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From: Simon Wright <simon@pushface.org>
Newsgroups: comp.lang.ada
Subject: Re: A thicker binding for Lapack
Date: Thu, 27 Dec 2012 20:37:40 +0000
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Date: 2012-12-27T20:37:40+00:00
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jpwoodruff@gmail.com writes:

> My trials at maintaining parameter definitions that echo the Fortran
> binding have led only to grief.  The integer inputs N, NRHS, LDA, LDB
> make precious little sense, considering the transposition of the
> matrices that takes place inside the body of procedure sgesv.

Completely agree with this.

> After several drafts I'm thinking that a thick binding might look
> like this:
>
>    procedure SGESV
>       (A   : in out Real_Arrays.Real_Matrix;
>       IPIV : out Integer_Vector;
>       B    : in out Real_Arrays.Real_Matrix;
>       INFO : out Integer) ;

[see extract from SGESV man page below]

There may be some deep reason for making A in-out, but if you don't see
a need to preserve the internal LU decomposition I'd make a copy
internally, and also keep IPIV internal.

Also, I'd make B 'in' and use a third 'out' parameter Result.

And, perhaps INFO should be replaced by Constraint_Error?

[from SGESV man page]

PURPOSE
       SGESV computes the solution to a real system of linear equations
          A * X = B, where A is an N-by-N matrix and X  and  B  are  N-by-NRHS
       matrices.   The  LU  decomposition with partial pivoting and row inter-
       changes is used to factor A as
          A = P * L * U,
       where P is a permutation matrix, L is unit lower triangular, and  U  is
       upper  triangular.   The  factored  form of A is then used to solve the
       system of equations A * X = B.

ARGUMENTS
       [...]

       A       (input/output) REAL array, dimension (LDA,N)
               On entry, the N-by-N coefficient matrix A.  On exit,  the  fac-
               tors  L and U from the factorization A = P*L*U; the unit diago-
               nal elements of L are not stored.

       [...]

       IPIV    (output) INTEGER array, dimension (N)
               The pivot indices that define the permutation matrix P;  row  i
               of the matrix was interchanged with row IPIV(i).

       B       (input/output) REAL array, dimension (LDB,NRHS)
               On entry, the N-by-NRHS matrix of right hand side matrix B.  On
               exit, if INFO = 0, the N-by-NRHS solution matrix X.

       [...]

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value
               > 0:  if INFO = i, U(i,i) is exactly zero.   The  factorization
               has  been  completed,  but the factor U is exactly singular, so
               the solution could not be computed.