[petsc-users] J^T J p calculation

[Matthew Knepley]

On Thu, Apr 9, 2020 at 3:41 PM Park, Heeho via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Hi PETSc developers,
>
>
> I am trying to formulate
>
>
> p^T J^T J p
>
>
> where p is a solution vector length n, J is Jacobian n-by-n matrix.
>
>
> Ref: https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm under
> Large-scale optimization
>
>
> It is known that for parallel computations, the best way to perform this
> computation (with csr matrix) is
>
>
> J^T J p = SUM_i [ c_i ( c_i dot p) ] which results in a vector.
>
I don't think so. Why not just do

  y = J p

  y^t y = p^T J^T J p

  Thanks,

    Matt


> In PFLOTRAN, we use mpibaij matrix. I could not find a PETSc command to
> perform this with one command.
>
> Is there one I couldn't find? if not, is using MATGETROW with C for-loop a
> good way to do this?
>
>
> I currently use, MatMult(J,p,w); MatMultTranspose(J,w,w2);
> VecDotRealPart(p,w2);
>
>
> Best,
>
>
> Heeho Daniel Park
>
> ! ------------------------------------ !
> Sandia National Laboratories
> Org: 08844, R&D
> Work: 505-844-1319
> ! ------------------------------------ !
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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