PCGetFactoredMatrix

[John R. Wicks]

I am specifically interested in knowing if one can expect the residual
matrix (A - LU) to be significantly more sparse than the original matrix, A.
Does anyone know if this is the case for sparse A?

> -----Original Message-----
> From: owner-petsc-users at mcs.anl.gov 
> [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Barry Smith
> Sent: Thursday, November 29, 2007 3:43 PM
> To: petsc-users at mcs.anl.gov
> Subject: Re: PCGetFactoredMatrix
> 
> 
> 
>     John,
> 
>       There is no immediate way to do this.
> For the SeqAIJ format, we store both the LU in a single CSR 
> format. with for each row first the part of L (below the 
> diagonal) then 1/D_i then the part of U for that row. You can 
> see how the triangular solves are done by looking at 
> src/mat/impls/aij/seq/aijfact.c the routine  
> MatSolve_SeqAIJ()
> Note that it is actually more complicated due to the row and column  
> permutations
> (the factored matrix is stored in the ordering of the 
> permutations). For BAIJ matrix the storage is similar except 
> it is stored by block  
> instead of point
> and the inverse of the block diagonal is stored.
> 
> One could take the MatSolve_SeqAIJ() routine and modify it to do the  
> matrix
> vector product without too much difficulty.
> 
> If you decide to do this we would gladly include it in our 
> distribution.
> 
>     Barry
> 
> One can ask why we don't provide this functionality in PETSc since  
> computing
> A - LU is a reasonable thing to do if one wants to understand the  
> convergence
> of the method. The answer is two-fold 1) time and energy and 
> 2) though  
> we
> like everyone to use PETSc we driven more by people who are not  
> interested
> in the solution algorithms etc but only in getting the answer easily  
> and relatively
> efficiently.
> 
> 
> On Nov 29, 2007, at 12:07 PM, John R. Wicks wrote:
> 
> > I would like to compute the residual A - LU, where LU is the ILU 
> > factorization of A.  What is the most convenient way of doing so?
> >
> >> -----Original Message-----
> >> From: owner-petsc-users at mcs.anl.gov 
> >> [mailto:owner-petsc-users at mcs.anl.gov] On Behalf Of Matthew Knepley
> >> Sent: Thursday, November 29, 2007 12:04 PM
> >> To: petsc-users at mcs.anl.gov
> >> Subject: Re: PCGetFactoredMatrix
> >>
> >>
> >> It depends on the package, but the petsc stuff stores L 
> and U in one 
> >> matrix.
> >>
> >>   Matt
> >>
> >> On Nov 29, 2007 9:03 AM, John R. Wicks <jwicks at cs.brown.edu> wrote:
> >>> The documentation for PCGetFactoredMatrix is not clear.  
> What does 
> >>> this return for ILU(0), for example? Does it return the
> >> product LU or
> >>> the in place factorization?
> >>>
> >>>
> >>
> >>
> >>
> >> --
> >> 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
> >>
> >
>