!-----------------------------------------------------------------
!
! Purpose
! =======
!
! LA_GETRF computes an LU factorization of a general regtangle
! matrix A using partial pivoting with row interchanges.
!
! The factorization has the form A = PLU
! where P is a permutation matrix, L is lower triangular
! with unit diagonal elements (lower trapezoidal if m > n),
! and U is upper triangular (upper trapezoidal if m < n),
! where m=size(A,1) and n=size(A,2).
! 
! When A is square (m = n), LA_GETRF optionally estimates the 
! reciprocal of the condition number of a general matrix A, in either 
! the 1-norm or the infinity-norm.
! An estimate is obtained for norm(inv(A)), and the reciprocal of the
! condition number is computed as RCOND = 1 / (norm(A) * norm(inv(A))).
!
! Arguments
! =========
!
! SUBROUTINE LA_GETRF ( A, IPIV, RCOND, NORM, INFO )
!    <type>(<wp>), INTENT(INOUT) :: A(:,:)
!    INTEGER, INTENT( OUT ) :: IPIV( : )
!    REAL(<wp>), INTENT( OUT ), OPTIONAL :: RCOND
!    CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: NORM
!    INTEGER, INTENT(OUT), OPTIONAL :: INFO
!    where
!    <type> ::= REAL | COMPLEX
!    <wp>   ::= KIND(1.0) | KIND(1.0D0)
!
! ====================
!
! A     (input/output) either REAL or COMPLEX array, shape (:,:).
!       On entry, the matrix A.
!       On exit, the factors L and U from the factorization A = PLU; 
!          the unit diagonal elements of L are not stored.
!
! IPIV  (output) INTEGER array, shape (:),
!       size(IPIV) == min(size(A,1),size(A,2)). 
!       IPIV indices that define the permutation matrix P;
!       row i of the matrix A was interchanged with row IPIV(i).
!
! RCOND Optional (output) REAL
!       The reciprocal of the condition number of the matrix A for
!       the case m = n, computed as RCOND = 1/(norm(A) * norm(inv(A))).
!       RCOND should be present if NORM is present. 
!       If m /= n then RCOND is returned as zero.
!
! NORM  Optional (input) CHARACTER*1
!       Specifies whether the 1-norm condition number or the
!       infinity-norm condition number is required:
!          = '1', 'O' or 'o':  1-norm;
!          = 'I', 'i':         infinity-norm.
!       If NORM is not present, the 1-norm is used.
!
! INFO  Optional (output) INTEGER.
!       If INFO is present
!          = 0: successful exit
!          < 0: if INFO = -k, the k-th argument had an illegal value
!          > 0: if INFO = k, U(k,k) is exactly zero.  The factorization
!               has been completed, but the factor U is exactly
!               singular, so the solution could not be computed.
!       If INFO is not present and an error occurs, then the program is
!          terminated with an error message.
!-------------------------------

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