testdata/lapack/TESTING/LIN/dchktb.f
*> \brief \b DCHKTB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK,
* NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNS, NOUT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
* DOUBLE PRECISION AB( * ), AINV( * ), B( * ), RWORK( * ),
* $ WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCHKTB tests DTBTRS, -RFS, and -CON, and DLATBS.
*> \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] 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] 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 DOUBLE PRECISION
*> 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[in] NMAX
*> \verbatim
*> NMAX is INTEGER
*> The leading dimension of the work arrays.
*> NMAX >= the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension
*> (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension
*> (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (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 December 2016
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
$ NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK,
$ NOUT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
DOUBLE PRECISION AB( * ), AINV( * ), B( * ), RWORK( * ),
$ WORK( * ), X( * ), XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPE1, NTYPES
PARAMETER ( NTYPE1 = 9, NTYPES = 17 )
INTEGER NTESTS
PARAMETER ( NTESTS = 8 )
INTEGER NTRAN
PARAMETER ( NTRAN = 3 )
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN,
$ IUPLO, J, K, KD, LDA, LDAB, N, NERRS, NFAIL,
$ NIMAT, NIMAT2, NK, NRHS, NRUN
DOUBLE PRECISION AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
$ SCALE
* ..
* .. Local Arrays ..
CHARACTER TRANSS( NTRAN ), UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLANTB, DLANTR
EXTERNAL LSAME, DLANTB, DLANTR
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, DCOPY, DERRTR, DGET04,
$ DLACPY, DLARHS, DLASET, DLATBS, DLATTB, DTBCON,
$ DTBRFS, DTBSV, DTBT02, DTBT03, DTBT05, DTBT06,
$ DTBTRS
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'TB'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL DERRTR( PATH, NOUT )
INFOT = 0
*
DO 140 IN = 1, NN
*
* Do for each value of N in NVAL
*
N = NVAL( IN )
LDA = MAX( 1, N )
XTYPE = 'N'
NIMAT = NTYPE1
NIMAT2 = NTYPES
IF( N.LE.0 ) THEN
NIMAT = 1
NIMAT2 = NTYPE1 + 1
END IF
*
NK = MIN( N+1, 4 )
DO 130 IK = 1, NK
*
* Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes
* it easier to skip redundant values for small values of N.
*
IF( IK.EQ.1 ) THEN
KD = 0
ELSE IF( IK.EQ.2 ) THEN
KD = MAX( N, 0 )
ELSE IF( IK.EQ.3 ) THEN
KD = ( 3*N-1 ) / 4
ELSE IF( IK.EQ.4 ) THEN
KD = ( N+1 ) / 4
END IF
LDAB = KD + 1
*
DO 90 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 90
*
DO 80 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
*
* Call DLATTB to generate a triangular test matrix.
*
SRNAMT = 'DLATTB'
CALL DLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED,
$ N, KD, AB, LDAB, X, WORK, INFO )
*
* Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
IF( LSAME( DIAG, 'N' ) ) THEN
IDIAG = 1
ELSE
IDIAG = 2
END IF
*
* Form the inverse of A so we can get a good estimate
* of RCONDC = 1/(norm(A) * norm(inv(A))).
*
CALL DLASET( 'Full', N, N, ZERO, ONE, AINV, LDA )
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
CALL DTBSV( UPLO, 'No transpose', DIAG, J, KD,
$ AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 )
20 CONTINUE
ELSE
DO 30 J = 1, N
CALL DTBSV( UPLO, 'No transpose', DIAG, N-J+1,
$ KD, AB( ( J-1 )*LDAB+1 ), LDAB,
$ AINV( ( J-1 )*LDA+J ), 1 )
30 CONTINUE
END IF
*
* Compute the 1-norm condition number of A.
*
ANORM = DLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB,
$ RWORK )
AINVNM = DLANTR( '1', UPLO, DIAG, N, N, AINV, LDA,
$ RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORM ) / AINVNM
END IF
*
* Compute the infinity-norm condition number of A.
*
ANORM = DLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB,
$ RWORK )
AINVNM = DLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
$ RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORM ) / AINVNM
END IF
*
DO 60 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
XTYPE = 'N'
*
DO 50 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, or A**H.
*
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
*
*+ TEST 1
* Solve and compute residual for op(A)*x = b.
*
SRNAMT = 'DLARHS'
CALL DLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD,
$ IDIAG, NRHS, AB, LDAB, XACT, LDA,
$ B, LDA, ISEED, INFO )
XTYPE = 'C'
CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'DTBTRS'
CALL DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, X, LDA, INFO )
*
* Check error code from DTBTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DTBTRS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, KD,
$ KD, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, X, LDA, B, LDA, WORK,
$ RESULT( 1 ) )
*
*+ TEST 2
* Check solution from generated exact solution.
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 2 ) )
*
*+ TESTS 3, 4, and 5
* Use iterative refinement to improve the solution
* and compute error bounds.
*
SRNAMT = 'DTBRFS'
CALL DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, B, LDA, X, LDA, RWORK,
$ RWORK( NRHS+1 ), WORK, IWORK,
$ INFO )
*
* Check error code from DTBRFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DTBRFS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, KD,
$ KD, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
CALL DTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, B, LDA, X, LDA, XACT, LDA,
$ RWORK, RWORK( NRHS+1 ),
$ RESULT( 4 ) )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 40 K = 1, 5
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )UPLO, TRANS,
$ DIAG, N, KD, NRHS, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
40 CONTINUE
NRUN = NRUN + 5
50 CONTINUE
60 CONTINUE
*
*+ TEST 6
* Get an estimate of RCOND = 1/CNDNUM.
*
DO 70 ITRAN = 1, 2
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
SRNAMT = 'DTBCON'
CALL DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB,
$ RCOND, WORK, IWORK, INFO )
*
* Check error code from DTBCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DTBCON', INFO, 0,
$ NORM // UPLO // DIAG, N, N, KD, KD,
$ -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB,
$ LDAB, RWORK, RESULT( 6 ) )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 ) 'DTBCON', NORM, UPLO,
$ DIAG, N, KD, IMAT, 6, RESULT( 6 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
70 CONTINUE
80 CONTINUE
90 CONTINUE
*
* Use pathological test matrices to test DLATBS.
*
DO 120 IMAT = NTYPE1 + 1, NIMAT2
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 120
*
DO 110 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
DO 100 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, and A**H.
*
TRANS = TRANSS( ITRAN )
*
* Call DLATTB to generate a triangular test matrix.
*
SRNAMT = 'DLATTB'
CALL DLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD,
$ AB, LDAB, X, WORK, INFO )
*
*+ TEST 7
* Solve the system op(A)*x = b
*
SRNAMT = 'DLATBS'
CALL DCOPY( N, X, 1, B, 1 )
CALL DLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB,
$ LDAB, B, SCALE, RWORK, INFO )
*
* Check error code from DLATBS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DLATBS', INFO, 0,
$ UPLO // TRANS // DIAG // 'N', N, N,
$ KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL DTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
$ WORK, RESULT( 7 ) )
*
*+ TEST 8
* Solve op(A)*x = b again with NORMIN = 'Y'.
*
CALL DCOPY( N, X, 1, B, 1 )
CALL DLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB,
$ LDAB, B, SCALE, RWORK, INFO )
*
* Check error code from DLATBS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DLATBS', INFO, 0,
$ UPLO // TRANS // DIAG // 'Y', N, N,
$ KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL DTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
$ WORK, RESULT( 8 ) )
*
* 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 = 9997 )'DLATBS', UPLO, TRANS,
$ DIAG, 'N', N, KD, IMAT, 7, RESULT( 7 )
NFAIL = NFAIL + 1
END IF
IF( RESULT( 8 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )'DLATBS', UPLO, TRANS,
$ DIAG, 'Y', N, KD, IMAT, 8, RESULT( 8 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 2
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''',
$ DIAG=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I5,
$ ', type ', I2, ', test(', I2, ')=', G12.5 )
9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',',
$ I5, ',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
$ G12.5 )
9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
$ A1, ''',', I5, ',', I5, ', ... ), type ', I2, ', test(',
$ I1, ')=', G12.5 )
RETURN
*
* End of DCHKTB
*
END