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|
*> \brief \b SCHKGB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
* NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
* X, XACT, WORK, RWORK, IWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER LA, LAFAC, NM, NN, NNB, NNS, NOUT
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
* $ NVAL( * )
* REAL A( * ), AFAC( * ), B( * ), RWORK( * ),
* $ WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SCHKGB tests SGBTRF, -TRS, -RFS, and -CON
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NM
*> \verbatim
*> NM is INTEGER
*> The number of values of M contained in the vector MVAL.
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*> NNB is INTEGER
*> The number of values of NB contained in the vector NBVAL.
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*> NBVAL is INTEGER array, dimension (NNB)
*> The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*> TSTERR is LOGICAL
*> Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is REAL array, dimension (LA)
*> \endverbatim
*>
*> \param[in] LA
*> \verbatim
*> LA is INTEGER
*> The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX
*> where KLMAX is the largest entry in the local array KLVAL,
*> KUMAX is the largest entry in the local array KUVAL and
*> NMAX is the largest entry in the input array NVAL.
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*> AFAC is REAL array, dimension (LAFAC)
*> \endverbatim
*>
*> \param[in] LAFAC
*> \verbatim
*> LAFAC is INTEGER
*> The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX
*> where KLMAX is the largest entry in the local array KLVAL,
*> KUMAX is the largest entry in the local array KUVAL and
*> NMAX is the largest entry in the input array NVAL.
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is REAL array, dimension (NMAX*NSMAX)
*> where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension
*> (NMAX*max(3,NSMAX,NMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension
*> (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*NMAX)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SCHKGB( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
$ NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B,
$ X, XACT, WORK, RWORK, IWORK, 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 ..
LOGICAL TSTERR
INTEGER LA, LAFAC, NM, NN, NNB, NNS, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
$ NVAL( * )
REAL A( * ), AFAC( * ), B( * ), RWORK( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
INTEGER NTYPES, NTESTS
PARAMETER ( NTYPES = 8, NTESTS = 7 )
INTEGER NBW, NTRAN
PARAMETER ( NBW = 4, NTRAN = 3 )
* ..
* .. Local Scalars ..
LOGICAL TRFCON, ZEROT
CHARACTER DIST, NORM, TRANS, TYPE, XTYPE
CHARACTER*3 PATH
INTEGER I, I1, I2, IKL, IKU, IM, IMAT, IN, INB, INFO,
$ IOFF, IRHS, ITRAN, IZERO, J, K, KL, KOFF, KU,
$ LDA, LDAFAC, LDB, M, MODE, N, NB, NERRS, NFAIL,
$ NIMAT, NKL, NKU, NRHS, NRUN
REAL AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, RCOND,
$ RCONDC, RCONDI, RCONDO
* ..
* .. Local Arrays ..
CHARACTER TRANSS( NTRAN )
INTEGER ISEED( 4 ), ISEEDY( 4 ), KLVAL( NBW ),
$ KUVAL( NBW )
REAL RESULT( NTESTS )
* ..
* .. External Functions ..
REAL SGET06, SLANGB, SLANGE
EXTERNAL SGET06, SLANGB, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRGE, SGBCON,
$ SGBRFS, SGBT01, SGBT02, SGBT05, SGBTRF, SGBTRS,
$ SGET04, SLACPY, SLARHS, SLASET, SLATB4, SLATMS,
$ XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 / ,
$ TRANSS / 'N', 'T', 'C' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'GB'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL SERRGE( PATH, NOUT )
INFOT = 0
CALL XLAENV( 2, 2 )
*
* Initialize the first value for the lower and upper bandwidths.
*
KLVAL( 1 ) = 0
KUVAL( 1 ) = 0
*
* Do for each value of M in MVAL
*
DO 160 IM = 1, NM
M = MVAL( IM )
*
* Set values to use for the lower bandwidth.
*
KLVAL( 2 ) = M + ( M+1 ) / 4
*
* KLVAL( 2 ) = MAX( M-1, 0 )
*
KLVAL( 3 ) = ( 3*M-1 ) / 4
KLVAL( 4 ) = ( M+1 ) / 4
*
* Do for each value of N in NVAL
*
DO 150 IN = 1, NN
N = NVAL( IN )
XTYPE = 'N'
*
* Set values to use for the upper bandwidth.
*
KUVAL( 2 ) = N + ( N+1 ) / 4
*
* KUVAL( 2 ) = MAX( N-1, 0 )
*
KUVAL( 3 ) = ( 3*N-1 ) / 4
KUVAL( 4 ) = ( N+1 ) / 4
*
* Set limits on the number of loop iterations.
*
NKL = MIN( M+1, 4 )
IF( N.EQ.0 )
$ NKL = 2
NKU = MIN( N+1, 4 )
IF( M.EQ.0 )
$ NKU = 2
NIMAT = NTYPES
IF( M.LE.0 .OR. N.LE.0 )
$ NIMAT = 1
*
DO 140 IKL = 1, NKL
*
* Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This
* order makes it easier to skip redundant values for small
* values of M.
*
KL = KLVAL( IKL )
DO 130 IKU = 1, NKU
*
* Do for KU = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This
* order makes it easier to skip redundant values for
* small values of N.
*
KU = KUVAL( IKU )
*
* Check that A and AFAC are big enough to generate this
* matrix.
*
LDA = KL + KU + 1
LDAFAC = 2*KL + KU + 1
IF( ( LDA*N ).GT.LA .OR. ( LDAFAC*N ).GT.LAFAC ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
IF( N*( KL+KU+1 ).GT.LA ) THEN
WRITE( NOUT, FMT = 9999 )LA, M, N, KL, KU,
$ N*( KL+KU+1 )
NERRS = NERRS + 1
END IF
IF( N*( 2*KL+KU+1 ).GT.LAFAC ) THEN
WRITE( NOUT, FMT = 9998 )LAFAC, M, N, KL, KU,
$ N*( 2*KL+KU+1 )
NERRS = NERRS + 1
END IF
GO TO 130
END IF
*
DO 120 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 120
*
* Skip types 2, 3, or 4 if the matrix size is too
* small.
*
ZEROT = IMAT.GE.2 .AND. IMAT.LE.4
IF( ZEROT .AND. N.LT.IMAT-1 )
$ GO TO 120
*
IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN
*
* Set up parameters with SLATB4 and generate a
* test matrix with SLATMS.
*
CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU,
$ ANORM, MODE, CNDNUM, DIST )
*
KOFF = MAX( 1, KU+2-N )
DO 20 I = 1, KOFF - 1
A( I ) = ZERO
20 CONTINUE
SRNAMT = 'SLATMS'
CALL SLATMS( M, N, DIST, ISEED, TYPE, RWORK,
$ MODE, CNDNUM, ANORM, KL, KU, 'Z',
$ A( KOFF ), LDA, WORK, INFO )
*
* Check the error code from SLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M,
$ N, KL, KU, -1, IMAT, NFAIL,
$ NERRS, NOUT )
GO TO 120
END IF
ELSE IF( IZERO.GT.0 ) THEN
*
* Use the same matrix for types 3 and 4 as for
* type 2 by copying back the zeroed out column.
*
CALL SCOPY( I2-I1+1, B, 1, A( IOFF+I1 ), 1 )
END IF
*
* For types 2, 3, and 4, zero one or more columns of
* the matrix to test that INFO is returned correctly.
*
IZERO = 0
IF( ZEROT ) THEN
IF( IMAT.EQ.2 ) THEN
IZERO = 1
ELSE IF( IMAT.EQ.3 ) THEN
IZERO = MIN( M, N )
ELSE
IZERO = MIN( M, N ) / 2 + 1
END IF
IOFF = ( IZERO-1 )*LDA
IF( IMAT.LT.4 ) THEN
*
* Store the column to be zeroed out in B.
*
I1 = MAX( 1, KU+2-IZERO )
I2 = MIN( KL+KU+1, KU+1+( M-IZERO ) )
CALL SCOPY( I2-I1+1, A( IOFF+I1 ), 1, B, 1 )
*
DO 30 I = I1, I2
A( IOFF+I ) = ZERO
30 CONTINUE
ELSE
DO 50 J = IZERO, N
DO 40 I = MAX( 1, KU+2-J ),
$ MIN( KL+KU+1, KU+1+( M-J ) )
A( IOFF+I ) = ZERO
40 CONTINUE
IOFF = IOFF + LDA
50 CONTINUE
END IF
END IF
*
* These lines, if used in place of the calls in the
* loop over INB, cause the code to bomb on a Sun
* SPARCstation.
*
* ANORMO = SLANGB( 'O', N, KL, KU, A, LDA, RWORK )
* ANORMI = SLANGB( 'I', N, KL, KU, A, LDA, RWORK )
*
* Do for each blocksize in NBVAL
*
DO 110 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
* Compute the LU factorization of the band matrix.
*
IF( M.GT.0 .AND. N.GT.0 )
$ CALL SLACPY( 'Full', KL+KU+1, N, A, LDA,
$ AFAC( KL+1 ), LDAFAC )
SRNAMT = 'SGBTRF'
CALL SGBTRF( M, N, KL, KU, AFAC, LDAFAC, IWORK,
$ INFO )
*
* Check error code from SGBTRF.
*
IF( INFO.NE.IZERO )
$ CALL ALAERH( PATH, 'SGBTRF', INFO, IZERO,
$ ' ', M, N, KL, KU, NB, IMAT,
$ NFAIL, NERRS, NOUT )
TRFCON = .FALSE.
*
*+ TEST 1
* Reconstruct matrix from factors and compute
* residual.
*
CALL SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC,
$ IWORK, WORK, RESULT( 1 ) )
*
* Print information about the tests so far that
* did not pass the threshold.
*
IF( RESULT( 1 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )M, N, KL, KU, NB,
$ IMAT, 1, RESULT( 1 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
*
* Skip the remaining tests if this is not the
* first block size or if M .ne. N.
*
IF( INB.GT.1 .OR. M.NE.N )
$ GO TO 110
*
ANORMO = SLANGB( 'O', N, KL, KU, A, LDA, RWORK )
ANORMI = SLANGB( 'I', N, KL, KU, A, LDA, RWORK )
*
IF( INFO.EQ.0 ) THEN
*
* Form the inverse of A so we can get a good
* estimate of CNDNUM = norm(A) * norm(inv(A)).
*
LDB = MAX( 1, N )
CALL SLASET( 'Full', N, N, ZERO, ONE, WORK,
$ LDB )
SRNAMT = 'SGBTRS'
CALL SGBTRS( 'No transpose', N, KL, KU, N,
$ AFAC, LDAFAC, IWORK, WORK, LDB,
$ INFO )
*
* Compute the 1-norm condition number of A.
*
AINVNM = SLANGE( 'O', N, N, WORK, LDB,
$ RWORK )
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORMO ) / AINVNM
END IF
*
* Compute the infinity-norm condition number of
* A.
*
AINVNM = SLANGE( 'I', N, N, WORK, LDB,
$ RWORK )
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORMI ) / AINVNM
END IF
ELSE
*
* Do only the condition estimate if INFO.NE.0.
*
TRFCON = .TRUE.
RCONDO = ZERO
RCONDI = ZERO
END IF
*
* Skip the solve tests if the matrix is singular.
*
IF( TRFCON )
$ GO TO 90
*
DO 80 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
XTYPE = 'N'
*
DO 70 ITRAN = 1, NTRAN
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
RCONDC = RCONDO
NORM = 'O'
ELSE
RCONDC = RCONDI
NORM = 'I'
END IF
*
*+ TEST 2:
* Solve and compute residual for A * X = B.
*
SRNAMT = 'SLARHS'
CALL SLARHS( PATH, XTYPE, ' ', TRANS, N,
$ N, KL, KU, NRHS, A, LDA,
$ XACT, LDB, B, LDB, ISEED,
$ INFO )
XTYPE = 'C'
CALL SLACPY( 'Full', N, NRHS, B, LDB, X,
$ LDB )
*
SRNAMT = 'SGBTRS'
CALL SGBTRS( TRANS, N, KL, KU, NRHS, AFAC,
$ LDAFAC, IWORK, X, LDB, INFO )
*
* Check error code from SGBTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SGBTRS', INFO, 0,
$ TRANS, N, N, KL, KU, -1,
$ IMAT, NFAIL, NERRS, NOUT )
*
CALL SLACPY( 'Full', N, NRHS, B, LDB,
$ WORK, LDB )
CALL SGBT02( TRANS, M, N, KL, KU, NRHS, A,
$ LDA, X, LDB, WORK, LDB,
$ RESULT( 2 ) )
*
*+ TEST 3:
* Check solution from generated exact
* solution.
*
CALL SGET04( N, NRHS, X, LDB, XACT, LDB,
$ RCONDC, RESULT( 3 ) )
*
*+ TESTS 4, 5, 6:
* Use iterative refinement to improve the
* solution.
*
SRNAMT = 'SGBRFS'
CALL SGBRFS( TRANS, N, KL, KU, NRHS, A,
$ LDA, AFAC, LDAFAC, IWORK, B,
$ LDB, X, LDB, RWORK,
$ RWORK( NRHS+1 ), WORK,
$ IWORK( N+1 ), INFO )
*
* Check error code from SGBRFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SGBRFS', INFO, 0,
$ TRANS, N, N, KL, KU, NRHS,
$ IMAT, NFAIL, NERRS, NOUT )
*
CALL SGET04( N, NRHS, X, LDB, XACT, LDB,
$ RCONDC, RESULT( 4 ) )
CALL SGBT05( TRANS, N, KL, KU, NRHS, A,
$ LDA, B, LDB, X, LDB, XACT,
$ LDB, RWORK, RWORK( NRHS+1 ),
$ RESULT( 5 ) )
DO 60 K = 2, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9996 )TRANS, N,
$ KL, KU, NRHS, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
60 CONTINUE
NRUN = NRUN + 5
70 CONTINUE
80 CONTINUE
*
*+ TEST 7:
* Get an estimate of RCOND = 1/CNDNUM.
*
90 CONTINUE
DO 100 ITRAN = 1, 2
IF( ITRAN.EQ.1 ) THEN
ANORM = ANORMO
RCONDC = RCONDO
NORM = 'O'
ELSE
ANORM = ANORMI
RCONDC = RCONDI
NORM = 'I'
END IF
SRNAMT = 'SGBCON'
CALL SGBCON( NORM, N, KL, KU, AFAC, LDAFAC,
$ IWORK, ANORM, RCOND, WORK,
$ IWORK( N+1 ), INFO )
*
* Check error code from SGBCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SGBCON', INFO, 0,
$ NORM, N, N, KL, KU, -1, IMAT,
$ NFAIL, NERRS, NOUT )
*
RESULT( 7 ) = SGET06( RCOND, RCONDC )
*
* Print information about the tests that did
* not pass the threshold.
*
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9995 )NORM, N, KL, KU,
$ IMAT, 7, RESULT( 7 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
100 CONTINUE
*
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
160 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' *** In SCHKGB, LA=', I5, ' is too small for M=', I5,
$ ', N=', I5, ', KL=', I4, ', KU=', I4,
$ / ' ==> Increase LA to at least ', I5 )
9998 FORMAT( ' *** In SCHKGB, LAFAC=', I5, ' is too small for M=', I5,
$ ', N=', I5, ', KL=', I4, ', KU=', I4,
$ / ' ==> Increase LAFAC to at least ', I5 )
9997 FORMAT( ' M =', I5, ', N =', I5, ', KL=', I5, ', KU=', I5,
$ ', NB =', I4, ', type ', I1, ', test(', I1, ')=', G12.5 )
9996 FORMAT( ' TRANS=''', A1, ''', N=', I5, ', KL=', I5, ', KU=', I5,
$ ', NRHS=', I3, ', type ', I1, ', test(', I1, ')=', G12.5 )
9995 FORMAT( ' NORM =''', A1, ''', N=', I5, ', KL=', I5, ', KU=', I5,
$ ',', 10X, ' type ', I1, ', test(', I1, ')=', G12.5 )
*
RETURN
*
* End of SCHKGB
*
END
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