*> \brief \b SCHKSP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKSP( 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 *> *> SCHKSP tests SSPTRF, -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(2,NSMAX)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, *> dimension (NMAX+2*NSMAX) *> \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 SCHKSP( 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 = 10 ) INTEGER NTESTS PARAMETER ( NTESTS = 8 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO, $ IZERO, J, K, KL, KU, LDA, MODE, N, NERRS, $ NFAIL, NIMAT, NPP, NRHS, NRUN, NT REAL ANORM, CNDNUM, RCOND, RCONDC * .. * .. Local Arrays .. CHARACTER UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME REAL SGET06, SLANSP EXTERNAL LSAME, SGET06, SLANSP * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRSY, SGET04, $ SLACPY, SLARHS, SLATB4, SLATMS, SPPT02, SPPT03, $ SPPT05, SSPCON, SSPRFS, SSPT01, SSPTRF, SSPTRI, $ SSPTRS * .. * .. 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 / DATA UPLOS / 'U', 'L' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'SP' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRSY( PATH, NOUT ) INFOT = 0 * * Do for each value of N in NVAL * DO 170 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * IZERO = 0 DO 160 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 160 * * 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 160 * * Do first for UPLO = 'U', then for UPLO = 'L' * DO 150 IUPLO = 1, 2 UPLO = UPLOS( IUPLO ) IF( LSAME( UPLO, 'U' ) ) THEN PACKIT = 'C' ELSE PACKIT = 'R' END IF * * 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 150 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 )*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 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 + J 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 + N - J 90 CONTINUE END IF END IF ELSE IZERO = 0 END IF * * Compute the L*D*L' or U*D*U' factorization of the matrix. * NPP = N*( N+1 ) / 2 CALL SCOPY( NPP, A, 1, AFAC, 1 ) SRNAMT = 'SSPTRF' CALL SSPTRF( UPLO, N, AFAC, IWORK, 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 SSPTRF. * IF( INFO.NE.K ) $ CALL ALAERH( PATH, 'SSPTRF', INFO, K, UPLO, N, N, -1, $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) IF( INFO.NE.0 ) THEN TRFCON = .TRUE. ELSE TRFCON = .FALSE. END IF * *+ TEST 1 * Reconstruct matrix from factors and compute residual. * CALL SSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA, RWORK, $ RESULT( 1 ) ) NT = 1 * *+ TEST 2 * Form the inverse and compute the residual. * IF( .NOT.TRFCON ) THEN CALL SCOPY( NPP, AFAC, 1, AINV, 1 ) SRNAMT = 'SSPTRI' CALL SSPTRI( UPLO, N, AINV, IWORK, WORK, INFO ) * * Check error code from SSPTRI. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSPTRI', INFO, 0, UPLO, N, N, $ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) * CALL SPPT03( UPLO, N, A, AINV, WORK, LDA, RWORK, $ RCONDC, RESULT( 2 ) ) NT = 2 END IF * * 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 ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K, $ RESULT( K ) NFAIL = NFAIL + 1 END IF 110 CONTINUE NRUN = NRUN + NT * * Do only the condition estimate if INFO is not 0. * IF( TRFCON ) THEN RCONDC = ZERO GO TO 140 END IF * DO 130 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 = 'SSPTRS' CALL SSPTRS( UPLO, N, NRHS, AFAC, IWORK, X, LDA, $ INFO ) * * Check error code from SSPTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSPTRS', 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 = 'SSPRFS' CALL SSPRFS( UPLO, N, NRHS, A, AFAC, IWORK, B, LDA, X, $ LDA, RWORK, RWORK( NRHS+1 ), WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SSPRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSPRFS', 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 120 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 120 CONTINUE NRUN = NRUN + 5 130 CONTINUE * *+ TEST 8 * Get an estimate of RCOND = 1/CNDNUM. * 140 CONTINUE ANORM = SLANSP( '1', UPLO, N, A, RWORK ) SRNAMT = 'SSPCON' CALL SSPCON( UPLO, N, AFAC, IWORK, ANORM, RCOND, WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SSPCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSPCON', 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 = 9999 )UPLO, N, IMAT, 8, $ RESULT( 8 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 150 CONTINUE 160 CONTINUE 170 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 SCHKSP * END