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From: Simon Wright <simon@pushface.org>
Newsgroups: comp.lang.ada
Subject: Question on procedure parameter style
Date: Thu, 23 Dec 2010 17:59:06 +0000
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Date: 2010-12-23T17:59:06+00:00
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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.