[Pw_forum] Problems with nscf diago with many bands

[Paolo Giannozzi]

On Sep 30, 2008, at 16:13 , Conor Hogan wrote:

> Hello again, forget that last message, problem solved:
>
> <      CG style diagonalization
> <      ethr =  5.00E-06,  avg # of iterations = 34.7
> <      PWSCF        :  3m47.44s CPU time,     3m59.01s wall time
>
>>      Davidson diagonalization with overlap
>>      ethr =  5.00E-06,  avg # of iterations = 27.2
>>      PWSCF        :  7m41.49s CPU time,     7m47.46s wall time
>
> Wasn't expecting to see CG faster! PW continues to amaze me with its
> brutal efficiency :)


it is not CG that is faster, it is Davidson that is slower :)

Iterative diagonalization is designed to be fast when the number M of
desired solutions (i.e. KS state) is much smaller than the dimension
of vectors (i.e. the number of PW). If this is not true, iterative
diagonalization loses much of its appeal. Likely, the CPU usage in
your iterative diagonalization is dominated by conventional subspace
diagonalization, requiring O(M^3) operations (see CPU time spent in
*diagh). Davidson performs more of them and with larger matrix size
than CG. This does not explain the failures you get: my experience is
that Davidson is usually better but more sensitive to numerical  
problems.
Anyway: is CG is good for such cases, yet another reason to keep it  
alive.

Paolo
---
Paolo Giannozzi, Dept of Physics, University of Udine
via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222