Thanks Patrick, this is useful. all the best --cjc On 14 February 2017 at 16:29, Patrick Farrell < patrick.farrell@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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