*> \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 (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 SCHKPO( 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 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