Julie
e18d437924
GitHub is now enabling us to track accurately version and date. No need for this anymore.
503 lines
15 KiB
FortranFixed
503 lines
15 KiB
FortranFixed
*> \brief \b SCHKPP
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
|
|
* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
|
|
* IWORK, NOUT )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* LOGICAL TSTERR
|
|
* INTEGER NMAX, NN, NNS, NOUT
|
|
* REAL THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* LOGICAL DOTYPE( * )
|
|
* INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
|
|
* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
|
|
* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SCHKPP tests SPPTRF, -TRI, -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] 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+1)/2)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] AFAC
|
|
*> \verbatim
|
|
*> AFAC is REAL array, dimension
|
|
*> (NMAX*(NMAX+1)/2)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] AINV
|
|
*> \verbatim
|
|
*> AINV is REAL array, dimension
|
|
*> (NMAX*(NMAX+1)/2)
|
|
*> \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.
|
|
*
|
|
*> \ingroup single_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
|
|
$ NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
|
|
$ IWORK, NOUT )
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
LOGICAL TSTERR
|
|
INTEGER NMAX, NN, NNS, NOUT
|
|
REAL THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
LOGICAL DOTYPE( * )
|
|
INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
|
|
REAL A( * ), AFAC( * ), AINV( * ), B( * ),
|
|
$ RWORK( * ), WORK( * ), X( * ), XACT( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO
|
|
PARAMETER ( ZERO = 0.0E+0 )
|
|
INTEGER NTYPES
|
|
PARAMETER ( NTYPES = 9 )
|
|
INTEGER NTESTS
|
|
PARAMETER ( NTESTS = 8 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL ZEROT
|
|
CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
|
|
CHARACTER*3 PATH
|
|
INTEGER I, IMAT, IN, INFO, IOFF, IRHS, IUPLO, IZERO, K,
|
|
$ KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT, NPP,
|
|
$ NRHS, NRUN
|
|
REAL ANORM, CNDNUM, RCOND, RCONDC
|
|
* ..
|
|
* .. Local Arrays ..
|
|
CHARACTER PACKS( 2 ), UPLOS( 2 )
|
|
INTEGER ISEED( 4 ), ISEEDY( 4 )
|
|
REAL RESULT( NTESTS )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SGET06, SLANSP
|
|
EXTERNAL SGET06, SLANSP
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRPO, SGET04,
|
|
$ SLACPY, SLARHS, SLATB4, SLATMS, SPPCON, SPPRFS,
|
|
$ SPPT01, SPPT02, SPPT03, SPPT05, SPPTRF, SPPTRI,
|
|
$ SPPTRS
|
|
* ..
|
|
* .. Scalars in Common ..
|
|
LOGICAL LERR, OK
|
|
CHARACTER*32 SRNAMT
|
|
INTEGER INFOT, NUNIT
|
|
* ..
|
|
* .. Common blocks ..
|
|
COMMON / INFOC / INFOT, NUNIT, OK, LERR
|
|
COMMON / SRNAMC / SRNAMT
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA ISEEDY / 1988, 1989, 1990, 1991 /
|
|
DATA UPLOS / 'U', 'L' / , PACKS / 'C', 'R' /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Initialize constants and the random number seed.
|
|
*
|
|
PATH( 1: 1 ) = 'Single precision'
|
|
PATH( 2: 3 ) = 'PP'
|
|
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
|
|
*
|
|
* Do for each value of N in NVAL
|
|
*
|
|
DO 110 IN = 1, NN
|
|
N = NVAL( IN )
|
|
LDA = MAX( N, 1 )
|
|
XTYPE = 'N'
|
|
NIMAT = NTYPES
|
|
IF( N.LE.0 )
|
|
$ NIMAT = 1
|
|
*
|
|
DO 100 IMAT = 1, NIMAT
|
|
*
|
|
* Do the tests only if DOTYPE( IMAT ) is true.
|
|
*
|
|
IF( .NOT.DOTYPE( IMAT ) )
|
|
$ GO TO 100
|
|
*
|
|
* Skip types 3, 4, or 5 if the matrix size is too small.
|
|
*
|
|
ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
|
|
IF( ZEROT .AND. N.LT.IMAT-2 )
|
|
$ GO TO 100
|
|
*
|
|
* Do first for UPLO = 'U', then for UPLO = 'L'
|
|
*
|
|
DO 90 IUPLO = 1, 2
|
|
UPLO = UPLOS( IUPLO )
|
|
PACKIT = PACKS( IUPLO )
|
|
*
|
|
* 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, KL, KU, PACKIT, A, LDA, WORK,
|
|
$ INFO )
|
|
*
|
|
* Check error code from SLATMS.
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
|
|
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
GO TO 90
|
|
END IF
|
|
*
|
|
* For types 3-5, zero one row and column of the matrix to
|
|
* test that INFO is returned correctly.
|
|
*
|
|
IF( ZEROT ) THEN
|
|
IF( IMAT.EQ.3 ) THEN
|
|
IZERO = 1
|
|
ELSE IF( IMAT.EQ.4 ) THEN
|
|
IZERO = N
|
|
ELSE
|
|
IZERO = N / 2 + 1
|
|
END IF
|
|
*
|
|
* Set row and column IZERO of A to 0.
|
|
*
|
|
IF( IUPLO.EQ.1 ) THEN
|
|
IOFF = ( IZERO-1 )*IZERO / 2
|
|
DO 20 I = 1, IZERO - 1
|
|
A( IOFF+I ) = ZERO
|
|
20 CONTINUE
|
|
IOFF = IOFF + IZERO
|
|
DO 30 I = IZERO, N
|
|
A( IOFF ) = ZERO
|
|
IOFF = IOFF + I
|
|
30 CONTINUE
|
|
ELSE
|
|
IOFF = IZERO
|
|
DO 40 I = 1, IZERO - 1
|
|
A( IOFF ) = ZERO
|
|
IOFF = IOFF + N - I
|
|
40 CONTINUE
|
|
IOFF = IOFF - IZERO
|
|
DO 50 I = IZERO, N
|
|
A( IOFF+I ) = ZERO
|
|
50 CONTINUE
|
|
END IF
|
|
ELSE
|
|
IZERO = 0
|
|
END IF
|
|
*
|
|
* Compute the L*L' or U'*U factorization of the matrix.
|
|
*
|
|
NPP = N*( N+1 ) / 2
|
|
CALL SCOPY( NPP, A, 1, AFAC, 1 )
|
|
SRNAMT = 'SPPTRF'
|
|
CALL SPPTRF( UPLO, N, AFAC, INFO )
|
|
*
|
|
* Check error code from SPPTRF.
|
|
*
|
|
IF( INFO.NE.IZERO ) THEN
|
|
CALL ALAERH( PATH, 'SPPTRF', INFO, IZERO, UPLO, N, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
GO TO 90
|
|
END IF
|
|
*
|
|
* Skip the tests if INFO is not 0.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ GO TO 90
|
|
*
|
|
*+ TEST 1
|
|
* Reconstruct matrix from factors and compute residual.
|
|
*
|
|
CALL SCOPY( NPP, AFAC, 1, AINV, 1 )
|
|
CALL SPPT01( UPLO, N, A, AINV, RWORK, RESULT( 1 ) )
|
|
*
|
|
*+ TEST 2
|
|
* Form the inverse and compute the residual.
|
|
*
|
|
CALL SCOPY( NPP, AFAC, 1, AINV, 1 )
|
|
SRNAMT = 'SPPTRI'
|
|
CALL SPPTRI( UPLO, N, AINV, INFO )
|
|
*
|
|
* Check error code from SPPTRI.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SPPTRI', INFO, 0, UPLO, N, N, -1,
|
|
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
CALL SPPT03( UPLO, N, A, AINV, WORK, LDA, RWORK, RCONDC,
|
|
$ RESULT( 2 ) )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
DO 60 K = 1, 2
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K,
|
|
$ RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
60 CONTINUE
|
|
NRUN = NRUN + 2
|
|
*
|
|
DO 80 IRHS = 1, NNS
|
|
NRHS = NSVAL( IRHS )
|
|
*
|
|
*+ TEST 3
|
|
* Solve and compute residual for A * X = B.
|
|
*
|
|
SRNAMT = 'SLARHS'
|
|
CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
|
|
$ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
|
|
$ INFO )
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
|
*
|
|
SRNAMT = 'SPPTRS'
|
|
CALL SPPTRS( UPLO, N, NRHS, AFAC, X, LDA, INFO )
|
|
*
|
|
* Check error code from SPPTRS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SPPTRS', INFO, 0, UPLO, N, N,
|
|
$ -1, -1, NRHS, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
|
CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
|
|
$ RWORK, RESULT( 3 ) )
|
|
*
|
|
*+ TEST 4
|
|
* Check solution from generated exact solution.
|
|
*
|
|
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 4 ) )
|
|
*
|
|
*+ TESTS 5, 6, and 7
|
|
* Use iterative refinement to improve the solution.
|
|
*
|
|
SRNAMT = 'SPPRFS'
|
|
CALL SPPRFS( UPLO, N, NRHS, A, AFAC, B, LDA, X, LDA,
|
|
$ RWORK, RWORK( NRHS+1 ), WORK, IWORK,
|
|
$ INFO )
|
|
*
|
|
* Check error code from SPPRFS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SPPRFS', INFO, 0, UPLO, N, N,
|
|
$ -1, -1, NRHS, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 5 ) )
|
|
CALL SPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA, XACT,
|
|
$ LDA, RWORK, RWORK( NRHS+1 ),
|
|
$ RESULT( 6 ) )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
DO 70 K = 3, 7
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
|
|
$ K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
70 CONTINUE
|
|
NRUN = NRUN + 5
|
|
80 CONTINUE
|
|
*
|
|
*+ TEST 8
|
|
* Get an estimate of RCOND = 1/CNDNUM.
|
|
*
|
|
ANORM = SLANSP( '1', UPLO, N, A, RWORK )
|
|
SRNAMT = 'SPPCON'
|
|
CALL SPPCON( UPLO, N, AFAC, ANORM, RCOND, WORK, IWORK,
|
|
$ INFO )
|
|
*
|
|
* Check error code from SPPCON.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SPPCON', INFO, 0, UPLO, N, N, -1,
|
|
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
RESULT( 8 ) = SGET06( RCOND, RCONDC )
|
|
*
|
|
* Print the test ratio if greater than or equal to THRESH.
|
|
*
|
|
IF( RESULT( 8 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, 8,
|
|
$ RESULT( 8 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', type ', I2, ', test ',
|
|
$ I2, ', ratio =', G12.5 )
|
|
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
|
|
$ I2, ', test(', I2, ') =', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of SCHKPP
|
|
*
|
|
END
|