ANN: miscellaneous Math routines, GPL'd

ANN: miscellaneous Math routines, GPL'd

[johnscpg]

Dear All,

For those of you who like Ada with their numerics (is there
anyone who doesn't?!) I have released a collection of math
routines under the GPL license. Find them at:

  http://web.am.qub.ac.uk/users/j.parker/miscellany

The full set is tarred in the file:

  miscellany.10may09.tar.gz

in the directory given above.

Most are old classics I have found useful over the years
(SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
The random number generators are very new; the documentation
should explain why I recommend them. The random number generators
and the Arbitrary precision floating point are designed to
make good use of the new 64-bit CPU's.

Cheers,
Jonathan

j.parker/at/qub/point/ac/point/uk

Re: ANN: miscellaneous Math routines, GPL'd

[John B. Matthews]

In article 
<9dbcdcd0-3c15-4165-9336-3d5778df2ca3@e20g2000vbc.googlegroups.com>,
 johnscpg@googlemail.com wrote:

> For those of you who like Ada with their numerics (is there
> anyone who doesn't?!) I have released a collection of math
> routines under the GPL license. Find them at:
> 
>   http://web.am.qub.ac.uk/users/j.parker/miscellany
> 
> The full set is tarred in the file:
> 
>   miscellany.10may09.tar.gz
> 
> in the directory given above.
> 
> Most are old classics I have found useful over the years
> (SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
> The random number generators are very new; the documentation
> should explain why I recommend them. The random number generators
> and the Arbitrary precision floating point are designed to
> make good use of the new 64-bit CPU's.

Excellent. You might like to see my experimental implementation of 
Generic_Roots, using the Durand-Kerner-Weierstrass method and 
distributed under the GNAT modified GPL:

<http://home.roadrunner.com/~jbmatthews/misc/groots.html> 

-- 
John B. Matthews
trashgod at gmail dot com
<http://sites.google.com/site/drjohnbmatthews>

Re: ANN: miscellaneous Math routines, GPL'd

[johnscpg]

On May 12, 7:45 pm, "John B. Matthews" <nos...@nospam.invalid> wrote:
> In article
> <9dbcdcd0-3c15-4165-9336-3d5778df2...@e20g2000vbc.googlegroups.com>,
>
>
>
>  johns...@googlemail.com wrote:
> > For those of you who like Ada with their numerics (is there
> > anyone who doesn't?!) I have released a collection of math
> > routines under the GPL license. Find them at:
>
> >  http://web.am.qub.ac.uk/users/j.parker/miscellany
>
> > The full set is tarred in the file:
>
> >   miscellany.10may09.tar.gz
>
> > in the directory given above.
>
> > Most are old classics I have found useful over the years
> > (SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
> > The random number generators are very new; the documentation
> > should explain why I recommend them. The random number generators
> > and the Arbitrary precision floating point are designed to
> > make good use of the new 64-bit CPU's.
>
> Excellent. You might like to see my experimental implementation of
> Generic_Roots, using the Durand-Kerner-Weierstrass method and
> distributed under the GNAT modified GPL:
>
> <http://home.roadrunner.com/~jbmatthews/misc/groots.html>
>
> --
> John B. Matthews
> trashgod at gmail dot com
> <http://sites.google.com/site/drjohnbmatthews>

Thanks for the pointer.  Root finding BTW is one of those problems
that cries out for extended precision floating pt.  Its rarely
time-sensitive (rarely in inner loops), but very sensitive
to precision ...  last time I did it, it was on mathematica
in extended precision .. I prefer Ada!  If I did in Fortran I'ld
always use REAL*16 (Quad-precision, 32 digit floats) but only one
Fortran (intel ifort) supports this as far as I know (except IBM's
fortran
on powerpc). If I ever find the time I'll hook
up your root finder to my Extended Precision package.

cheers
jonathan

Re: ANN: miscellaneous Math routines, GPL'd

[John B. Matthews]

In article 
<cb936fa3-df11-4563-b283-b0bfed0ba070@o27g2000vbd.googlegroups.com>,
 johnscpg@googlemail.com wrote:

> On May 12, 7:45 pm, "John B. Matthews" <nos...@nospam.invalid> wrote:
> > In article
> > <9dbcdcd0-3c15-4165-9336-3d5778df2...@e20g2000vbc.googlegroups.com>,
> >
> >  johns...@googlemail.com wrote:
> > > For those of you who like Ada with their numerics (is there
> > > anyone who doesn't?!) I have released a collection of math
> > > routines under the GPL license. Find them at:
> >
> > >  http://web.am.qub.ac.uk/users/j.parker/miscellany
> >
> > > The full set is tarred in the file:
> >
> > >   miscellany.10may09.tar.gz
> >
> > > in the directory given above.
> >
> > > Most are old classics I have found useful over the years
> > > (SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
> > > The random number generators are very new; the documentation
> > > should explain why I recommend them. The random number generators
> > > and the Arbitrary precision floating point are designed to
> > > make good use of the new 64-bit CPU's.
> >
> > Excellent. You might like to see my experimental implementation of
> > Generic_Roots, using the Durand-Kerner-Weierstrass method and
> > distributed under the GNAT modified GPL:
> >
> > <http://home.roadrunner.com/~jbmatthews/misc/groots.html>
[...]
> Thanks for the pointer.  Root finding BTW is one of those problems 
> that cries out for extended precision floating pt.  Its rarely 
> time-sensitive (rarely in inner loops), but very sensitive to 
> precision ...  last time I did it, it was on mathematica in extended 
> precision .. I prefer Ada!  If I did in Fortran I'ld always use 
> REAL*16 (Quad-precision, 32 digit floats) but only one Fortran (intel 
> ifort) supports this as far as I know (except IBM's fortran on 
> powerpc).

Ah, yes. I noticed the difference running examples on PPC & x86. IIUC, 
the latter uses an 80-bit format internally.

> If I ever find the time I'll hook up your root finder to my 
> Extended Precision package.

Outstanding. As both are GMGPL, please feel free to incorporate any of 
my work in your project.

-- 
John B. Matthews
trashgod at gmail dot com
<http://sites.google.com/site/drjohnbmatthews>

Re: ANN: miscellaneous Math routines, GPL'd

[Dmitry A. Kazakov]

On Tue, 12 May 2009 09:38:49 -0700 (PDT), johnscpg@googlemail.com wrote:

> For those of you who like Ada with their numerics (is there
> anyone who doesn't?!) I have released a collection of math
> routines under the GPL license. Find them at:
> 
>   http://web.am.qub.ac.uk/users/j.parker/miscellany

Many thanks for a great contribution!

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

Re: ANN: miscellaneous Math routines, GPL'd

[lanceboyle]

On May 12, 9:38 am, johns...@googlemail.com wrote:
> Dear All,
>
> For those of you who like Ada with their numerics (is there
> anyone who doesn't?!) I have released a collection of math
> routines under the GPL license. Find them at:
>
>  http://web.am.qub.ac.uk/users/j.parker/miscellany
>
> The full set is tarred in the file:
>
>   miscellany.10may09.tar.gz
>
> in the directory given above.
>
> Most are old classics I have found useful over the years
> (SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
> The random number generators are very new; the documentation
> should explain why I recommend them. The random number generators
> and the Arbitrary precision floating point are designed to
> make good use of the new 64-bit CPU's.
>
> Cheers,
> Jonathan
>
> j.parker/at/qub/point/ac/point/uk

Wow--numerical code that I can actually read! This looks awesome.

I suppose that it would not be hard to adapt the code to use the
vector and matrix declarations in the Annex G.3 part of Ada 2005, e.g.

type Real_Vector is array (Integer range <>) of Real'Base;
type Real_Matrix is array (Integer range <>, Integer range <>)
                                                   of Real'Base;

replacing the scattered declarations such as

type Data_Array is array (Array_Index) of Real;
type A_Matrix is array(R_Index, C_Index) of Real;

I really like the "standardized" way of these Ada 2005 declarations.

Jerry

Re: ANN: miscellaneous Math routines, GPL'd

[johnscpg]

On May 12, 10:02 pm, "lancebo...@qwest.net" <lancebo...@qwest.net>
wrote:
> On May 12, 9:38 am, johns...@googlemail.com wrote:
>
>
>
> > Dear All,
>
> > For those of you who like Ada with their numerics (is there
> > anyone who doesn't?!) I have released a collection of math
> > routines under the GPL license. Find them at:
>
> >  http://web.am.qub.ac.uk/users/j.parker/miscellany
>
> > The full set is tarred in the file:
>
> >   miscellany.10may09.tar.gz
>
> > in the directory given above.
>
> > Most are old classics I have found useful over the years
> > (SVD, QR, LU, Runge-Kutta, FFT, Arbitrary precision floating point).
> > The random number generators are very new; the documentation
> > should explain why I recommend them. The random number generators
> > and the Arbitrary precision floating point are designed to
> > make good use of the new 64-bit CPU's.
>
> > Cheers,
> > Jonathan
>
> > j.parker/at/qub/point/ac/point/uk
>
> Wow--numerical code that I can actually read! This looks awesome.
>
> I suppose that it would not be hard to adapt the code to use the
> vector and matrix declarations in the Annex G.3 part of Ada 2005, e.g.
>
> type Real_Vector is array (Integer range <>) of Real'Base;
> type Real_Matrix is array (Integer range <>, Integer range <>)
>                                                    of Real'Base;
>
> replacing the scattered declarations such as
>
> type Data_Array is array (Array_Index) of Real;
> type A_Matrix is array(R_Index, C_Index) of Real;
>
> I really like the "standardized" way of these Ada 2005 declarations.
>
> Jerry


To instantiate the lin. alg. generics (in directory linearly)
using the unconstrained arrays you typed above, declare a subtype m3:

   subtype Index is Integer range 1..191;

 --type Real_Matrix is array (Integer range <>, Integer  range <>) of
Real;

   subtype m3 is Real_Matrix (Index, Index);

The generics can now be instantiated with m3.

Another interesting question is whether the generics (and the
subprograms
declared by the generic package) should be using unconstrained arrays:

  generic
     type Real is digits <>;
     type Matrix is array (Integer range <>, Integer  range <>) of
Real;

In the old days if I did that the program would run way slow.. seemed
to put the compiler under much stress ... maybe ok now but I am not
going to be the one to prove it.

Here's another problem:  Very common for an application to
require transformation of an arbitrary diagonal block of a
matrix (or any block) rather than the full matrix.
Unconstrained arrays don't provide any special benefit here ...
you still have to copy
the block to another matrix, or handle it the way I do in
these routines (tell the routine to operate on a specified block
only). Once you've gone to this trouble, the benefit of
unconstrained arrays is small.

Another irritation:  suppose user declares

  V : Vector (1..10);
  M : Matrix (0..9, 0..9);
or worse
  M : Matrix (0..9, 2..11);
or worse still
  M : Matrix (0..11, 2..11);

How do you handle it?
1. shift indices during iteration inside loops in the lin alg program.
2. slide arrays so indices coincide.
3. Raise constraint_error;
4. Assume they won't do it.

I do 3. (See for example procedure Choleski_Decompose at end of
Disorderly-Random-Deviates.adb  and near bottom of
Disorderly-Random-Deviates.ads.)   But I'm not sure what to do.
(I was going ask here on comp.lang.ada, but got lazy.)
Generics with constrained arrays work ok for me here.

cheers,
jonathan

Re: ANN: miscellaneous Math routines, GPL'd

[gautier_niouzes]

On 13 Mai, 11:25, johns...@googlemail.com wrote:

> Another irritation:  suppose user declares
>
>   V : Vector (1..10);
>   M : Matrix (0..9, 0..9);
> or worse
>   M : Matrix (0..9, 2..11);
> or worse still
>   M : Matrix (0..11, 2..11);
>
> How do you handle it?
> 1. shift indices during iteration inside loops in the lin alg program.
> 2. slide arrays so indices coincide.
> 3. Raise constraint_error;
> 4. Assume they won't do it.
>
> I do 3. (See for example procedure Choleski_Decompose at end of
> Disorderly-Random-Deviates.adb  and near bottom of
> Disorderly-Random-Deviates.ads.)   But I'm not sure what to do.
> (I was going ask here on comp.lang.ada, but got lazy.)
> Generics with constrained arrays work ok for me here.

It's done here:
http://www.cs.umbc.edu/~squire/adaclass/gnatmath95 ,
generic_real_linear_equations.ads .

For using with Ada 2005's matrices, all you need is to replace
package Generic_Real_Arrays by Ada.Numerics.Generic_Real_Arrays
:-)
_________________________________________________________
Gautier's Ada programming -- http://sf.net/users/gdemont/

NB: For a direct answer, e-mail address on the Web site!

Re: ANN: miscellaneous Math routines, GPL'd

[johnscpg]

On May 13, 12:52 pm, gautier_niou...@hotmail.com wrote:
> On 13 Mai, 11:25, johns...@googlemail.com wrote:
>
>
>
> > Another irritation:  suppose user declares
>
> >   V : Vector (1..10);
> >   M : Matrix (0..9, 0..9);
> > or worse
> >   M : Matrix (0..9, 2..11);
> > or worse still
> >   M : Matrix (0..11, 2..11);
>
> > How do you handle it?
> > 1. shift indices during iteration inside loops in the lin alg program.
> > 2. slide arrays so indices coincide.
> > 3. Raise constraint_error;
> > 4. Assume they won't do it.
>
> > I do 3. (See for example procedure Choleski_Decompose at end of
> > Disorderly-Random-Deviates.adb  and near bottom of
> > Disorderly-Random-Deviates.ads.)   But I'm not sure what to do.
> > (I was going ask here on comp.lang.ada, but got lazy.)
> > Generics with constrained arrays work ok for me here.
>
> It's done here:http://www.cs.umbc.edu/~squire/adaclass/gnatmath95,
> generic_real_linear_equations.ads .
>
> For using with Ada 2005's matrices, all you need is to replace
> package Generic_Real_Arrays by Ada.Numerics.Generic_Real_Arrays
> :-)
> _________________________________________________________
> Gautier's Ada programming --http://sf.net/users/gdemont/
>
> NB: For a direct answer, e-mail address on the Web site!

Thanks Gautier!  After a quick inspection, I notice a lot
of method 1, (shifting indices inside loops), but sometimes the
author copies the entire input array over to a new local array
with the desired indices (usually 1..N).  Also
raises an exception if there's a length mismatch.

cheers,
jonathan