*> \brief \b SCHKGK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKGK( NIN, NOUT ) * * .. Scalar Arguments .. * INTEGER NIN, NOUT * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SCHKGK tests SGGBAK, 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. * *> \date November 2011 * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SCHKGK( NIN, NOUT ) * * -- LAPACK test routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. 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 ) REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO REAL ANORM, BNORM, EPS, RMAX, VMAX * .. * .. Local Arrays .. INTEGER LMAX( 4 ) REAL 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 .. REAL SLAMCH, SLANGE EXTERNAL SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SGEMM, SGGBAK, SGGBAL, SLACPY * .. * .. 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 = SLAMCH( '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 = SLANGE( 'M', N, N, A, LDA, WORK ) BNORM = SLANGE( 'M', N, N, B, LDB, WORK ) * CALL SLACPY( 'FULL', N, N, A, LDA, AF, LDA ) CALL SLACPY( 'FULL', N, N, B, LDB, BF, LDB ) * CALL SGGBAL( '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 SLACPY( 'FULL', N, M, VL, LDVL, VLF, LDVL ) CALL SLACPY( 'FULL', N, M, VR, LDVR, VRF, LDVR ) * CALL SGGBAK( 'B', 'L', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL, $ INFO ) IF( INFO.NE.0 ) THEN NINFO = NINFO + 1 LMAX( 2 ) = KNT END IF * CALL SGGBAK( 'B', 'R', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR, $ INFO ) IF( INFO.NE.0 ) THEN NINFO = NINFO + 1 LMAX( 3 ) = KNT END IF * * Test of SGGBAK * * Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR * where tilde(A) denotes the transformed matrix. * CALL SGEMM( 'N', 'N', N, M, N, ONE, AF, LDA, VR, LDVR, ZERO, WORK, $ LDWORK ) CALL SGEMM( 'T', 'N', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO, $ E, LDE ) * CALL SGEMM( 'N', 'N', N, M, N, ONE, A, LDA, VRF, LDVR, ZERO, WORK, $ LDWORK ) CALL SGEMM( '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 ) ) IF( VMAX.GT.RMAX ) THEN LMAX( 4 ) = KNT RMAX = VMAX END IF * * Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR * CALL SGEMM( 'N', 'N', N, M, N, ONE, BF, LDB, VR, LDVR, ZERO, WORK, $ LDWORK ) CALL SGEMM( 'T', 'N', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO, $ E, LDE ) * CALL SGEMM( 'N', 'N', N, M, N, ONE, B, LDB, VRF, LDVR, ZERO, WORK, $ LDWORK ) CALL SGEMM( '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 ) ) IF( VMAX.GT.RMAX ) THEN LMAX( 4 ) = KNT RMAX = VMAX END IF * GO TO 10 * 100 CONTINUE * WRITE( NOUT, FMT = 9999 ) 9999 FORMAT( 1X, '.. test output of SGGBAK .. ' ) * WRITE( NOUT, FMT = 9998 )RMAX 9998 FORMAT( ' value of largest test error =', E12.3 ) WRITE( NOUT, FMT = 9997 )LMAX( 1 ) 9997 FORMAT( ' example number where SGGBAL info is not 0 =', I4 ) WRITE( NOUT, FMT = 9996 )LMAX( 2 ) 9996 FORMAT( ' example number where SGGBAK(L) info is not 0 =', I4 ) WRITE( NOUT, FMT = 9995 )LMAX( 3 ) 9995 FORMAT( ' example number where SGGBAK(R) info is not 0 =', I4 ) WRITE( NOUT, FMT = 9994 )LMAX( 4 ) 9994 FORMAT( ' example number having largest error =', I4 ) WRITE( NOUT, FMT = 9992 )NINFO 9992 FORMAT( ' number of examples where info is not 0 =', I4 ) WRITE( NOUT, FMT = 9991 )KNT 9991 FORMAT( ' total number of examples tested =', I4 ) * RETURN * * End of SCHKGK * END