Re: [eigen] first benchmark of large and sparse matrix

[Benoît Jacob <jacob@xxxxxxxxxxxxxxx>]

On Monday 23 June 2008 10:13:37 Gael Guennebaud wrote:
> On Mon, Jun 23, 2008 at 7:30 AM, Benoît Jacob <jacob@xxxxxxxxxxxxxxx> wrote:
> > On Monday 23 June 2008 07:05:30 Benoît Jacob wrote:
> >> this is of high interest for Krita and for Step and probably has
> >> countless interesting applications
> >
> > I forgot to mention that support for sparse matrices should be of high
> > interest to OpenBabel (chemistry lib, also considering eigen2): if I
> > remember well they sometimes apply solving algorithms to the adjacency
> > matrix of a molecule, so for a molecule with N atoms the matrix is NxN
> > and has 2N nonzero entries. As far as I remember they used to apply dense
> > algorithms, so N^3 complexity which is only doable for small N (like
> > 10^2) while some molecules they deal with have up to 10^5 atoms.
>
> hm... if there are only 2N nonzero entries then using a sparse matrix
> is  pointless:

I don't know much about sparse matrices, I believed that the less nonzero 
entries the more sense it made to use a sparse matrix. 

> the overhead is one int per nonzero entry.

Precisely, since there are few nonzero entries, this is acceptable!

Indeed, if the entries are only 0 and 1 then it is not optimal to store as a 
sparse matrix, but still, that is already quite good and far better than 
dense storage; moreover, I don't know if chemists do that, but at least in 
math it's useful to work with adjacency matrices of graphs with arbitrary 
values associated to graph edges, so in this case it's really a sparse 
matrix.

> Also, I think it's very important to support natively linear system
> solvers as I know many users would never accept a dependency on
> another lib.... especially if this lib depends itself on lapack that
> is the case of most of them.

OK. Let's see if we can use GMM++ code: GMM++ is LGPL 2.1-or-later.

http://www.gnu.org/licenses/gpl-faq.html#AllCompatibility

- normally, we can't copy and paste their code
- but we can write to the author, he's cool
- or we can ship some GMM++ code in separate files, without relicensing.

Cheers,
Benoit

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