Re: [eigen] Status of givens QR decomposition

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On Tue, Jan 26, 2010 at 1:52 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
2010/1/26 Thomas Capricelli <orzel@xxxxxxxxxxxxxxx>:
> As a following to:
> I'd like to say that i have a very important use case for givens-QR with big matrices in the NonlinearOptimization module. This is useful in the variant of the Levenberg Marquardt algorithm for very big matrices, so-called 'storage efficient': the qr decomposition is done with givens rotation, presumably because this is the only decomposition that can be done incrementally : the matrix to decompose is not known as a whole, but is constructed line by line, 'updating' the qr decomposition and deleting the line.


> Andrea, Benoit, what is the status of this fork ? As I have write permission, I've merged with mainline once or twice, but the fork seems abandoned... was there a use case ? not anymore ?

I haven't touched it in a long time. The original use case was small
matrices, where it is faster than householder. Now you mention large
matrices that are not fully known in advance: interesting.

Finally, about the old debate about whether to store the list of
givens permutations, let me mention that in the different setting of
SVD, I have now decide to try this approach too. It's different as I'm
only storing N Givens rotations per sweep, as opposed to N^2/2 in
GivensQR, but perhaps still worth mentioning.

Let's revive this thread a little bit :)

I'm curious to have a general idea of the solution method you want to implement here (SVD based on Givens rotations, storing only N rotations/sweep). Is there a paper that you could refer me to?. One sweet thing of using Givens rotations (as opposed to say Householder reflections) is that their computation can be easily parallelized across multiple cores.

On a separate note, I'd like to ask if there would be interest in having a SVD implementation tailored for the case of using one decomposition instance to solve multiple "similar" problems. By similar I'm referring to solve initially for matrix A, and then for a perturbed  matrix A + deltaA, and so on. In such cases, results from previous computations can greatly increase performance. The KDL developers [1] brought to my attention a paper that details this solution strategy (also based on Givens rotations), which can be found here [2]. They have also a working implementation [3] that uses eigen matrices, but its internals are not "eigenized".

Finally, I wanted to ask the more general question of what SVD implementations will likely make it to 3.0.




> btw, Am I the only one needing givens QR decompozition on the list ? anyone ?

It is for sure needed at least by everyone needing QR decomposition of
very small matrices.

If you need to make intrusive changes in Andrea's fork, perhaps it's
easiest for you to fork it, you can then re-merge with Andrea if he
expresses agreement with your changes. I personally don't have time
right now to think about that... :(


Adolfo Rodríguez Tsouroukdissian, Ph. D.

Robotics engineer
Tel. +34.93.414.53.47
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