analyze preconditioned operator?

[Matthew Knepley]

On Fri, Oct 10, 2008 at 3:11 PM, Matt Funk <mafunk at nmsu.edu> wrote:
> Ok,
>
> thanks, i think i finally got the main idea (the emphasize here being on 'i
> think' which might not mean much ...)
>
> One other question though:
> What do i declare ctx to be: PetscObject * ctx ?

No, you declare a struct which holds

  a) The original matrix

  b) The preconditioner

  c) A work vector

or you would not be able to code the apply method.

> Another question related to KSPComputeExplicitOperator:
>
> I was trying to use KSPComputeExplicitOperator and i am having issues with it
> as well. My matrix is a sparse matrix of length ((2*73)^3) with a maximum of
> ~30 entries per row.

This is way way way too big to form the operator explicitly.

> I believe that in order to use KSPComputeExplicitOperator i need to set up a
> matrix, allocate the memory for it and then pass it to the routine.
> From what i gather on the reference page this matrix needs to be of type
> MatDense? (if so then i cannot use KSPComputeExplicitOperator due to the size
> of the resulting matrix)
> However, it said on the website that when multiple procs are used it uses a
> sparse format.
> So why cannot i not use a sparse format in serial?

1) This operator is in general not sparse at all

2) We only use a sparse format in parllel because matMPIDense was
having problems

It is instructive to look at what the code is doing. The function is
very short and you
can get to it right from the link on the manpage.

  Matt

> thanks
> matt
>
>
> On Thursday 09 October 2008, Matthew Knepley wrote:
>> On Thu, Oct 9, 2008 at 5:58 PM, Matt Funk <mafunk at nmsu.edu> wrote:
>> > So then,
>> >
>> > is it then correct to say that this code "registers" this extra operation
>> > (i.e. applying the preconditioner) with the matrix context such that
>> > whenever a matrix operation involving this matrix is invoked (like
>> > MatMult for example) the pc-applying fcn (i.e. myApply() ) is called
>> > first?
>>
>> The idea here is to replace a given matrix A, which you are passing to
>> SLEPc, with another matrix M, which is a shell matrix. When MatMult() is
>> called on M, we call MatMult on A, and then PCApply on the result.
>>
>>   Matt
>>
>> > matt
>> >
>> > ps: sorry for being a little slow on the uptake here ...
>> >
>> > On Thursday 09 October 2008, Matthew Knepley wrote:
>> >> On Thu, Oct 9, 2008 at 5:25 PM, Matt Funk <mafunk at nmsu.edu> wrote:
>> >> > Hi Matt,
>> >> >
>> >> > so, the basic idea with this code is to apply the pc to each column
>> >> > vector of the matrix? Is that right?
>> >>
>> >> No, that is what KSPGetExplicitOperator() does. This applies the
>> >> operator in a matrix-free way.
>> >>
>> >> > Also, in your example: when is myApply actually invoked? I also looked
>> >> > at the example listed under the MatShellSetOperation reference page.
>> >>
>> >> When MatMult(A) is called.
>> >>
>> >>   Matt
>> >>
>> >> > Is the function then actually internally called when
>> >> > MatShellSetOperation is called, or when KSPSetOperators is called or
>> >> > KSPSolve?
>> >> >
>> >> > The reason i am asking is that if it is called when KSPSolve called
>> >> > then there is a problem because for the analysis i never call KSPSolve
>> >> > directly.
>> >> >
>> >> > thanks
>> >> > matt
>> >> >
>> >> > On Thursday 09 October 2008, Matthew Knepley wrote:
>> >> >> On Thu, Oct 9, 2008 at 4:32 PM, Matt Funk <mafunk at nmsu.edu> wrote:
>> >> >> > mmhh,
>> >> >> >
>> >> >> > i think i am missing something. Doesn't PCApply() apply the
>> >> >> > preconditioner to a vector? So how would that work (easily) with a
>> >> >> > matrix?
>> >> >>
>> >> >> You do not apply it to the matrix. Here is a skeleton (maybe has
>> >> >> mistakes)
>> >> >>
>> >> >> void myApply(Mat A, Vec x, Vec y) {
>> >> >>   MatShellGetContext(A, &ctx);
>> >> >>   MatMult(ctx->M, x, ctx->work);
>> >> >>   PCApply(ctx->pc, ctx->work, y);
>> >> >> }
>> >> >>
>> >> >> MatShellSetOperation(A, MATOP_MULT, myApply)
>> >> >>
>> >> >>   Matt
>> >> >>
>> >> >> > matt
>> >> >> >
>> >> >> > On Thursday 09 October 2008, Matthew Knepley wrote:
>> >> >> >> CApply().
>
>
>



-- 
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