dchkgk.f

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*> \brief \b DCHKGK
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DCHKGK( NIN, NOUT )
*
*       .. Scalar Arguments ..
*       INTEGER            NIN, NOUT
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DCHKGK tests DGGBAK, a routine for backward balancing  of
*> a matrix pair (A, B).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NIN
*> \verbatim
*>          NIN is INTEGER
*>          The logical unit number for input.  NIN > 0.
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>          The logical unit number for output.  NOUT > 0.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE dchkgk( NIN, NOUT )
*
*  -- 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            NIN, NOUT
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            LDA, LDB, LDVL, LDVR
      parameter( lda = 50, ldb = 50, ldvl = 50, ldvr = 50 )
      INTEGER            LDE, LDF, LDWORK
      parameter( lde = 50, ldf = 50, ldwork = 50 )
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IHI, ILO, INFO, J, KNT, M, N, NINFO
      DOUBLE PRECISION   ANORM, BNORM, EPS, RMAX, VMAX
*     ..
*     .. Local Arrays ..
      INTEGER            LMAX( 4 )
      DOUBLE PRECISION   A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ),
     $                   BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ),
     $                   LSCALE( LDA ), RSCALE( LDA ), VL( LDVL, LDVL ),
     $                   VLF( LDVL, LDVL ), VR( LDVR, LDVR ),
     $                   VRF( LDVR, LDVR ), WORK( LDWORK, LDWORK )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           dlamch, dlange
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dggbak, dggbal, dlacpy
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. Executable Statements ..
*
*     Initialization
*
      lmax( 1 ) = 0
      lmax( 2 ) = 0
      lmax( 3 ) = 0
      lmax( 4 ) = 0
      ninfo = 0
      knt = 0
      rmax = zero
*
      eps = dlamch( 'Precision' )
*
   10 CONTINUE
      READ( nin, fmt = * )n, m
      IF( n.EQ.0 )
     $   GO TO 100
*
      DO 20 i = 1, n
         READ( nin, fmt = * )( a( i, j ), j = 1, n )
   20 CONTINUE
*
      DO 30 i = 1, n
         READ( nin, fmt = * )( b( i, j ), j = 1, n )
   30 CONTINUE
*
      DO 40 i = 1, n
         READ( nin, fmt = * )( vl( i, j ), j = 1, m )
   40 CONTINUE
*
      DO 50 i = 1, n
         READ( nin, fmt = * )( vr( i, j ), j = 1, m )
   50 CONTINUE
*
      knt = knt + 1
*
      anorm = dlange( 'M', n, n, a, lda, work )
      bnorm = dlange( 'M', n, n, b, ldb, work )
*
      CALL dlacpy( 'FULL', n, n, a, lda, af, lda )
      CALL dlacpy( 'FULL', n, n, b, ldb, bf, ldb )
*
      CALL dggbal( 'B', n, a, lda, b, ldb, ilo, ihi, lscale, rscale,
     $             work, info )
      IF( info.NE.0 ) THEN
         ninfo = ninfo + 1
         lmax( 1 ) = knt
      END IF
*
      CALL dlacpy( 'FULL', n, m, vl, ldvl, vlf, ldvl )
      CALL dlacpy( 'FULL', n, m, vr, ldvr, vrf, ldvr )
*
      CALL dggbak( 'B', 'l', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL,
     $             INFO )
.NE.      IF( INFO0 ) THEN
         NINFO = NINFO + 1
         LMAX( 2 ) = KNT
      END IF
*
      CALL DGGBAK( 'b', 'r', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR,
     $             INFO )
.NE.      IF( INFO0 ) THEN
         NINFO = NINFO + 1
         LMAX( 3 ) = KNT
      END IF
*
*     Test of DGGBAK
*
*     Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR
*     where tilde(A) denotes the transformed matrix.
*
      CALL DGEMM( 'n', 'n', N, M, N, ONE, AF, LDA, VR, LDVR, ZERO, WORK,
     $            LDWORK )
      CALL DGEMM( 't', 'n', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO,
     $            E, LDE )
*
      CALL DGEMM( 'n', 'n', N, M, N, ONE, A, LDA, VRF, LDVR, ZERO, WORK,
     $            LDWORK )
      CALL DGEMM( 't', 'n', M, M, N, ONE, VLF, LDVL, WORK, LDWORK, ZERO,
     $            F, LDF )
*
      VMAX = ZERO
      DO 70 J = 1, M
         DO 60 I = 1, M
            VMAX = MAX( VMAX, ABS( E( I, J )-F( I, J ) ) )
   60    CONTINUE
   70 CONTINUE
      VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
.GT.      IF( VMAXRMAX ) THEN
         LMAX( 4 ) = KNT
         RMAX = VMAX
      END IF
*
*     Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR
*
      CALL DGEMM( 'n', 'n', N, M, N, ONE, BF, LDB, VR, LDVR, ZERO, WORK,
     $            LDWORK )
      CALL DGEMM( 't', 'n', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO,
     $            E, LDE )
*
      CALL DGEMM( 'n', 'n', N, M, N, ONE, B, LDB, VRF, LDVR, ZERO, WORK,
     $            LDWORK )
      CALL DGEMM( 't', 'n', M, M, N, ONE, VLF, LDVL, WORK, LDWORK, ZERO,
     $            F, LDF )
*
      VMAX = ZERO
      DO 90 J = 1, M
         DO 80 I = 1, M
            VMAX = MAX( VMAX, ABS( E( I, J )-F( I, J ) ) )
   80    CONTINUE
   90 CONTINUE
      VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
.GT.      IF( VMAXRMAX ) THEN
         LMAX( 4 ) = KNT
         RMAX = VMAX
      END IF
*
      GO TO 10
*
  100 CONTINUE
*
      WRITE( NOUT, FMT = 9999 )
 9999 FORMAT( 1X, '.. test output of dggbak .. ' )
*
      WRITE( NOUT, FMT = 9998 )RMAX
 9998 FORMAT( ' value of largest test error                  =', D12.3 )
      WRITE( NOUT, FMT = 9997 )LMAX( 1 )
 9997 FORMAT( ' example number where dggbal info is not 0    =', I4 )
      WRITE( NOUT, FMT = 9996 )LMAX( 2 )
 9996 FORMAT( ' example number where dggbak(l) info is not 0 =', I4 )
      WRITE( NOUT, FMT = 9995 )LMAX( 3 )
 9995 FORMAT( ' example number where dggbak(r) info is not 0 =', I4 )
      WRITE( NOUT, FMT = 9994 )LMAX( 4 )
 9994 FORMAT( ' example number having largest error          =', I4 )
      WRITE( NOUT, FMT = 9993 )NINFO
 9993 FORMAT( ' number of examples where info is not 0       =', I4 )
      WRITE( NOUT, FMT = 9992 )KNT
 9992 FORMAT( ' total number of examples tested              =', I4 )
*
      RETURN
*
*     End of DCHKGK
*
      END