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 > >> > > >
