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SUBROUTINE SCHKGK( NIN, NOUT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER NIN, NOUT
* ..
*
* Purpose
* =======
*
* SCHKGK tests SGGBAK, a routine for backward balancing of
* a matrix pair (A, B).
*
* Arguments
* =========
*
* NIN (input) INTEGER
* The logical unit number for input. NIN > 0.
*
* NOUT (input) INTEGER
* The logical unit number for output. NOUT > 0.
*
* =====================================================================
*
* .. 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
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