Re: Ann: Mathpaqs, release Feb. 2011

[Gautier write-only <gautier_niouzes@hotmail.com>]

On 22 fév, 00:59, "Nasser M. Abbasi" <n...@12000.org> wrote:

> I do not use Ada now, but I was looking at your ConjGrad solver,
> and was just wondering, why new Matrix and Vectors are
> defined in that package, since with Ada now, there exist
> such types now?
>
> For example, in  ConjGrad.ads it says
>
> type Vector is array(Index range <>) of Real
>
> type Any_matrix (<>) is private;

These types are *not* defined in the package (since they appear before
the keyword "package" :-) ). They are imported as generic parameters.
So you can use whatever vector and matrix types, including Ada 2005's
Real_Vector and Real_Matrix.

So I guess the next question would be: why not using Real_Vector and
Real_Matrix by default ? My answer would be:
- you can use the package also with an Ada 95 compiler, even one which
doesn't yet has been extended with the new 2005 math packages
- more important: you can use non-trivial matrix types, like band
matrices or sparse matrices.

Consider the example here:
  http://www.youtube.com/watch?v=_NIZmYd8oUw
The mesh is 220x220 points, which is still probably a "toy" size for
finite element problems. But you have then 220*220=48,400 dimensions
and then 48400*48400=2,342,560,000 cells in a matrix like Real_Matrix,
which makes around 16 GB in storage with double precision! Even if you
have enough RAM on your computer, the solver might run very slowly
because of poor CPU cache-ing (and perhaps also because of the 2
billion multiplications and additions for each iteration!).
A sparse matrix storage takes a few MB instead.

Regards
Gautier