Re: [eigen] Sparse Matrices in Eigen

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

On Fri, Jun 18, 2010 at 8:05 PM, Sameer Agarwal
<sameeragarwal@xxxxxxxxxx> wrote:
> HI Gael,
> Thanks for the detailed reply.
>
>>
>> yes, I agree such construction method can be quite convenient.
>> Regarding the API, maybe it would be better to directly have
>> SparseMatrix constructors taking a list of Triplet as follow:
>>
>> template<typename TripletIterator>
>> SparseMatrix(Index rows, Index cols, const TripletIterator& begin,
>> const TripletIterator& end);
>>
>> Where typeof(*TripletIterator) must provide the rowId(), columnId(),
>> and value() functions (or whatever other names if you don't like
>> them). Of course we would provide a default template Triplet class.
>>
>> Here TripletIterator could be std::vector<Triplet>::iterator, Triplet*,
>> etc....
>>
>> Do you really want to be able to use three different buffers ?
>
> As I mentioned in my other emails, three buffers is what we get from the
> fortran/matlab/cholmod world. Also, it is quite often the case for
> optimization algorithms that the sparsity remains the same and only the
> values array changes. I like being able to just access that instead of
> passing the whole iterator passed around. Also it allows me to store and
> access contiguous blocks in the values array. A high level interface like an
> iterator is nice, but I would like a low level three buffer interface too.

ah indeed, decoupling the sparsity and the values is very important.

>>
>> > vector + scalar (maybe)
>> > vector - scalar (maybe)
>>
>> not available and I'm not sure it makes sense because theoretically
>> that means all zeros become equal to the scalar, and so the matrix
>> become dense. Maybe we could offer a method to return the list of non
>> zeros as an Eigen dense vector, so that the user can do all kind of
>> low level operations on these values.
>
> An iterator over the non-zero values of the sparse object...
>
>>
>> > One direction we could look into is wrapping the OSKI library
>> > http://bebop.cs.berkeley.edu/oski/
>>
>> yes, I've checked a few recent paper on that topic, but it seems the
>> only way to really speed up thing is through an analysis of the sparse
>> matrix which is often as expensive than the product itself, and so the
>> only situation to get significant speed up is when the spmv product is
>> performed multiple times on a matrix having the same nonzero pattern.
>> Nevertheless, I'll bench oski.
>
> So OSKI only tunes the multiplies if it thinks the computational effort is
> worth it. You can give it hints about the work load and such.

Yes I saw that. In my first experiments, it seems that tuning can help
in very special cases only, and the tuning step is very very costly,
like 50 times the cost of a single spmv.. I'm really not sure it's
worth the effort supporting OSKI as an optional backend.

Note that creating an oski matrix from an Eigen one is trivial:

oski_matrix om = oski_CreateMatCSC(sm._outerIndexPtr(),
sm._innerIndexPtr(), sm._valuePtr(), sm.rows(), sm.cols(),
SHARE_INPUTMAT, 1, INDEX_ZERO_BASED);

>>
>> > 3. Iterative Methods
>> > A library of sparse iterative solvers built on top of the sparse matrix
>> > support. This may or may not be part of Eigen proper. A very useful
>> > thing to
>> > have here are implementations of a variety of basic preconditioning
>> > schemes.
>> > Not just for square/symmetric systems but also for rectangular systems
>> > and
>> > non-symmetric systems.
>>
>> This is definitely a must to have, and this is also a good way to test
>> the basic API is fine. Recently, Daniel Lowengrub kindly proposed his
>> help to improve the Sparse module, and I oriented him to this
>> particular task.
>
> Is there a plan for what you/Daniel plan to do on this front?

Nothing precise yet. I guess that when Daniel will be ready to start
he will start a discussion on this list. Of course, that not mean you
have to censure yourself during the meantime ;)

gael

> Sameer
>