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Cloned library LAPACK-3.11.0 with extra build files for internal package management.
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LAPACK-3.11.0/TESTING/LIN/schkpo.f

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*> \brief \b SCHKPO
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SCHKPO( 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
*>
*> SCHKPO tests SPOTRF, -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] 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[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.
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, 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, 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 ZERO
PARAMETER ( ZERO = 0.0E+0 )
INTEGER NTYPES
PARAMETER ( NTYPES = 9 )
INTEGER NTESTS
PARAMETER ( NTESTS = 8 )
* ..
* .. Local Scalars ..
LOGICAL ZEROT
CHARACTER DIST, TYPE, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, IMAT, IN, INB, INFO, IOFF, IRHS, IUPLO,
$ IZERO, K, KL, KU, LDA, MODE, N, NB, NERRS,
$ NFAIL, NIMAT, NRHS, NRUN
REAL ANORM, CNDNUM, RCOND, RCONDC
* ..
* .. Local Arrays ..
CHARACTER UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
REAL RESULT( NTESTS )
* ..
* .. External Functions ..
REAL SGET06, SLANSY
EXTERNAL SGET06, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, SERRPO, SGET04, SLACPY,
$ SLARHS, SLATB4, SLATMS, SPOCON, SPORFS, SPOT01,
$ SPOT02, SPOT03, SPOT05, SPOTRF, SPOTRI, SPOTRS,
$ XLAENV
* ..
* .. 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' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Single precision'
PATH( 2: 3 ) = 'PO'
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 )
*
* Do for each value of N in NVAL
*
DO 120 IN = 1, NN
N = NVAL( IN )
LDA = MAX( N, 1 )
XTYPE = 'N'
NIMAT = NTYPES
IF( N.LE.0 )
$ NIMAT = 1
*
IZERO = 0
DO 110 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 110
*
* 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 110
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
DO 100 IUPLO = 1, 2
UPLO = UPLOS( 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, UPLO, 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 100
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
IOFF = ( IZERO-1 )*LDA
*
* Set row and column IZERO of A to 0.
*
IF( IUPLO.EQ.1 ) THEN
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 + LDA
30 CONTINUE
ELSE
IOFF = IZERO
DO 40 I = 1, IZERO - 1
A( IOFF ) = ZERO
IOFF = IOFF + LDA
40 CONTINUE
IOFF = IOFF - IZERO
DO 50 I = IZERO, N
A( IOFF+I ) = ZERO
50 CONTINUE
END IF
ELSE
IZERO = 0
END IF
*
* Do for each value of NB in NBVAL
*
DO 90 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
*
* Compute the L*L' or U'*U factorization of the matrix.
*
CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
SRNAMT = 'SPOTRF'
CALL SPOTRF( UPLO, N, AFAC, LDA, INFO )
*
* Check error code from SPOTRF.
*
IF( INFO.NE.IZERO ) THEN
CALL ALAERH( PATH, 'SPOTRF', INFO, IZERO, UPLO, N,
$ N, -1, -1, NB, 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 SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
CALL SPOT01( UPLO, N, A, LDA, AINV, LDA, RWORK,
$ RESULT( 1 ) )
*
*+ TEST 2
* Form the inverse and compute the residual.
*
CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
SRNAMT = 'SPOTRI'
CALL SPOTRI( UPLO, N, AINV, LDA, INFO )
*
* Check error code from SPOTRI.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPOTRI', INFO, 0, UPLO, N, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL SPOT03( UPLO, N, A, LDA, AINV, LDA, 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, NB, IMAT, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
60 CONTINUE
NRUN = NRUN + 2
*
* Skip the rest of the tests unless this is the first
* blocksize.
*
IF( INB.NE.1 )
$ GO TO 90
*
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 = 'SPOTRS'
CALL SPOTRS( UPLO, N, NRHS, AFAC, LDA, X, LDA,
$ INFO )
*
* Check error code from SPOTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPOTRS', INFO, 0, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
CALL SPOT02( UPLO, N, NRHS, A, LDA, 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 = 'SPORFS'
CALL SPORFS( UPLO, N, NRHS, A, LDA, AFAC, LDA, B,
$ LDA, X, LDA, RWORK, RWORK( NRHS+1 ),
$ WORK, IWORK, INFO )
*
* Check error code from SPORFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPORFS', INFO, 0, UPLO, N,
$ N, -1, -1, NRHS, IMAT, NFAIL,
$ NERRS, NOUT )
*
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 5 ) )
CALL SPOT05( UPLO, N, NRHS, A, LDA, 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 = SLANSY( '1', UPLO, N, A, LDA, RWORK )
SRNAMT = 'SPOCON'
CALL SPOCON( UPLO, N, AFAC, LDA, ANORM, RCOND, WORK,
$ IWORK, INFO )
*
* Check error code from SPOCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'SPOCON', INFO, 0, UPLO, N, N,
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
RESULT( 8 ) = SGET06( RCOND, RCONDC )
*
* Print the test ratio if it is .GE. THRESH.
*
IF( RESULT( 8 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 8,
$ RESULT( 8 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
90 CONTINUE
100 CONTINUE
110 CONTINUE
120 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
$ I2, ', test ', I2, ', ratio =', G12.5 )
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
$ I2, ', test(', I2, ') =', G12.5 )
9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
$ ', test(', I2, ') =', G12.5 )
RETURN
*
* End of SCHKPO
*
END