!-----------------------------------------------------------------
!
! Purpose
! =======
!
! LA_GERFS improves the computed solution X of a system of linear 
! equations   A X = B  or  A^T X = B
! and provides error bounds and backward error estimates for
! the solution. LA_GERFS uses the LU factors computed by LA_GETRF.
!
! Arguments
! =========
! SUBROUTINE LA_GERFS (A, AF, IPIV, B, X, TRANS, FERR, BERR, INFO)
!    <type>(<wp>), INTENT(IN)  :: A(:,:), AF(:,:), <rhs>
!    INTEGER, INTENT(IN) :: IPIV(:)
!    <type>(<wp>), INTENT(INOUT) :: <sol>
!    REAL(<wp>), INTENT(OUT), OPTIONAL :: <err>
!    CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: TRANS
!    INTEGER, INTENT(OUT), OPTIONAL :: INFO
!    where
!    <type> ::= REAL | COMPLEX
!    <wp>   ::= KIND(1.0) | KIND(1.0D0)
!    <rhs>  ::= B(:,:) | B(:)
!    <sol>  ::= X(:,:) | X(:)
!    <err>  ::= FERR(:), BERR(:) | FERR, BERR
!
! =====================
!
! A     (input) either REAL or COMPLEX square array,
!       shape (:,:), size(A,1) == size(A,2).
!       The original matrix A.
!
! AF    (input) either REAL or COMPLEX square array,
!       shape (:,:), size(AF,1) == size(AF,2) == size(A,1).
!       The factors L and U from the factorization A = PLU
!       as computed by LA_GETRF.
!
! IPIV  (input) INTEGER array, shape (:), size(IPIV) == size(A,1).
!       The pivot indices from LA_GETRF; for 1<=i<=size(A,1), row i
!       of the matrix was interchanged with row IPIV(i).
!
! B     (input) either REAL or COMPLEX rectangular array,
!       shape either (:,:) or (:), size(B,1) or size(B) == size(A,1).
!       The right hand side vector(s) of matrix B for
!       the system of equations AX = B.
!
! X     (input/output) either REAL or COMPLEX rectangular array,
!       shape either (:,:) or (:), size(X,1) or size(X) == size(A,1).
!       On entry, the solution matrix X, as computed by LA_GETRS.
!       On exit, the improved solution matrix X.
!
! TRANS Optional (input) CHARACTER*1
!       If TRANS is present, it specifies the form of the system 
!       of equations:
!          = 'N':  A X = B    (No transpose)
!          = 'T':  A^T X = B  (Transpose)
!          = 'C':  A^H X = B  (Conjugate transpose = Transpose)
!       otherwise TRANS = 'N' is assumed.
!
! FERR  Optional (output) either REAL array of shape (:) or REAL
!       scalar. If it is an array, size(FERR) == size(X,2).
!       The estimated forward error bound for each solution vector
!       X(j) (the j-th column of the solution matrix X).
!       If XTRUE is the true solution corresponding to X(j), FERR(j)
!       is an estimated upper bound for the magnitude of the largest
!       element in (X(j) - XTRUE) divided by the magnitude of the
!       largest element in X(j).  The estimate is as reliable as
!       the estimate for RCOND, and is almost always a slight
!       overestimate of the true error.
!
! BERR  Optional (output) either REAL array of shape (:) or REAL
!       scalar. If it is an array, size(BERR) == size(X,2).
!       The componentwise relative backward error of each solution
!       vector X(j) (i.e., the smallest relative change in
!       any element of A or B that makes X(j) an exact solution).
!
! INFO  Optional (output) INTEGER.
!       If INFO is present
!          = 0: successful exit
!          < 0: if INFO = -k, the k-th argument had an illegal value
!       If INFO is not present and an error occurs, then the program is
!          terminated with an error message.
!
! Internal Parameters
! ===================
!
! ITMAX is the maximum number of steps of iterative refinement.
! It is set to 5 in the LAPACK77 subroutines
! -----------------------------------

.