Question on procedure parameter style

Question on procedure parameter style

[Simon Wright]

Hi all,

Working on adding generalized eigenvalues to
https://sourceforge.net/projects/gnat-math-extn/, I've started with

   --  Obtain the generalized eigenvalues and the right generalized
   --  eigenvectors of a pair of non-symmetric real matrices.
   --
   --  A generalized eigenvalue for a pair of matrices (A,B) is a
   --  scalar lambda or a ratio alpha/beta = lambda, such that A -
   --  lambda*B is singular (or, equivalently, beta*A - alpha*B is
   --  singular).
   --
   --  It is usually represented as the pair (alpha,beta), as there
   --  is a reasonable interpretation for beta = 0, and even for both
   --  being zero.
   --
   --  The right eigenvector v(j) corresponding to the eigenvalue
   --  lambda(j) of (A,B) satisfies
   --            A * v(j) = lambda(j) * B * v(j).
   --
   --  Alphas'Range and Betas'Range must be the same as A'Range (1).
   --  The ranges of A, B and Vectors must be the same.
   procedure Generalized_Eigensystem
     (A       :     Real_Arrays.Real_Matrix;
      B       :     Real_Arrays.Real_Matrix;
      Alphas  : out Complex_Arrays.Complex_Vector;
      Betas   : out Real_Arrays.Real_Vector;
      Vectors : out Real_Arrays.Real_Matrix);

The comment is adapted from the man page for LAPACK's SGGEV. (BTW,
clearly lambda is complex; is it OK to refer to lambda as a _scalar_?)

My question is, what do people think about this way of returning the
eigenvalues (in Alphas & Betas)? An alternative would be to declare
types

   type Real_Eigenvalue is record
      Alpha : Complex;
      Beta  : Real;
   end record;
   type Real_Eigenvalue_Vector
   is array (Integer range <>) of Real_Eigenvalue;

and replace the Alphas and Betas 'out' parameters by

      Values : out Real_Eigenvalue_Vector;

but then I have the problem that for the complex generalized eigenvalue
problem I'd have to write

   type Complex_Eigenvalue is record
      Alpha : Complex;
      Beta  : Complex;
   end record;
   type Complex_Eigenvalue_Vector
   is array (Integer range <>) of Complex_Eigenvalue;

which is all geting a bit confusing (I was going to say "complex"...).

Thanks in advance for any comments.

Re: Question on procedure parameter style

[Ada novice]

On Dec 23, 6:59 pm, Simon Wright <si...@pushface.org> wrote:
> Hi all,
>
> Working on adding generalized eigenvalues tohttps://sourceforge.net/projects/gnat-math-extn/, I've started with

Thanks Simon for considering implementing the generalized eigenvalue
problem. It's a very useful tool for many people.

Wish you all the best in this endeavour.

Cheers
YC

Re: Question on procedure parameter style

[Simon Wright]

Simon Wright <simon@pushface.org> writes:

> My question is, what do people think about this way of returning the
> eigenvalues (in Alphas & Betas)? An alternative would be to declare
> types
>
>    type Real_Eigenvalue is record
>       Alpha : Complex;
>       Beta  : Real;
>    end record;
>    type Real_Eigenvalue_Vector
>    is array (Integer range <>) of Real_Eigenvalue;
>
> and replace the Alphas and Betas 'out' parameters by
>
>       Values : out Real_Eigenvalue_Vector;
>
> but then I have the problem that for the complex generalized eigenvalue
> problem I'd have to write
>
>    type Complex_Eigenvalue is record
>       Alpha : Complex;
>       Beta  : Complex;
>    end record;
>    type Complex_Eigenvalue_Vector
>    is array (Integer range <>) of Complex_Eigenvalue;

I've now read up on this at
http://en.wikipedia.org/wiki/Generalized_eigenvalue_problem#Generalized_eigenvalue_problem,
and there's a hint there that lambda is in fact complex.

So I think I'll go with

   type General_Eigenvalue is record
      Alpha : General;
      Beta  : General;
   end record;
   type General_Eigenvalue_Vector
   is array (Integer range <>) of General_Eigenvalue;

for both the Real and the Complex problem.

Also, instead of Generalized_Eigensystem, the procedure will be called
just Eigensystem (another overloading).

Re: Question on procedure parameter style

[Simon Wright]

Simon Wright <simon@pushface.org> writes:

>    type General_Eigenvalue is record
>       Alpha : General;
>       Beta  : General;
>    end record;
>    type General_Eigenvalue_Vector
>    is array (Integer range <>) of General_Eigenvalue;

M-x replace-string was the wrong operation here. I meant to say

   type General_Eigenvalue is record
      Alpha : Complex;
      Beta  : Complex;
   end record;
   type General_Eigenvalue_Vector
   is array (Integer range <>) of General_Eigenvalue;