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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] LU decomposition with partial pivoting ?
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Tue, 11 May 2010 11:51:30 -0400
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partial pivoting LU for non-square is not a big priority for a couple
of reasons. It needs to be done differently depending on whether
rows>cols or cols>rows. LAPACK doesn't do it (afaicr). Then the use
cases are very few. Indeed, partial pivoting LU is mostly used for
solving, but exact solving on rectangular matrices is rather uncommon,
i.e. with rectangular matrices on typically uses least squares
solving.
Benoit
2010/5/11 <vincent.lejeune@xxxxxxxxxx>:
>
> Hi,
>
>
>
> Eigen tells me that it does not support partial pivoting for non square
>
> Matrix...Is this a definitive decision from dev team, or will it change in
>
> a future release ?
>
>
>
> On Wed, 5 May 2010 16:52:52 +0200, Gael Guennebaud
>
> <gael.guennebaud@xxxxxxxxx> wrote:
>
>> Hi,
>
>>
>
>> in the devel branch we already have partial pivoting LU with a quite
>
>> efficient blocked implementation.
>
>>
>
>> I strongly encourage you to switch to the devel branch. Perhaps, the
>
> only
>
>> annoying thing with the devel branch is that the doc is not up to date
>
>> everywhere...
>
>>
>
>> gael.
>
>>
>
>>
>
>>
>
>> On Wed, May 5, 2010 at 4:41 PM, <vincent.lejeune@xxxxxxxxxx> wrote:
>
>>
>
>>>
>
>>> Hi,
>
>>>
>
>>>
>
>>>
>
>>> it seems that the LU decomposition routine provided by Eigen are doing
>
>>>
>
>>> full pivoting.
>
>>>
>
>>> However, LU decomposition in Lapack is done with only partial pivoting
>
>>>
>
>>> (see DGETRF).
>
>>>
>
>>>
>
>>>
>
>>> I was wondering if it was planned to expose a routine that do only
>
>>> partial
>
>>>
>
>>> pivoting (ie swap of rows only, not columns).
>
>>>
>
>>> Although full pivoting give better result in term of precisions, it is
>
>>>
>
>>> usually slower, because of cache unfriendlyness. On the other hand,
>
>>> partial
>
>>>
>
>>> pivoting allow to "tile" the LU algorithm, allowing more
>
> parallelisation
>
>>>
>
>>> for very big matrix...It would be easier to use gpu computing
>
>>> capabilities
>
>>>
>
>>> if the algorithm do partial pivoting only.
>
>>>
>
>>>
>
>>>
>
>>> Regards,
>
>>>
>
>>> Vincent.
>
>>>
>
>>>
>
>>>
>
>
>