[firedrake] square root of matrix

[Colin Cotter]

Thanks Patrick, this is useful.

all the best
--cjc

On 14 February 2017 at 16:29, Patrick Farrell <
patrick.farrell at maths.ox.ac.uk> wrote:

> On 14/02/17 08:21, Colin Cotter wrote:
> > Dear all,
> >   For weird reasons I'd like to solve Ux = y where U is the Cholesky
> square root of a given symmetric positive definite matrix A. Is there a way
> to abuse the
> > PETSc solver interface into doing this?
> >
>
> Hi Colin,
>
> I have partial information about your question.
>
> I need to access the Cholesky factorisation data to verify
> the second-order sufficiency conditions for constrained minimisation
> problems. (I'm using dolfin, but it shouldn't matter very much
> for your purposes.) My petsc4py code looks like
>
>          pc = PETSc.PC().create(comm)
>          pc.setOperators(A.mat())
>          pc.setType("cholesky")
>          pc.setFactorSolverPackage("mumps")
>          pc.setUp()
>
> to calculate the Cholesky factorisation, then
>
>          F = pc.getFactorMatrix()
>          (neg, zero, pos) = F.getInertia()
>
> to compute the inertia of the matrix. (I also need
> some MUMPS options, but I presume you don't care about
> these, since you're not asking it to compute the inertia.)
>
> Maybe you can get the sparse matrix representation out of
> F and solve a linear system with it, who knows.
>
> Cheerio,
>
> Patrick
>
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-- 
http://www.imperial.ac.uk/people/colin.cotter

www.cambridge.org/9781107663916
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