Re: matrix inversion

[Randall Mackie <randy@xxxxxxxxxxxx>]

Matt,

I suspect it is my collegue who asked the earlier questions about
matrix inverses this week, although I didn't realize that until
after I sent my original message.

I also suggested he just get the LU factorizations, but he insists
he needs the actual values to embed in another larger system
he'll solve.

I suppose that with the LU factorizations, you can just do
successive solves with a vector with zeros and a 1 in the appropriate
place to generate the elements you need, no?

I've asked him for more clarification on what he needs exactly.

Thanks, Randy


Matthew Knepley wrote:
> On 9/21/07, Randall Mackie <randy@xxxxxxxxxxxx> wrote:
> > Matt,
> >
> > There may be very valid reasons why one would want a matrix inverse,
> > say in the context of solving optimizations where you need the
> > inverse of the covariance matrix, and you need those values to
> > embed in another system.
>
> I do not agree. What are you going to do with the inverse that cannot be
> done with LU? Backsolves against a matrix are commonplace.
>
>   Matt
>
> > In this case, just getting the action of the inverse times a vector
> > is not what is needed.
> >
> > Randy
> >
> >
> > Matthew Knepley wrote:
> > > On 9/21/07, Randall Mackie <randy@xxxxxxxxxxxx> wrote:
> > > > I have a collegue who is considering to use PETSc for programming
> > > > his problem. He would like to know if you can get the actual
> > > > inverse of a matrix, because this inverse is embedded in another
> > > > larger system that is then solved.
> > > >
> > > > I suppose that if you solve the system directly, say with SuperLU
> > > > or MUMPS, you could get the actual inverse? I looked briefly through
> > > > the manual and documentation, but it didn't jump out at me.
> > > This makes several time this week people have asked for inverses. Never
> > > never never use the inverse. Its not stable. The storage blows up. That is
> > > why factorizations were invented. Numerical analysis courses have failed
> > > the country entirely. Just use a KSP and tell it -ksp_type preonly -pc_type lu
> > > and then you can customize the matrix type for different solvers. KSPSolve()
> > > will apply the matrix. If you want to get the action on an entire matrix, this
> > > is dense and we would have to put in the BLAS3 triangular solve calls.
> > >
> > >   Matt
> > >
> > > > Any advice here?
> > > >
> > > > Thanks, Randy
> > > >
> > > > --
> > > > Randall Mackie
> > > > GSY-USA, Inc.
> > > > PMB# 643
> > > > 2261 Market St.,
> > > > San Francisco, CA 94114-1600
> > > > Tel (415) 469-8649
> > > > Fax (415) 469-5044
> > > >
> > > > California Registered Geophysicist
> > > > License No. GP 1034
> > --
> > Randall Mackie
> > GSY-USA, Inc.
> > PMB# 643
> > 2261 Market St.,
> > San Francisco, CA 94114-1600
> > Tel (415) 469-8649
> > Fax (415) 469-5044
> >
> > California Registered Geophysicist
> > License No. GP 1034

--
Randall Mackie
GSY-USA, Inc.
PMB# 643
2261 Market St.,
San Francisco, CA 94114-1600
Tel (415) 469-8649
Fax (415) 469-5044

California Registered Geophysicist
License No. GP 1034