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240 lines
6.5 KiB
240 lines
6.5 KiB
2 years ago
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*> \brief \b SCHKGK
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SCHKGK( NIN, NOUT )
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*
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* .. Scalar Arguments ..
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* INTEGER NIN, NOUT
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SCHKGK tests SGGBAK, a routine for backward balancing of
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*> a matrix pair (A, B).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NIN
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*> \verbatim
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*> NIN is INTEGER
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*> The logical unit number for input. NIN > 0.
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The logical unit number for output. NOUT > 0.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SCHKGK( NIN, NOUT )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER NIN, NOUT
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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INTEGER LDA, LDB, LDVL, LDVR
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PARAMETER ( LDA = 50, LDB = 50, LDVL = 50, LDVR = 50 )
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INTEGER LDE, LDF, LDWORK
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PARAMETER ( LDE = 50, LDF = 50, LDWORK = 50 )
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO
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REAL ANORM, BNORM, EPS, RMAX, VMAX
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* ..
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* .. Local Arrays ..
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INTEGER LMAX( 4 )
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REAL A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ),
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$ BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ),
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$ LSCALE( LDA ), RSCALE( LDA ), VL( LDVL, LDVL ),
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$ VLF( LDVL, LDVL ), VR( LDVR, LDVR ),
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$ VRF( LDVR, LDVR ), WORK( LDWORK, LDWORK )
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SGGBAK, SGGBAL, SLACPY
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Executable Statements ..
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*
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* Initialization
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*
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LMAX( 1 ) = 0
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LMAX( 2 ) = 0
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LMAX( 3 ) = 0
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LMAX( 4 ) = 0
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NINFO = 0
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KNT = 0
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RMAX = ZERO
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*
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EPS = SLAMCH( 'Precision' )
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*
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10 CONTINUE
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READ( NIN, FMT = * )N, M
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IF( N.EQ.0 )
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$ GO TO 100
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*
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DO 20 I = 1, N
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READ( NIN, FMT = * )( A( I, J ), J = 1, N )
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20 CONTINUE
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*
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DO 30 I = 1, N
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READ( NIN, FMT = * )( B( I, J ), J = 1, N )
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30 CONTINUE
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*
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DO 40 I = 1, N
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READ( NIN, FMT = * )( VL( I, J ), J = 1, M )
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40 CONTINUE
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*
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DO 50 I = 1, N
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READ( NIN, FMT = * )( VR( I, J ), J = 1, M )
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50 CONTINUE
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*
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KNT = KNT + 1
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*
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ANORM = SLANGE( 'M', N, N, A, LDA, WORK )
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BNORM = SLANGE( 'M', N, N, B, LDB, WORK )
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*
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CALL SLACPY( 'FULL', N, N, A, LDA, AF, LDA )
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CALL SLACPY( 'FULL', N, N, B, LDB, BF, LDB )
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*
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CALL SGGBAL( 'B', N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
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$ WORK, INFO )
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IF( INFO.NE.0 ) THEN
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NINFO = NINFO + 1
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LMAX( 1 ) = KNT
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END IF
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*
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CALL SLACPY( 'FULL', N, M, VL, LDVL, VLF, LDVL )
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CALL SLACPY( 'FULL', N, M, VR, LDVR, VRF, LDVR )
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*
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CALL SGGBAK( 'B', 'L', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL,
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$ INFO )
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IF( INFO.NE.0 ) THEN
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NINFO = NINFO + 1
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LMAX( 2 ) = KNT
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END IF
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*
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CALL SGGBAK( 'B', 'R', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR,
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$ INFO )
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IF( INFO.NE.0 ) THEN
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NINFO = NINFO + 1
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LMAX( 3 ) = KNT
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END IF
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*
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* Test of SGGBAK
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*
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* Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR
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* where tilde(A) denotes the transformed matrix.
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*
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CALL SGEMM( 'N', 'N', N, M, N, ONE, AF, LDA, VR, LDVR, ZERO, WORK,
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$ LDWORK )
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CALL SGEMM( 'T', 'N', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO,
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$ E, LDE )
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*
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CALL SGEMM( 'N', 'N', N, M, N, ONE, A, LDA, VRF, LDVR, ZERO, WORK,
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$ LDWORK )
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CALL SGEMM( 'T', 'N', M, M, N, ONE, VLF, LDVL, WORK, LDWORK, ZERO,
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$ F, LDF )
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*
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VMAX = ZERO
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DO 70 J = 1, M
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DO 60 I = 1, M
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VMAX = MAX( VMAX, ABS( E( I, J )-F( I, J ) ) )
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60 CONTINUE
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70 CONTINUE
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VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
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IF( VMAX.GT.RMAX ) THEN
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LMAX( 4 ) = KNT
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RMAX = VMAX
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END IF
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*
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* Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR
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*
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CALL SGEMM( 'N', 'N', N, M, N, ONE, BF, LDB, VR, LDVR, ZERO, WORK,
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$ LDWORK )
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CALL SGEMM( 'T', 'N', M, M, N, ONE, VL, LDVL, WORK, LDWORK, ZERO,
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$ E, LDE )
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*
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CALL SGEMM( 'N', 'N', N, M, N, ONE, B, LDB, VRF, LDVR, ZERO, WORK,
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$ LDWORK )
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CALL SGEMM( 'T', 'N', M, M, N, ONE, VLF, LDVL, WORK, LDWORK, ZERO,
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$ F, LDF )
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*
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VMAX = ZERO
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DO 90 J = 1, M
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DO 80 I = 1, M
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VMAX = MAX( VMAX, ABS( E( I, J )-F( I, J ) ) )
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80 CONTINUE
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90 CONTINUE
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VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
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IF( VMAX.GT.RMAX ) THEN
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LMAX( 4 ) = KNT
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RMAX = VMAX
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END IF
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*
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GO TO 10
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*
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100 CONTINUE
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*
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WRITE( NOUT, FMT = 9999 )
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9999 FORMAT( 1X, '.. test output of SGGBAK .. ' )
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*
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WRITE( NOUT, FMT = 9998 )RMAX
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9998 FORMAT( ' value of largest test error =', E12.3 )
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WRITE( NOUT, FMT = 9997 )LMAX( 1 )
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9997 FORMAT( ' example number where SGGBAL info is not 0 =', I4 )
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WRITE( NOUT, FMT = 9996 )LMAX( 2 )
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9996 FORMAT( ' example number where SGGBAK(L) info is not 0 =', I4 )
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WRITE( NOUT, FMT = 9995 )LMAX( 3 )
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9995 FORMAT( ' example number where SGGBAK(R) info is not 0 =', I4 )
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WRITE( NOUT, FMT = 9994 )LMAX( 4 )
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9994 FORMAT( ' example number having largest error =', I4 )
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WRITE( NOUT, FMT = 9992 )NINFO
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9992 FORMAT( ' number of examples where info is not 0 =', I4 )
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WRITE( NOUT, FMT = 9991 )KNT
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9991 FORMAT( ' total number of examples tested =', I4 )
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*
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RETURN
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*
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* End of SCHKGK
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*
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END
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