matrix inversion

[Barry Smith]

   Randy,

    I have sent your user an example of how it may be done sequentially.
We can add support for doing it in parallel but I doubt that his matrix
is big enough to need it (more than say 2000 by 2000).

  Barry


On Fri, 21 Sep 2007, Randall Mackie wrote:

> 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 at geosystem.us> 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 at geosystem.us> 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
> > > 
> > > 
> > 
> > 
> 
>