Re: ANN: Ada 2005 Math Extensions, 20100901 release

[Ada novice <ycalleecharan@gmx.com>]

On Sep 5, 2:32 am, jonathan <johns...@googlemail.com> wrote:
> On Sep 4, 12:12 pm, Ada novice <ycalleecha...@gmx.com> wrote:
>
> > I tried compiling test_extensions.adb but I get an error message:
>
> >     20. with Ada.Numerics.Generic_Complex_Arrays;
> >     21. with Ada.Numerics.Generic_Arrays;
> >              |
> >         >>> "Ada.Numerics.Generic_Arrays" is not a predefined library
> > unit
>
> > ...
> > YC
>
> Don't worry, I got the same error message, knew I would
> not be smart enough to fix it, and just replaced all
> the dots with underscores. Now my version is named
> ada_numerics_generic_arrays.adb

Did you change the occurrences of the dots in the files :
ada-numerics-generic_arrays.ad(b,s)?

>
> I got around to attaching my suite of test matrices to
> the new LAPACK binding.  

This is exciting news.

A few rambling observations..
> First the good news is that the binding seems to work
> the way it's supposed to .. no problems to report there.
> This is good news because it is much easier to fill in
> missing LAPACK routines now that Simon has shown us how
> to do it. In particular I seem to recall that you (YC)
> requested a routine for generalized Eigen systems:
>    A*v = lambda*B*v
> for matrices A and B. That should be easy to add to
> the present interface.

Yes I did propose that earlier.


The not-so-good news is that I
> tested Lapack's eigendecomposition for real general
> (non-symmetric) matrices, dgeev, and I was surprized
> to see it fail catastrophically on 3
> or 4 matrices in the test suite, and perform poorly
> on another 7 or 8.  It worked fine on small matrices
> (N x N = 16 x 16) but degraded rapidly for larger N,
> so I don't think I am misinterpreting the test results.
> This was so surprizing I dusted off an Ada translation of
> the ancient EISPACK hqr2.f I did a while ago. It never
> worked very well either, so I decided to throw out the
> EISPACK Hessenberg reduction and replace it with one based
> on Givens rotations. Now it works correctly on all the
> matrices in the test suite. I've tested it up to
> 2901 x 2901 matrices without problem (it took mere 18.3
> hours on 60 matrices). I've always liked Givens rotations!
> The package is called Peters_Eigen, (after the original
> author) and I put it in a public directory:

I'm not currently working with so large matrices. It was interesting
to
read how large matrices needed different methods. On a related note,
in
Finite Element Analysis (FEM), usually we end up with sparse matrices.
Does Ada makes provision for such type of matrices? I didn't come
across
other sources mentioning sparse matrices except in Feldman's Software
Construction and Data Structures with Ada 95 textbook.

>
> http://web.am.qub.ac.uk/users/j.parker/miscellany/eig_stuff/
>
> It's quickly written and lightly tested, but you may want
> to play with it... instructions for compiling the test/
> demo routine peters_eigen_test_1.adb with gnatmake on the
> command line are in the README ... no LAPACK, very easy.
> I did a test on 787 x 787 matrices comparing LAPACK with
> Peters_Eigen. Results are in the file bench1.txt in the
> public directory.  The LAPACK test procedure is identical
> to the Peters_Eigen test procedure.  The LAPACK run
> took 550 seconds on the 60 matrices. Peters_Eigen took
> 676 seconds.
>
> J.

Thanks for your efforts.


cheers
YC