matrix package with Ada

matrix package with Ada

[fitta]

Hi, being new to Ada I'm looking for a matrix package that can compute
eigenvalues and eigenvectors. I understand that Ada 05 can only do
this for symmetric matrices. I read that there was one package --- Ada
95 matrix package that was developed at Drexel University. It is
supposed to be located at:

http://dflwww.ece.drexel.edu/

but the link is dead. A search on the web has directed me to this
site:

http://www.taygeta.com/ada.html

but the compressed file for Ada 95 matrix package is corrupted.


Does anyone know where I can find the above-mentioned package? And are
there other alternatives or other packages?


Thanks.

Re: matrix package with Ada

[MRE]

Hi Fitta,

downloading the packages from http://www.taygeta.com/ada.html and
decompressing worked without a problem for me.

Everything compiled nicely and works.

Maybe you could try it again?

Best regards,

Marc

On 10 Jul., 15:25, fitta <fit...@hotmail.com> wrote:
> Hi, being new to Ada I'm looking for a matrix package that can compute
> eigenvalues and eigenvectors. I understand that Ada 05 can only do
> this for symmetric matrices. I read that there was one package --- Ada
> 95 matrix package that was developed at Drexel University. It is
> supposed to be located at:
>
> http://dflwww.ece.drexel.edu/
>
> but the link is dead. A search on the web has directed me to this
> site:
>
> http://www.taygeta.com/ada.html
>
> but the compressed file for Ada 95 matrix package is corrupted.
>
> Does anyone know where I can find the above-mentioned package? And are
> there other alternatives or other packages?
>
> Thanks.

Re: matrix package with Ada

[fitta]

Thanks a lot. I could unzip it now. I have been using PeaZip to unzip
the package and it wasn't working. I've tried with 7-zip and the
decompression went fine. Thanks for letting me know---I had blind
faith in PeaZip! So I see:
Ada 95 Matrix Math Package
Version 1.01
First Release, August 1996
Current Release, September 1996

and

also that a to-do for this package remains: implement eigenvectors/
eigenvalues, singular value decomposition, and inverses for complex
matrices.

I haven't try the package yet but I'll hope it'll work for a real non-
symmetric matrix.


Thanks a lot again.

Re: matrix package with Ada

[tmoran]

> Version 1.01
> First Release, August 1996
> Current Release, September 1996

The version I have (apparently downloaded in 2005) has

 Version 1.02
 First Release, August 1996
 Current Release, December 1996
Changes since 1.01:
* fixed a bug that could allow exceptions to occur with vector and
  matrix indices at the extreme limits of Integer (thanks to Mars
  Gralia for notifying me of this)
* some reoganization of algorithms in Generic_Real_Arrays.Operations
* cosmetic fix to real_arrays_operations_test to print final
  results message

The to-do list is the same, plus
 * adapt some of the very robust LAPACK algorithms to the package

Re: matrix package with Ada

[Simon Wright]

tmoran@acm.org writes:

>> Version 1.01
>> First Release, August 1996
>> Current Release, September 1996

This is the one from http://www.taygeta.com/ada.html

> The version I have (apparently downloaded in 2005) has
>
>  Version 1.02
>  First Release, August 1996
>  Current Release, December 1996
> Changes since 1.01:
> * fixed a bug that could allow exceptions to occur with vector and
>   matrix indices at the extreme limits of Integer (thanks to Mars
>   Gralia for notifying me of this)
> * some reoganization of algorithms in Generic_Real_Arrays.Operations
> * cosmetic fix to real_arrays_operations_test to print final
>   results message
>
> The to-do list is the same, plus
>  * adapt some of the very robust LAPACK algorithms to the package

This is the one from http://archive.adaic.com/ase/ase02_02/comps/math1/

Re: matrix package with Ada

[Gautier write-only]

> And are there other alternatives or other packages?

Look there - excellent stuff:
  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/
The most amazing: add some "Ada." for the basic matrix packages
referenced, and you get Ada 2005 compatibility.

G.

Re: matrix package with Ada

[Gautier write-only]

On 10 juil, 17:42, fitta <fit...@hotmail.com> wrote:
> Thanks a lot. I could unzip it now. I have been using PeaZip to unzip
> the package and it wasn't working. I've tried with 7-zip and the
> decompression went fine. Thanks for letting me know---I had blind
> faith in PeaZip!

Only trust Zip-Ada ;-)

Re: matrix package with Ada

[Jerry]

On Jul 10, 1:22 pm, Gautier write-only <gautier_niou...@hotmail.com>
wrote:
> > And are there other alternatives or other packages?
>
> Look there - excellent stuff:
>  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/

Wow.

> The most amazing: add some "Ada." for the basic matrix packages
> referenced, and you get Ada 2005 compatibility.

Would you care to elaborate? It seems that the main thing would be to
use the declarations described in Annex G.3.

Jerry

>
> G.

Re: matrix package with Ada

[Jerry]

On Jul 10, 6:25 am, fitta <fit...@hotmail.com> wrote:
> Hi, being new to Ada I'm looking for a matrix package that can compute
> eigenvalues and eigenvectors. I understand that Ada 05 can only do
> this for symmetric matrices. I read that there was one package --- Ada
> 95 matrix package that was developed at Drexel University. It is
> supposed to be located at:
>
> http://dflwww.ece.drexel.edu/
>
> but the link is dead. A search on the web has directed me to this
> site:
>
> http://www.taygeta.com/ada.html
>
> but the compressed file for Ada 95 matrix package is corrupted.
>
> Does anyone know where I can find the above-mentioned package? And are
> there other alternatives or other packages?

Google

GSL Gnu Scientific Library Ada

There has been a SWIG effort for GSL, the Gnu Scientific Library. Has
anyone looked used this binding which was reported on this list?

Also, I frequently fall back to Numerical Recipes, translating from
Pascal to Ada.

Jerry
>
> Thanks.

Re: matrix package with Ada

[Ada novice]

That's interesting: a GSL Gnu Scientific Library for Ada.
Unfortunately it seems that the internet has not much information on
this binding.

YC

Re: matrix package with Ada

[Ada novice]

On Jul 10, 10:22 pm, Gautier write-only <gautier_niou...@hotmail.com>
wrote:
> > And are there other alternatives or other packages?
>
> Look there - excellent stuff:
>  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/
> The most amazing: add some "Ada." for the basic matrix packages
> referenced, and you get Ada 2005 compatibility.
>
> G.

I've tried to compile the file test_generic_complex_eigenvalues.ada
provided in this package (http://www.csee.umbc.edu/~squire/adaclass/
gnatmath95/) but it doesn't compile successfully. And The matrix
package from Drexel doesn't have any eigenvalues/eigenvectors
computation routine at all.

Looking at all this, I'm tempted to say how silly it is that Ada
doesn't provide good numerics capabilities. Ada 05 brought a big
improvement with more vector and matrix operations though it can't
handle the eigenvalues computation of a non-symmetric matrix. The next
version of Ada I read will be out in 2 years. I hope that there will
be better facilities for scientific programming in Ada than there is
today. Those on the Ada community should be made aware of the need for
more scientific computing power in Ada.

There are many libraries for Fortran and C/C++ for numerical
computations while Ada doesn't seem to have a decent one. One cannot
expect people to switch to Ada if there are no good numerical
computing libraries. Ada has been here for more than 25 years now but
maybe has remained confined to military applications for many years.
However free compilers are out there since many years and I hope that
good programmers with good understanding of numerical methods will be
motivated to have bindings for Ada.

YC

Re: matrix package with Ada

[jonathan]

On Jul 12, 2:38 pm, Ada novice <po...@gmx.us> wrote:
> On Jul 10, 10:22 pm, Gautier write-only <gautier_niou...@hotmail.com>
> wrote:
>
> > > And are there other alternatives or other packages?
>
> > Look there - excellent stuff:
> >  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/
> > The most amazing: add some "Ada." for the basic matrix packages
> > referenced, and you get Ada 2005 compatibility.
>
> > G.
>
> I've tried to compile the file test_generic_complex_eigenvalues.ada
> provided in this package (http://www.csee.umbc.edu/~squire/adaclass/
> gnatmath95/) but it doesn't compile successfully. And The matrix
> package from Drexel doesn't have any eigenvalues/eigenvectors
> computation routine at all.
>
> Looking at all this, I'm tempted to say how silly it is that Ada
> doesn't provide good numerics capabilities. Ada 05 brought a big
> improvement with more vector and matrix operations though it can't
> handle the eigenvalues computation of a non-symmetric matrix. The next
> version of Ada I read will be out in 2 years. I hope that there will
> be better facilities for scientific programming in Ada than there is
> today. Those on the Ada community should be made aware of the need for
> more scientific computing power in Ada.
>
> There are many libraries for Fortran and C/C++ for numerical
> computations while Ada doesn't seem to have a decent one. One cannot
> expect people to switch to Ada if there are no good numerical
> computing libraries. Ada has been here for more than 25 years now but
> maybe has remained confined to military applications for many years.
> However free compilers are out there since many years and I hope that
> good programmers with good understanding of numerical methods will be
> motivated to have bindings for Ada.
>
> YC

OK, after a bit of trouble I got it to run (using the latest gnat/gcc
compiler). There's 1 bug to fix 1st: around line 150 of the package
body

    generic_complex_linear_equations.adb

you need to change a line to initialize X with a complex number.

  --X(N) := 0.0; -- change this to:
    X(N) := COMPOSE_FROM_CARTESIAN( 0.0 , 0.0 ) ;

Finally, if you using GNAT, the file names have to end in either
.adb or .ads

The instructions for that are at the top of each file. For example
the test procedure should end in .adb if you are using gnat.

Notice also that you have to download quite a few packages to get
the eig-stuff to work.  The compiler error messages should tell you
if you are missing anything.

Finally! The test routine is user unfriendly.  (I hope you fix it up
for the rest of us.) You have to enter numbers.  First enter the
size of the matrix
(type the number 2, then enter.)
then enter one by one the 4 elements of the complex matrix, say:
(1.0, 2.0)
(2.0, 2.2)
(3.0, 2.4)
(4.0, 2.6)

I'm just guessing that that is what the program wants, but
it seemed to run when I tried it.

J.




numbers.

Re: matrix package with Ada

[Ada novice]

On Jul 12, 5:13 pm, jonathan <johns...@googlemail.com> wrote:
> On Jul 12, 2:38 pm, Ada novice <po...@gmx.us> wrote:
>
>
>
> > On Jul 10, 10:22 pm, Gautier write-only <gautier_niou...@hotmail.com>
> > wrote:
>
> > > > And are there other alternatives or other packages?
>
> > > Look there - excellent stuff:
> > >  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/
> > > The most amazing: add some "Ada." for the basic matrix packages
> > > referenced, and you get Ada 2005 compatibility.
>
> > > G.
>
> > I've tried to compile the file test_generic_complex_eigenvalues.ada
> > provided in this package (http://www.csee.umbc.edu/~squire/adaclass/
> > gnatmath95/) but it doesn't compile successfully. And The matrix
> > package from Drexel doesn't have any eigenvalues/eigenvectors
> > computation routine at all.
>
> > Looking at all this, I'm tempted to say how silly it is that Ada
> > doesn't provide good numerics capabilities. Ada 05 brought a big
> > improvement with more vector and matrix operations though it can't
> > handle the eigenvalues computation of a non-symmetric matrix. The next
> > version of Ada I read will be out in 2 years. I hope that there will
> > be better facilities for scientific programming in Ada than there is
> > today. Those on the Ada community should be made aware of the need for
> > more scientific computing power in Ada.
>
> > There are many libraries for Fortran and C/C++ for numerical
> > computations while Ada doesn't seem to have a decent one. One cannot
> > expect people to switch to Ada if there are no good numerical
> > computing libraries. Ada has been here for more than 25 years now but
> > maybe has remained confined to military applications for many years.
> > However free compilers are out there since many years and I hope that
> > good programmers with good understanding of numerical methods will be
> > motivated to have bindings for Ada.
>
> > YC
>
> OK, after a bit of trouble I got it to run (using the latest gnat/gcc
> compiler). There's 1 bug to fix 1st: around line 150 of the package
> body
>
>     generic_complex_linear_equations.adb
>
> you need to change a line to initialize X with a complex number.
>
>   --X(N) := 0.0; -- change this to:
>     X(N) := COMPOSE_FROM_CARTESIAN( 0.0 , 0.0 ) ;
>
> Finally, if you using GNAT, the file names have to end in either
> .adb or .ads
>
> The instructions for that are at the top of each file. For example
> the test procedure should end in .adb if you are using gnat.
>
> Notice also that you have to download quite a few packages to get
> the eig-stuff to work.  The compiler error messages should tell you
> if you are missing anything.
>
> Finally! The test routine is user unfriendly.  (I hope you fix it up
> for the rest of us.) You have to enter numbers.  First enter the
> size of the matrix
> (type the number 2, then enter.)
> then enter one by one the 4 elements of the complex matrix, say:
> (1.0, 2.0)
> (2.0, 2.2)
> (3.0, 2.4)
> (4.0, 2.6)
>
> I'm just guessing that that is what the program wants, but
> it seemed to run when I tried it.
>
> J.
>
> numbers.

Many thanks for your kind efforts. Now it works fine. I'm using the
gnat compiler. I have made some quick tests with this package and
compared the results with those from Matlab. The results match for the
eigenvalues. I just need some more time to see how the eigenvectors
are scaled. It is indeed very nice to see at last a package which
delivers!

The program doesn't exit well however. When the program
(test_generic_complex_eigenvalues.ada) it will display the results but
in my GPS editor the line 102 is highlighted. This is where the
program stops. If the program would run fine then I would have finally
got this line displayed: DONE test_generic_complex_eigenvalues (at the
bottom of test_generic_complex_eigenvalues.ada). Do you have the same
problem?


I'm still a novice in Ada and still learning. This is why I couldn't
fixed the bug in the package myself. Thus I thank you much again for
looking into the problem. Yes it would be nice to be able to call the
routine from a main program. I will work on that when time permits but
first things first: I will have to check the scaling used for the
eigenvectors.


YC

Re: matrix package with Ada

[Simon Wright]

jonathan <johnscpg@googlemail.com> writes:

> Finally! The test routine is user unfriendly.  (I hope you fix it up
> for the rest of us.) You have to enter numbers.

Actually, there's a file test_generic_complex_eigenvalues.dat ...

Re: matrix package with Ada

[Simon Wright]

Ada novice <posts@gmx.us> writes:

> Looking at all this, I'm tempted to say how silly it is that Ada
> doesn't provide good numerics capabilities. Ada 05 brought a big
> improvement with more vector and matrix operations though it can't
> handle the eigenvalues computation of a non-symmetric matrix. The next
> version of Ada I read will be out in 2 years. I hope that there will
> be better facilities for scientific programming in Ada than there is
> today. Those on the Ada community should be made aware of the need for
> more scientific computing power in Ada.

I think you are too late: the draft for the relevant part of Ada2012 is
at http://www.ada-auth.org/standards/12rm/html/RM-G-3.html. I believe
that the gate closed in November '09.

The issues on Ada2005 are at http://www.ada-auth.org/AI05-SUMMARY.HTML,
none of them ask for extended matrix operations, so no wonder there's no
change.

I know this is a chicken-and-egg thing.

Re: matrix package with Ada

[jonathan]

On Jul 12, 9:13 pm, Simon Wright <si...@pushface.org> wrote:
> jonathan <johns...@googlemail.com> writes:
> > Finally! The test routine is user unfriendly.  (I hope you fix it up
> > for the rest of us.) You have to enter numbers.
>
> Actually, there's a file test_generic_complex_eigenvalues.dat ...

... and you have to enter these somehow, without prompt or
instruction.
In my Linux BASH shell it seems to be straightforward:

./test_generic_complex_eigenvalues <
test_generic_complex_eigenvalues.dat > output.txt

I hope that's right.  Now if I compare with the expected output,

diff  output.txt  test_generic_complex_eigenvalues.out

I find that all of the numbers in the 2 files are different.  Anything
to
worry about?  (I say no;-)

J.

Re: matrix package with Ada

[Ada novice]

On Jul 12, 11:09 pm, jonathan <johns...@googlemail.com> wrote:
> On Jul 12, 9:13 pm, Simon Wright <si...@pushface.org> wrote:
>
> > jonathan <johns...@googlemail.com> writes:
> > > Finally! The test routine is user unfriendly.  (I hope you fix it up
> > > for the rest of us.) You have to enter numbers.
>
> > Actually, there's a file test_generic_complex_eigenvalues.dat ...
>
> ... and you have to enter these somehow, without prompt or
> instruction.
> In my Linux BASH shell it seems to be straightforward:
>
> ./test_generic_complex_eigenvalues <
> test_generic_complex_eigenvalues.dat > output.txt
>
> I hope that's right.  Now if I compare with the expected output,
>
> diff  output.txt  test_generic_complex_eigenvalues.out
>
> I find that all of the numbers in the 2 files are different.  Anything
> to
> worry about?  (I say no;-)
>
> J.

I haven't had the time to test the dat file yet. Just one reminder
which I quote from an earlier post:

The program doesn't exit well however. When the program
(test_generic_complex_eigenvalues.ada) it will display the results but
in my GPS editor the line 102 is highlighted. This is where the
program stops. If the program would run fine then I would have finally
got this line displayed: DONE test_generic_complex_eigenvalues (at the
bottom of test_generic_complex_eigenvalues.ada).

Do you have the same problem?


YC

Re: matrix package with Ada

[jonathan]

On Jul 13, 8:07 am, Ada novice <po...@gmx.us> wrote:
> On Jul 12, 11:09 pm, jonathan <johns...@googlemail.com> wrote:
>
>
>
> > On Jul 12, 9:13 pm, Simon Wright <si...@pushface.org> wrote:
>
> > > jonathan <johns...@googlemail.com> writes:
> > > > Finally! The test routine is user unfriendly.  (I hope you fix it up
> > > > for the rest of us.) You have to enter numbers.
>
> > > Actually, there's a file test_generic_complex_eigenvalues.dat ...
>
> > ... and you have to enter these somehow, without prompt or
> > instruction.
> > In my Linux BASH shell it seems to be straightforward:
>
> > ./test_generic_complex_eigenvalues <
> > test_generic_complex_eigenvalues.dat > output.txt
>
> > I hope that's right.  Now if I compare with the expected output,
>
> > diff  output.txt  test_generic_complex_eigenvalues.out
>
> > I find that all of the numbers in the 2 files are different.  Anything
> > to
> > worry about?  (I say no;-)
>
> > J.
>
> I haven't had the time to test the dat file yet. Just one reminder
> which I quote from an earlier post:
>
> The program doesn't exit well however. When the program
> ( .ada) it will display the results but
> in my GPS editor the line 102 is highlighted. This is where the
> program stops. If the program would run fine then I would have finally
> got this line displayed: DONE test_generic_complex_eigenvalues (at the
> bottom of test_generic_complex_eigenvalues.ada).
>
> Do you have the same problem?
>
> YC

The way  test_generic_complex_eigenvalues  works is still mysterious
to me (I usually don't do things this way) so that's why I don't want
to say too much about how to use it. When I send the data file in
like this at the command line:
./test_generic_complex_eigenvalues <
test_generic_complex_eigenvalues.dat
then it seems to work, and for some reason stops without control-c.
When I copy the matrices from the data file with the mouse and then
paste them into command line prompt it works the 1st time, but
maybe not the second.

To me the important thing is that the tests pass, so we are off to
a good start!

J.

Re: matrix package with Ada

[Warren]

Gautier write-only expounded in news:af10bdc0-515e-4b17-a37c-47fa8809ff18
@y11g2000yqm.googlegroups.com:

>> And are there other alternatives or other packages?
> 
> Look there - excellent stuff:
>   http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/
> The most amazing: add some "Ada." for the basic matrix packages
> referenced, and you get Ada 2005 compatibility.
> 
> G.

There is some good stuff in there. I couldn't find a
source code license statement anywhere.  I wouldn't
mind using some of this in an open sourced project.

Warren

Re: matrix package with Ada

[Jeffrey R. Carter]

On 07/13/2010 10:43 AM, Ada novice wrote:
>
> Yes, I don't understand why it hangs. I've tried also the package from
> 83 but there the files are named "ada" which I've converted to "adb"
> but then it becomes a big mess to know which should be "adb" and which
> ones should be "ads" given the large amount of files in the library. I
> didn't know that Ada files had the extension "ada" in the past.

You can run gnatchop on the .ada files; it will output files with the correct 
GNAT-default names.

You can also delete irrelevant parts of the post you're replying to (as I have 
done here). That makes your posts easier to read and understand.

-- 
Jeff Carter
"When Roman engineers built a bridge, they had to stand under it
while the first legion marched across. If programmers today
worked under similar ground rules, they might well find
themselves getting much more interested in Ada!"
Robert Dewar
62

Re: matrix package with Ada

[Georg Bauhaus]

On 13.07.10 19:43, Ada novice wrote:

> Yes, I don't understand why it hangs. I've tried also the package from
> 83 but there the files are named "ada" which I've converted to "adb"
> but then it becomes a big mess to know which should be "adb" and which
> ones should be "ads" given the large amount of files in the library. I
> didn't know that Ada files had the extension "ada" in the past.

Ada source files can end in "ada", today, or in just
anything.  You can use GNAT's gnatname and gnatchop to convert
Ada source files to Ada source files that have one compilation unit
per file, ending in "ads" for specs and in "adb" for bodies.
This is how GNAT/GCC wants them.

Alternatively, you can write a ton of pragmas telling GNAT
where to find a unit, or add this info to a project file IIRC.

The "GNAT [GPL] User's Guide" has some background information.

"10 Handling Arbitrary File Naming Conventions Using `gnatname'
**************************************************************

"10.1 Arbitrary File Naming Conventions
======================================

"The GNAT compiler must be able to know the source file name of a
compilation unit.  When using the standard GNAT default file naming
conventions (`.ads' for specs, `.adb' for bodies), the GNAT compiler
does not need additional information.

"..."

Something like this should work:

mkdir for-gnat
cd for-gnat
for file in <list-of-original-files> loop
   gnatchop [-r] -w  file
end loop

Re: matrix package with Ada

[Ada novice]

I've tried earlier to delete the irrelevant parts but it seems I can't
do this once the message is posted. Anyhow, I've used
gnatchop [-r] -w  *.ada and I got like 19 warnings in the Ada 83
matrix
package. And the file test_generic_complex_eigenvalues.ada compiles
with lots of errors. So I've abandoned playing with it.

Thanks
YC

Re: matrix package with Ada

[Simon Wright]

jonathan <johnscpg@googlemail.com> writes:

> On Jul 12, 9:13 pm, Simon Wright <si...@pushface.org> wrote:
>> jonathan <johns...@googlemail.com> writes:
>> > Finally! The test routine is user unfriendly.  (I hope you fix it up
>> > for the rest of us.) You have to enter numbers.
>>
>> Actually, there's a file test_generic_complex_eigenvalues.dat ...
>
> ... and you have to enter these somehow, without prompt or
> instruction.

To a Unix fanboi, this seems obvious :-)

> In my Linux BASH shell it seems to be straightforward:
>
> ./test_generic_complex_eigenvalues <
> test_generic_complex_eigenvalues.dat > output.txt
>
> I hope that's right.  Now if I compare with the expected output,
>
> diff  output.txt  test_generic_complex_eigenvalues.out
>
> I find that all of the numbers in the 2 files are different.  Anything
> to worry about?  (I say no;-)

I found that not all of the numbers were different. Some of the
differences were very small. Sometimes vectors were given in the
opposite order (there's a note in the AI about that not being a
problem).

The internal checks did all pass, so presumably the differences are
tolerable. But IANAM so I don't know!

Re: matrix package with Ada

[Ada novice]

>
> I found that not all of the numbers were different. Some of the
> differences were very small. Sometimes vectors were given in the
> opposite order (there's a note in the AI about that not being a
> problem).

The eigenvalues are not given in an ascending order. Different
software implementations use different ways to present the eigenvalues
and eigenvectors (normalizations for the latter).

YC

Re: matrix package with Ada

[robin]

fitta wrote in message <445503bc-6b5c-4b60-b539-c51dcfa723bd@y11g2000yqm.googlegroups.com>...
>Thanks a lot. I could unzip it now. I have been using PeaZip to unzip
>the package and it wasn't working. I've tried with 7-zip and the
>decompression went fine. Thanks for letting me know---I had blind
>faith in PeaZip! So I see:
>Ada 95 Matrix Math Package
>Version 1.01
>First Release, August 1996
>Current Release, September 1996
>
>and
>
>also that a to-do for this package remains: implement eigenvectors/
>eigenvalues, singular value decomposition, and inverses for complex
>matrices.
>
>I haven't try the package yet but I'll hope it'll work for a real non-
>symmetric matrix.


If it doesn't, you could check out

http://members.dodo.com.au/~robin51/numeric.htm

which has several eigenvector algorithms in PL/I, including one for general matrixes.

Re: matrix package with Ada

[Simon Wright]

Ada novice <posts@gmx.us> writes:

>>
>> I found that not all of the numbers were different. Some of the
>> differences were very small. Sometimes vectors were given in the
>> opposite order (there's a note in the AI about that not being a
>> problem).
>
> The eigenvalues are not given in an ascending order. Different
> software implementations use different ways to present the eigenvalues
> and eigenvectors (normalizations for the latter).

But nominally these are the same software implementation. Still, the
.dat file is dated 31 Oct 1999, the .out file 26 May 2006, so the
implementation may well have changed in this respect.

Re: matrix package with Ada

[Randy Brukardt]

"Ada novice" <posts@gmx.us> wrote in message 
news:ec73f176-876e-4bcf-ab11-eed852129d34@x21g2000yqa.googlegroups.com...
...
> A friend uses F# for numerics and here also eigenvalue computation
> exists only for symmetric matrices as in Ada 05. I hope that in the
> next next Ada release, there would be more numeric facilities.

As far as I know, we haven't had a single request for more numeric 
facilities in Ada 2012, and I'm pretty sure that there are no open requests 
for the same.

If you want to see additional facilities, you need to ask (on Ada-Comment) 
and give examples of problems that you have that can't be solved with the 
current facilities. (Even better, would be to actively participate in the 
language revision process; we don't have enough numerics expertise to do a 
great job.)

In any case, the eigenvalue routines originally were supposed to work on all 
matrices. That was dropped as the algorithms to solve such things are 
supposedly suspect. Here's the discussion from AI95-0296-1 (which defines 
the G.3 packages):

We considered providing subprograms for the determination of eigenvalues and 
eigenvectors of general real and complex matrices. Such matrices can have 
complex eigenvalues and therefore provision for these would have to be in 
the complex package. However, there are mathematical difficulties with these 
general cases which are in strong contrast to the real symmetric and 
Hermitian matrices. Thus, Numerical Recipes by Press, Flannery, Teukolsky 
and Vetterling says regarding the real case:

"The algorithms for symmetric matrices ... are highly satisfactory in 
practice. By contrast, it is impossible to design equally satisfactory 
algorithms for the nonsymmetric case. There are two reasons for this. First, 
the eigenvalues of a
nonsymmetric matrix can be very sensitive to small changes in the matrix 
elements. Second, the matrix itself can be defective so that there is no 
complete set of eigenvectors. We emphasize that these difficulties are 
intrinsic properties of certain nonsymmetric matrices, and no numerical 
procedure can cure them."

Similar remarks apply to complex matrices where Hermitian matrices are 
well-behaved but non-Hermitian matrices can be troublesome.

In view of these computational difficulties and the fact that requiring the 
eigensystem of general matrices is uncommon, we decided not to provide such 
facilities.

[End of quote from AI95-0296-1.]

I recall that the situation is actually worse than reported here; some of 
the algorithms used may not terminate for some matricies. Algorithms that 
don't terminate aren't tolerable in the Ada predefined libraries!

I am no expert on numerics, but I have to wonder what other languages and/or 
packages do in such cases? Perhaps they just don't care (there is precedent 
for that; Ada takes great pains to define the accuracy of most of the 
numerical functions, most other languages say nothing at all). Clearly, this 
problem would need to be solved in some way before a general routine could 
in introduced (of course, the abstract above seems to imply that such a 
solution is impossible).

                                           Randy.

Re: matrix package with Ada

[Dmitry A. Kazakov]

On Mon, 19 Jul 2010 17:34:25 -0500, Randy Brukardt wrote:

> I am no expert on numerics, but I have to wonder what other languages and/or 
> packages do in such cases? Perhaps they just don't care (there is precedent 
> for that; Ada takes great pains to define the accuracy of most of the 
> numerical functions, most other languages say nothing at all). Clearly, this 
> problem would need to be solved in some way before a general routine could 
> in introduced (of course, the abstract above seems to imply that such a 
> solution is impossible).

"Accuracy requirements for the subprograms Solve, Inverse, Determinant,
Eigenvalues and Eigensystem are implementation defined."
      -- ARM G.3.1

I agree that it is not good from Ada design point of view. The requirement
should be: the accuracy is the precision of the corresponding Real type (or
else Constraint_Error).

This is an immense problem, especially for generic units, I have no idea
how to approach it using existing language means, not to mention
algorithmic issues.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

Re: matrix package with Ada

[Ada novice]

Thanks for all these information. I'll comment as appropriate:

On Jul 20, 12:34 am, "Randy Brukardt" <ra...@rrsoftware.com> wrote:

> As far as I know, we haven't had a single request for more numeric
> facilities in Ada 2012, and I'm pretty sure that there are no open requests
> for the same.

This can mean that people are still not much aware of Ada as a very
good and robust language for scientific programming. If we look at
recent publications, how many books discuss scientific computations
from the view of Ada, how many from the view say C++? For Ada, the sad
news is that we have practically no recent publication. There were
strong interest in the 1980s...e.g. the book Scientific Ada and
Applied Ada. What happened after that?

> If you want to see additional facilities, you need to ask (on Ada-Comment)
> and give examples of problems that you have that can't be solved with the
> current facilities. (Even better, would be to actively participate in the
> language revision process; we don't have enough numerics expertise to do a
> great job.)

I also don't have enough numerics expertise.  But if other languages
have successfully created numerical
libraries since 1970 or 1980, then I guess that the Ada committee
could do some outsourcing and put up a team that would look into the
matter. I read here that some Ada users translate the codes from the
book Numerical recipes in Pascal. Translation can be ok, but re-
writing the code in Ada's spirit using generics and so on would be far
better. If the Ada committee doesn't put efforts to create good
numerical libraries, then we can say that Ada won't be appealing to
someone needing numerical computations.

> In any case, the eigenvalue routines originally were supposed to work on all
> matrices. That was dropped as the algorithms to solve such things are
> supposedly suspect. Here's the discussion from AI95-0296-1 (which defines
> the G.3 packages):

> In view of these computational difficulties and the fact that requiring the
> eigensystem of general matrices is uncommon, we decided not to provide such
> facilities.

> [End of quote from AI95-0296-1.]

I don't think that eigensystem analysis of general non-symmetric
matrices is uncommon. Many real-life systems can only be modeled
better as non-symmetric systems and these abound in engineering. If
eigensystem analysis for only symmetric matrices would exist, then
many engineering achievements would not be possible. The fact that
other languages do provide support for non-symmetric matrices do
indicate that they are needed more often than one may think.

> I recall that the situation is actually worse than reported here; some of
> the algorithms used may not terminate for some matricies. Algorithms that
> don't terminate aren't tolerable in the Ada predefined libraries!

This is good that Ada takes much care in providing robust libraries.

> I am no expert on numerics, but I have to wonder what other languages and/or
> packages do in such cases? Perhaps they just don't care (there is precedent
> for that; Ada takes great pains to define the accuracy of most of the
> numerical functions, most other languages say nothing at all).

Still, as I mentioned the engineering community will be frustrated if
eigensystem analysis for non-symmetric matrices wouldn't exist. Other
languages have successfully implemented algorithms to deal with
general matrices. These algorithms usually have to pass some
benchmarks and these benchmarks are available in literature.

The problem with Ada remains that there is practically no recent books
(we have two in the 1980's that I know) which specifically that
discuss numerical techniques. A new person considering to use Ada
would be only puzzled to see why there are no such books after the
1990's. So that person will easily consider Fortran, C++ or something
else. If on the other hand, the Ada committee will provide robust
numeric libraries and some authors would consider writing books
demonstrating the power of Ada in numerical computing, then people
will become interested using Ada in scientific programming.

YC

Re: matrix package with Ada

[Nasser M. Abbasi]

On 7/25/2010 11:33 AM, Ada novice wrote:
> On Jul 20, 12:34 am, "Randy Brukardt"<ra...@rrsoftware.com>  wrote:

>
> This can mean that people are still not much aware of Ada as a very
> good and robust language for scientific programming.

It does not matter how good Ada is for  scientific programming.

2 things are needed for success here:

1. Thousands of ready to use mathematical/numerical functions out of the 
box.
2. Easy to use graphic interface for displaying of numerical results 
(plots, histograms, etc...)

Ada has neither of the above.

When it comes to scientific programming, Ada is like a very good cook 
who has no kitchen and no ingredients to make a dinner.

> If we look at
> recent publications, how many books discuss scientific computations
> from the view of Ada, how many from the view say C++? For Ada, the sad
> new is that we have practically no recent publication. There were
> strong interest in the 1980s...e.g. the book Scientific Ada and
> Applied Ada. What happened after that?
>

There was strong interest in Ada in the 1980's period.  This was clearly 
because of the mandate to use Ada on defense software projects.

Most people who use Ada these days are not interested in scientific 
programming, but more in system and other type of low level programming.

--Nasser

Re: matrix package with Ada

[jonathan]

I found another bug in  Generic_Complex_Eigenvalues.

(From the collection at  http://www.csee.umbc.edu/~squire/adaclass/gnatmath95/).

Wherever you find   2.0**( -23)   in the code, it should be replaced
with Acc_Init, where

  Acc_Init : constant Real := Real'Epsilon * 2.0**(-3);
  -- 2**(-23) for digits 6, and 2**(-53) for digits 15, assuming usual
IEEE.

At the moment  Generic_Complex_Eigenvalues  only gives you single
precision
(digits 6), so it fails as a generic in the floating point type Real.

Also the program works poorly on matrices that are ill-conditioned,
and
it fails catastrophically on singular matrices.  There is still
a large class of problems where it may be useful, but its limitations
should be loudly stated somewhere in  .ads  file.

J.

Re: matrix package with Ada

[jonathan]

> Wherever you find   2.0**( -23)   in the code, it should be replaced
> with Acc_Init, where
>
>   Acc_Init : constant Real := Real'Epsilon * 2.0**(-3);


Actually, it appears as   2.0 **( - 23 )  in the code, (so searching
for 23 works).

Re: matrix package with Ada

[jonathan]

> Also the program works poorly on matrices that are ill-conditioned,
> and it fails catastrophically on singular matrices.  There is still
> a large class of problems where it may be useful, but its limitations
> should be loudly stated somewhere in  .ads  file.
>
Actually, it has to fail on certain matrices .. my error .. I ran some
more tests, and the program seems to be working a lot better than
I thought.

J.