.morin.1@xxxxxxxxx> wrote:
> Hi
>
> I used the full_analysis.py script until convergence for the 4 diffusion
> models (sphere, prolate, oblate, ellipsoid), each on one different
> computer. Those computer, however, are quite similar, all 32-bits x86
> Gentoo Linux with same kernel, gcc, python, etc.
>
> For the final run, I switched on a different system, our dual core
> pseudo 64-bits NMR console computer running Red Hat Enterprise 4 with
> almost everything different from our Gentoo workstations which are
> really more up-to-date. Before starting the final run, I wanted to check
> if number rounding would be the same... Well, is wasn't and the run with
> the ellipsoid diffusion model ended up saying it wasn't converged yet :
>
> #####################
> # Convergence tests #
> #####################
> Chi-squared test:
>     chi2 (k-1): 7022.7261139599996
>     chi2 (k):   7022.7261139563052
>     The chi-squared value has not converged.
> Identical model-free models test:
>     The model-free models have converged.
> Identical parameter test:
>     Spin system: 26 PHE
>     Parameter:   S2f
>     Value (k-1): 0.84811676720047557
>     Value (k):   0.84811676720047491
>     The model-free parameters have not converged.
> Convergence:
>     [ No ]
>
> As is obvious, the differences are really small, but still relax thinks
> it's enough to spend many hours more trying to get absolute reproducibility.
>
> My question.
>
> Is it really necessary to get convergence on so small digits ? Probably
> yes, as it was designed this way... So, if yes, why ? Isn't it a problem
> for multi-computer processing ?
>
> Thanks !
>
>
> Séb :)
>
>
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