Re: [eigen] Skyline matrix

[guillaume saupin <guillaume.saupin@xxxxxx>]

Gael Guennebaud a écrit :
> this is not an easy question because we are still unsure how to manage 
> efficiently and with minimal code all these kind of "special" matrices.
>
> Of course an easy solution would be to make it inherit 
> SparseMatrixBase and let the generic algorithms based on sparse 
> iterators do the job. However, this approach won't be optimal because 
> the iterators won't take advantage of the specificity of a 
> SkylineMatrix which, e.g., should allow vectorization.
>
> Actually skyline matrices are very similar to banded matrices, and in 
> particular it seems to me that they are similar enough to share the 
> same algorithms. So for instance these two kind of matrices could 
> inherit the same matrix base and the algorithms could be implemented 
> in a generic way via the concept of "range inner vector" which is a 
> column (or a row) vector with an associated start index... We also 
> need efficient basic operators dealing with such vector. E.g. the 
> addition of two such vector can be efficiently done by first copying 
> the non overlapping part (start and end), and then sum the overlapping 
> part using Eigen's core module feature.

The way we implemented skyline matrix is not really similar to what is 
usually done for banded matrix, as we store the diagonal, the upper, and 
the lower elements in separate arrays. This way, we can achieve quite 
efficient LU decomposition (and solving) due to coherent  memory accesses.

So I don't think that our algorithms share common features with band 
matrix algorithms. They seem closer to what can be done with diagonal 
matrices.

Anyway, I've used the SparseMatrix code as a base for my SkylineMatrix 
code. Currently it only supports very basic operations. I'll implement 
the LU decomposition soon. I will also try to use vectorization.


guillaume
> These are just some initial thoughts and the discussion is very open!
>
> gael
>
> On Mon, Oct 19, 2009 at 12:55 PM, guillaume saupin 
> <guillaume.saupin@xxxxxx <mailto:guillaume.saupin@xxxxxx>> wrote:
>
>     Hello,
>
>     We are planning to use your library in our projects, but we need a
>     skyline matrix. Therefore I'd like to implement one for eigen, but
>     I don't now where to start.
>
>     Is there a specific class that can be a good starting point /
>     skeleton to start with ? The SparseMatrixBase might be a good choice.
>     Should this SkylineMatrix inherit from SparseMatrixBase, or be a
>     separate class ?
>
>     Thanks,
>
>     guillaume