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|
*> \brief \b SCHKPB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
* XACT, WORK, RWORK, IWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNB, NNS, NOUT
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SCHKPB tests SPBTRF, -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] 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 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 (NBVAL)
*> 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[in] NMAX
*> \verbatim
*> NMAX is INTEGER
*> The maximum value permitted for N, used in dimensioning the
*> work arrays.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is REAL array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*> AFAC is REAL array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*> AINV is REAL array, dimension (NMAX*NMAX)
*> \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))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL 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 November 2011
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
$ THRESH, TSTERR, NMAX, A, AFAC, AINV, 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 NMAX, NN, NNB, NNS, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
REAL A( * ), AFAC( * ), AINV( * ), 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
PARAMETER ( NBW = 4 )
* ..
* .. Local Scalars ..
LOGICAL ZEROT
CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, I1, I2, IKD, IMAT, IN, INB, INFO, IOFF,
$ IRHS, IUPLO, IW, IZERO, K, KD, KL, KOFF, KU,
$ LDA, LDAB, MODE, N, NB, NERRS, NFAIL, NIMAT,
$ NKD, NRHS, NRUN
REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW )
REAL RESULT( NTESTS )
* ..
* .. External Functions ..
REAL SGET06, SLANGE, SLANSB
EXTERNAL SGET06, SLANGE, SLANSB
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRPO, SGET04,
$ SLACPY, SLARHS, SLASET, SLATB4, SLATMS, SPBCON,
$ SPBRFS, SPBT01, SPBT02, SPBT05, SPBTRF, SPBTRS,
$ SSWAP, 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 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'PB'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL SERRPO( PATH, NOUT )
INFOT = 0
CALL XLAENV( 2, 2 )
KDVAL( 1 ) = 0
*
* Do for each value of N in NVAL
*
DO 90 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
*
* Set limits on the number of loop iterations.
*
NKD = MAX( 1, MIN( N, 4 ) )
NIMAT = NTYPES
IF( N.EQ.0 )
$ NIMAT = 1
*
KDVAL( 2 ) = N + ( N+1 ) / 4
KDVAL( 3 ) = ( 3*N-1 ) / 4
KDVAL( 4 ) = ( N+1 ) / 4
*
DO 80 IKD = 1, NKD
*
* Do for KD = 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.
*
KD = KDVAL( IKD )
LDAB = KD + 1
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 70 IUPLO = 1, 2
KOFF = 1
IF( IUPLO.EQ.1 ) THEN
UPLO = 'U'
KOFF = MAX( 1, KD+2-N )
PACKIT = 'Q'
ELSE
UPLO = 'L'
PACKIT = 'B'
END IF
*
DO 60 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 60
*
* 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 60
*
IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN
*
* Set up parameters with SLATB4 and generate a test
* matrix with SLATMS.
*
CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
$ MODE, CNDNUM, DIST )
*
SRNAMT = 'SLATMS'
CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
$ CNDNUM, ANORM, KD, KD, PACKIT,
$ A( KOFF ), LDAB, WORK, INFO )
*
* Check error code from SLATMS.
*
IF( INFO.NE.0 ) THEN
CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N,
$ N, KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
GO TO 60
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,
*
IW = 2*LDA + 1
IF( IUPLO.EQ.1 ) THEN
IOFF = ( IZERO-1 )*LDAB + KD + 1
CALL SCOPY( IZERO-I1, WORK( IW ), 1,
$ A( IOFF-IZERO+I1 ), 1 )
IW = IW + IZERO - I1
CALL SCOPY( I2-IZERO+1, WORK( IW ), 1,
$ A( IOFF ), MAX( LDAB-1, 1 ) )
ELSE
IOFF = ( I1-1 )*LDAB + 1
CALL SCOPY( IZERO-I1, WORK( IW ), 1,
$ A( IOFF+IZERO-I1 ),
$ MAX( LDAB-1, 1 ) )
IOFF = ( IZERO-1 )*LDAB + 1
IW = IW + IZERO - I1
CALL SCOPY( I2-IZERO+1, WORK( IW ), 1,
$ A( IOFF ), 1 )
END IF
END IF
*
* For types 2-4, zero one row and column 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 = N
ELSE
IZERO = N / 2 + 1
END IF
*
* Save the zeroed out row and column in WORK(*,3)
*
IW = 2*LDA
DO 20 I = 1, MIN( 2*KD+1, N )
WORK( IW+I ) = ZERO
20 CONTINUE
IW = IW + 1
I1 = MAX( IZERO-KD, 1 )
I2 = MIN( IZERO+KD, N )
*
IF( IUPLO.EQ.1 ) THEN
IOFF = ( IZERO-1 )*LDAB + KD + 1
CALL SSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1,
$ WORK( IW ), 1 )
IW = IW + IZERO - I1
CALL SSWAP( I2-IZERO+1, A( IOFF ),
$ MAX( LDAB-1, 1 ), WORK( IW ), 1 )
ELSE
IOFF = ( I1-1 )*LDAB + 1
CALL SSWAP( IZERO-I1, A( IOFF+IZERO-I1 ),
$ MAX( LDAB-1, 1 ), WORK( IW ), 1 )
IOFF = ( IZERO-1 )*LDAB + 1
IW = IW + IZERO - I1
CALL SSWAP( I2-IZERO+1, A( IOFF ), 1,
$ WORK( IW ), 1 )
END IF
END IF
*
* Do for each value of NB in NBVAL
*
DO 50 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
* Compute the L*L' or U'*U factorization of the band
* matrix.
*
CALL SLACPY( 'Full', KD+1, N, A, LDAB, AFAC, LDAB )
SRNAMT = 'SPBTRF'
CALL SPBTRF( UPLO, N, KD, AFAC, LDAB, INFO )
*
* Check error code from SPBTRF.
*
IF( INFO.NE.IZERO ) THEN
CALL ALAERH( PATH, 'SPBTRF', INFO, IZERO, UPLO,
$ N, N, KD, KD, NB, IMAT, NFAIL,
$ NERRS, NOUT )
GO TO 50
END IF
*
* Skip the tests if INFO is not 0.
*
IF( INFO.NE.0 )
$ GO TO 50
*
*+ TEST 1
* Reconstruct matrix from factors and compute
* residual.
*
CALL SLACPY( 'Full', KD+1, N, AFAC, LDAB, AINV,
$ LDAB )
CALL SPBT01( UPLO, N, KD, A, LDAB, AINV, LDAB,
$ RWORK, RESULT( 1 ) )
*
* Print the test ratio if it is .GE. THRESH.
*
IF( RESULT( 1 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )UPLO, N, KD, NB, IMAT,
$ 1, RESULT( 1 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
*
* Only do other tests if this is the first blocksize.
*
IF( INB.GT.1 )
$ GO TO 50
*
* Form the inverse of A so we can get a good estimate
* of RCONDC = 1/(norm(A) * norm(inv(A))).
*
CALL SLASET( 'Full', N, N, ZERO, ONE, AINV, LDA )
SRNAMT = 'SPBTRS'
CALL SPBTRS( UPLO, N, KD, N, AFAC, LDAB, AINV, LDA,
$ INFO )
*
* Compute RCONDC = 1/(norm(A) * norm(inv(A))).
*
ANORM = SLANSB( '1', UPLO, N, KD, A, LDAB, RWORK )
AINVNM = SLANGE( '1', N, N, AINV, LDA, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDC = ONE
ELSE
RCONDC = ( ONE / ANORM ) / AINVNM
END IF
*
DO 40 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
*
*+ TEST 2
* Solve and compute residual for A * X = B.
*
SRNAMT = 'SLARHS'
CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD,
$ KD, NRHS, A, LDAB, XACT, LDA, B,
$ LDA, ISEED, INFO )
CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'SPBTRS'
CALL SPBTRS( UPLO, N, KD, NRHS, AFAC, LDAB, X,
$ LDA, INFO )
*
* Check error code from SPBTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPBTRS', INFO, 0, UPLO,
$ N, N, KD, KD, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK,
$ LDA )
CALL SPBT02( UPLO, N, KD, NRHS, A, LDAB, X, LDA,
$ WORK, LDA, RWORK, RESULT( 2 ) )
*
*+ TEST 3
* Check solution from generated exact solution.
*
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
*
*+ TESTS 4, 5, and 6
* Use iterative refinement to improve the solution.
*
SRNAMT = 'SPBRFS'
CALL SPBRFS( UPLO, N, KD, NRHS, A, LDAB, AFAC,
$ LDAB, B, LDA, X, LDA, RWORK,
$ RWORK( NRHS+1 ), WORK, IWORK,
$ INFO )
*
* Check error code from SPBRFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPBRFS', INFO, 0, UPLO,
$ N, N, KD, KD, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 4 ) )
CALL SPBT05( UPLO, N, KD, NRHS, A, LDAB, B, LDA,
$ X, LDA, XACT, LDA, RWORK,
$ RWORK( NRHS+1 ), RESULT( 5 ) )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 30 K = 2, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )UPLO, N, KD,
$ NRHS, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
30 CONTINUE
NRUN = NRUN + 5
40 CONTINUE
*
*+ TEST 7
* Get an estimate of RCOND = 1/CNDNUM.
*
SRNAMT = 'SPBCON'
CALL SPBCON( UPLO, N, KD, AFAC, LDAB, ANORM, RCOND,
$ WORK, IWORK, INFO )
*
* Check error code from SPBCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPBCON', INFO, 0, UPLO, N,
$ N, KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
RESULT( 7 ) = SGET06( RCOND, RCONDC )
*
* Print the test ratio if it is .GE. THRESH.
*
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )UPLO, N, KD, IMAT, 7,
$ RESULT( 7 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
50 CONTINUE
60 CONTINUE
70 CONTINUE
80 CONTINUE
90 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NB=', I4,
$ ', type ', I2, ', test ', I2, ', ratio= ', G12.5 )
9998 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I3,
$ ', type ', I2, ', test(', I2, ') = ', G12.5 )
9997 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ',', 10X,
$ ' type ', I2, ', test(', I2, ') = ', G12.5 )
RETURN
*
* End of SCHKPB
*
END
|
