inverting independent, small dense matrices

[Matthew Knepley]

On Fri, Feb 13, 2009 at 5:29 PM, Shao-Ching Huang <schuang at ats.ucla.edu>wrote:

> Barry:
>
> How do I determine the "shift" value, to be passed into
>
>  Kernel_A_gets_inverse_A_4(MatScalar *a,PetscReal shift)
>
> ?
>
> I know that my 4x4 matrices are non-singular for sure.


Then you use 0.0;

  Matt


>
> Thanks.
>
> Shao-Ching
>
>
> Barry Smith wrote:
>
>>
>> On Feb 13, 2009, at 3:01 PM, Shao-Ching Huang wrote:
>>
>>  Hi
>>>
>>> I need to invert a bunch of independent, dense 4x4 matrices on each
>>> MPI process. (This is separate from the main computation, a parallel
>>> Ax=b solve.) I am thinking of using LAPACK's DGESV to invert these 4x4
>>> matrices.
>>>
>>>
>>     You would not want to use LAPACK's solvers for such tiny matrices.
>> LAPACK is optimized
>> for large dense matrices; the overhead is high for small matrices so that
>> actual performance will
>> be very slow calling LAPACK.
>>
>>  In my code, is it necessary to call LAPACK directly? Or does PETSc
>>> already have a convenient interface to LAPACK?
>>>
>>>      For PETSc's own internal use we have written custom inverters for
>> small matrices (these are used by
>> the factorization routines for BAIJ matrices).  They are called
>> Kernel_A_gets_inverse_A_* where * is the block size.
>> The prototypes for the functions are in src/inline/ilu.h and the actual
>> source code in files in src/mat/impls/baij/seq/dgef*.c
>>
>>   Barry
>>
>>
>>  The size 4x4 may be increased to 8x8 or so later, so I am not trying
>>> to use the closed-form inversion formula.
>>>
>>> Thanks,
>>>
>>> Shao-Ching
>>>
>>
>>


-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
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