matrix inversion

[Randall Mackie]

Thanks Barry,

I didn't realize you guys had already been in communication, but now
that I know that, perhaps I can help him by looking at what you sent.

Randy


Barry Smith wrote:
>    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
>>>>
>>>>
>>>
>>
> 

-- 
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