*> \brief \b SDRVSY_RK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, * \$ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, * \$ RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NMAX, NN, NOUT, NRHS * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), NVAL( * ) * REAL A( * ), AFAC( * ), E( * ), AINV( * ), B( * ), * \$ RWORK( * ), WORK( * ), X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> SDRVSY_RK tests the driver routines SSYSV_RK. *> \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] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand side vectors to be generated for *> each linear system. *> \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] E *> \verbatim *> E is REAL array, dimension (NMAX) *> \endverbatim *> *> \param[out] AINV *> \verbatim *> AINV is REAL array, dimension (NMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is REAL array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] X *> \verbatim *> X is REAL array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is REAL array, dimension (NMAX*NRHS) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (NMAX*max(2,NRHS)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (NMAX+2*NRHS) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (2*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 SDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, \$ NMAX, A, AFAC, E, 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, NOUT, NRHS REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NVAL( * ) REAL A( * ), AFAC( * ), AINV( * ), B( * ), E( * ), \$ RWORK( * ), WORK( * ), X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES, NTESTS PARAMETER ( NTYPES = 10, NTESTS = 3 ) INTEGER NFACT PARAMETER ( NFACT = 2 ) * .. * .. Local Scalars .. LOGICAL ZEROT CHARACTER DIST, FACT, TYPE, UPLO, XTYPE CHARACTER*3 PATH, MATPATH INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO, \$ IZERO, J, K, KL, KU, LDA, LWORK, MODE, N, \$ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT REAL AINVNM, ANORM, CNDNUM, RCONDC * .. * .. Local Arrays .. CHARACTER FACTS( NFACT ), UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. REAL SLANSY EXTERNAL SLANSY * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY, \$ SLARHS, SLATB4, SLATMS, SPOT02, SSYSV_RK, \$ SSYT01_3, SSYTRF_RK, SSYTRI_3, 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, MIN * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * * Test path * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'SK' * * Path to generate matrices * MATPATH( 1: 1 ) = 'Single precision' MATPATH( 2: 3 ) = 'SY' * NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE LWORK = MAX( 2*NMAX, NMAX*NRHS ) * * Test the error exits * IF( TSTERR ) \$ CALL SERRVX( PATH, NOUT ) INFOT = 0 * * Set the block size and minimum block size for which the block * routine should be used, which will be later returned by ILAENV. * NB = 1 NBMIN = 2 CALL XLAENV( 1, NB ) CALL XLAENV( 2, NBMIN ) * * Do for each value of N in NVAL * DO 180 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) \$ NIMAT = 1 * DO 170 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) \$ GO TO 170 * * Skip types 3, 4, 5, or 6 if the matrix size is too small. * ZEROT = IMAT.GE.3 .AND. IMAT.LE.6 IF( ZEROT .AND. N.LT.IMAT-2 ) \$ GO TO 170 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 160 IUPLO = 1, 2 UPLO = UPLOS( IUPLO ) * * Begin generate the test matrix A. * * Set up parameters with SLATB4 for the matrix generator * based on the type of matrix to be generated. * CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM, \$ MODE, CNDNUM, DIST ) * * Generate a matrix with SLATMS. * 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 and handle error. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1, \$ -1, -1, IMAT, NFAIL, NERRS, NOUT ) * * Skip all tests for this generated matrix * GO TO 160 END IF * * For types 3-6, zero one or more rows and columns 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 * IF( IMAT.LT.6 ) THEN * * Set row and column IZERO to zero. * IF( IUPLO.EQ.1 ) THEN IOFF = ( IZERO-1 )*LDA 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 IOFF = 0 IF( IUPLO.EQ.1 ) THEN * * Set the first IZERO rows and columns to zero. * DO 70 J = 1, N I2 = MIN( J, IZERO ) DO 60 I = 1, I2 A( IOFF+I ) = ZERO 60 CONTINUE IOFF = IOFF + LDA 70 CONTINUE ELSE * * Set the last IZERO rows and columns to zero. * DO 90 J = 1, N I1 = MAX( J, IZERO ) DO 80 I = I1, N A( IOFF+I ) = ZERO 80 CONTINUE IOFF = IOFF + LDA 90 CONTINUE END IF END IF ELSE IZERO = 0 END IF * * End generate the test matrix A. * DO 150 IFACT = 1, NFACT * * Do first for FACT = 'F', then for other values. * FACT = FACTS( IFACT ) * * Compute the condition number * IF( ZEROT ) THEN IF( IFACT.EQ.1 ) \$ GO TO 150 RCONDC = ZERO * ELSE IF( IFACT.EQ.1 ) THEN * * Compute the 1-norm of A. * ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) * * Factor the matrix A. * CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) CALL SSYTRF_RK( UPLO, N, AFAC, LDA, E, IWORK, WORK, \$ LWORK, INFO ) * * Compute inv(A) and take its norm. * CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA ) LWORK = (N+NB+1)*(NB+3) * * We need to compute the inverse to compute * RCONDC that is used later in TEST3. * CALL SSYTRI_3( UPLO, N, AINV, LDA, E, IWORK, \$ WORK, LWORK, INFO ) AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK ) * * Compute the 1-norm condition number of A. * IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF END IF * * Form an exact solution and set the right hand side. * SRNAMT = 'SLARHS' CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU, \$ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED, \$ INFO ) XTYPE = 'C' * * --- Test SSYSV_RK --- * IF( IFACT.EQ.2 ) THEN CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * * Factor the matrix and solve the system using * SSYSV_RK. * SRNAMT = 'SSYSV_RK' CALL SSYSV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK, \$ X, LDA, WORK, LWORK, INFO ) * * Adjust the expected value of INFO to account for * pivoting. * K = IZERO IF( K.GT.0 ) THEN 100 CONTINUE IF( IWORK( K ).LT.0 ) THEN IF( IWORK( K ).NE.-K ) THEN K = -IWORK( K ) GO TO 100 END IF ELSE IF( IWORK( K ).NE.K ) THEN K = IWORK( K ) GO TO 100 END IF END IF * * Check error code from SSYSV_RK and handle error. * IF( INFO.NE.K ) THEN CALL ALAERH( PATH, 'SSYSV_RK', INFO, K, UPLO, \$ N, N, -1, -1, NRHS, IMAT, NFAIL, \$ NERRS, NOUT ) GO TO 120 ELSE IF( INFO.NE.0 ) THEN GO TO 120 END IF * *+ TEST 1 Reconstruct matrix from factors and compute * residual. * CALL SSYT01_3( UPLO, N, A, LDA, AFAC, LDA, E, \$ IWORK, AINV, LDA, RWORK, \$ RESULT( 1 ) ) * *+ TEST 2 Compute residual of the computed solution. * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL SPOT02( UPLO, N, NRHS, A, LDA, 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 ) ) NT = 3 * * Print information about the tests that did not pass * the threshold. * DO 110 K = 1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) \$ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )'SSYSV_RK', UPLO, \$ N, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 110 CONTINUE NRUN = NRUN + NT 120 CONTINUE END IF * 150 CONTINUE * 160 CONTINUE 170 CONTINUE 180 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2, \$ ', test ', I2, ', ratio =', G12.5 ) RETURN * * End of SDRVSY_RK * END