Re: [eigen] Positive Definitenes?

[Gabriel <gabrielvc@xxxxxxxxx>]

Thanks for your answers, I will check the approaches to check for efficiency. This operation would have to be done several times, and I do need to solve a matrix equation K x = b, with K the matrix, and b a known vector, and this is done a lot of times. 

Is there an error handler implemented? In my code this operation is performed hundreds of times and I would need to automatize some sort of workaround when the matrix is not positive definite. This would signal an error in my code, my matrices have to bee p.d. all the time, so I would implement something to forget the systems in which p.d. gets "lost". 

Gabriel

On Wed, Mar 3, 2010 at 6:56 AM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:

2010/3/3 Cyril Flaig <cflaig@xxxxxxxxxxx>:

> On 2010-03-02 19:27, Benoit Jacob wrote:
>> 2010/3/2 Cyril Flaig <cflaig@xxxxxxxxxxx>:
>>> The Cholesky decomposition works only if the matrix is positive
>>> definite. If the decomposition fails then eigen sets a
>>> m_isPositiveDefinite to false, doesn't it?
>>>
>>> Or is this deprecated and not used in the new version?
>>
>> This is deprecated indeed.
>
> As far as I know. The fastest way to determine the postive definitnes is
> to check the diagonal if all entries are >=0.

This is indeed a necessary condition for positiveness.

> If this is true then
> attempt a Cholesky decomposition. If it exists then the matrix is
> positive definite.

The problem with this approach is that it's an all-or-nothing test
that one has to perform at the time of the decomposition itself.
Making this useful in practice would require us to let the user pass a
choice of a threshold at the time of the decomposition itself (so an
API change) and even then, that would be pretty bad as, if the user
passes a higher threshold, he compromises the accuracy of a subsequent
solve(). So this forces a compromise between the invertibility check
and the precision of solve().

Benoit

>
> -cyril
>
>

-- 
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