OpenBLAS/lapack-netlib/TESTING/LIN/dget03.f

*> \brief \b DGET03
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
*                          RCOND, RESID )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDAINV, LDWORK, N
*       DOUBLE PRECISION   RCOND, RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
*      $                   WORK( LDWORK, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGET03 computes the residual for a general matrix times its inverse:
*>    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of rows and columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The original N x N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AINV
*> \verbatim
*>          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
*>          The inverse of the matrix A.
*> \endverbatim
*>
*> \param[in] LDAINV
*> \verbatim
*>          LDAINV is INTEGER
*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*>          LDWORK is INTEGER
*>          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is DOUBLE PRECISION
*>          The reciprocal of the condition number of A, computed as
*>          ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE DGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
     $                   RCOND, RESID )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LDAINV, LDWORK, N
      DOUBLE PRECISION   RCOND, RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
     $                   WORK( LDWORK, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      DOUBLE PRECISION   AINVNM, ANORM, EPS
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           DLAMCH, DLANGE
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( N.LE.0 ) THEN
         RCOND = ONE
         RESID = ZERO
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      EPS = DLAMCH( 'Epsilon' )
      ANORM = DLANGE( '1', N, N, A, LDA, RWORK )
      AINVNM = DLANGE( '1', N, N, AINV, LDAINV, RWORK )
      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
         RCOND = ZERO
         RESID = ONE / EPS
         RETURN
      END IF
      RCOND = ( ONE / ANORM ) / AINVNM
*
*     Compute I - A * AINV
*
      CALL DGEMM( 'No transpose', 'No transpose', N, N, N, -ONE, AINV,
     $            LDAINV, A, LDA, ZERO, WORK, LDWORK )
      DO 10 I = 1, N
         WORK( I, I ) = ONE + WORK( I, I )
   10 CONTINUE
*
*     Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
*
      RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
*
      RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
*
      RETURN
*
*     End of DGET03
*
      END