*> \brief \b SCHKSY * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKSY( 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 *> *> SCHKSY tests SSYTRF, -TRI2, -TRS, -TRS2, -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 (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. * *> \date April 2012 * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SCHKSY( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, $ XACT, WORK, RWORK, IWORK, NOUT ) * * -- LAPACK test routine (version 3.4.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. 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 = 10 ) INTEGER NTESTS PARAMETER ( NTESTS = 9 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, TYPE, UPLO, XTYPE CHARACTER*3 PATH INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS, $ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE, $ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT 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, SERRSY, SGET04, SLACPY, $ SLARHS, SLATB4, SLATMS, SPOT02, SPOT03, SPOT05, $ SSYCON, SSYCONV, SSYRFS, SSYT01, SSYTRF, $ SSYTRI2, SSYTRS, SSYTRS2, XLAENV * .. * .. 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 ) = 'SY' 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 * * Set the minimum block size for which the block routine should * be used, which will be later returned by ILAENV * CALL XLAENV( 2, 2 ) * * 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 * IZERO = 0 * * Do for each value of matrix type IMAT * 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( PATH, 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 ) GO TO 160 END IF * * For matrix 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 for each value of NB in NBVAL * DO 150 INB = 1, NNB * * Set the optimal blocksize, which will be later * returned by ILAENV. * NB = NBVAL( INB ) CALL XLAENV( 1, NB ) * * Copy the test matrix A into matrix AFAC which * will be factorized in place. This is needed to * preserve the test matrix A for subsequent tests. * CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) * * Compute the L*D*L**T or U*D*U**T factorization of the * matrix. IWORK stores details of the interchanges and * the block structure of D. AINV is a work array for * block factorization, LWORK is the length of AINV. * LWORK = MAX( 2, NB )*LDA SRNAMT = 'SSYTRF' CALL SSYTRF( UPLO, N, AFAC, LDA, IWORK, AINV, 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 SSYTRF and handle error. * IF( INFO.NE.K ) $ CALL ALAERH( PATH, 'SSYTRF', INFO, K, UPLO, N, N, $ -1, -1, NB, IMAT, NFAIL, NERRS, NOUT ) * * Set the condition estimate flag if the INFO is not 0. * IF( INFO.NE.0 ) THEN TRFCON = .TRUE. ELSE TRFCON = .FALSE. END IF * *+ TEST 1 * Reconstruct matrix from factors and compute residual. * CALL SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK, AINV, $ LDA, RWORK, RESULT( 1 ) ) NT = 1 * *+ TEST 2 * Form the inverse and compute the residual, * if the factorization was competed without INFO > 0 * (i.e. there is no zero rows and columns). * Do it only for the first block size. * IF( INB.EQ.1 .AND. .NOT.TRFCON ) THEN CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA ) SRNAMT = 'SSYTRI2' LWORK = (N+NB+1)*(NB+3) CALL SSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK, $ LWORK, INFO ) * * Check error code from SSYTRI2 and handle error. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSYTRI2', INFO, -1, UPLO, N, $ N, -1, -1, -1, IMAT, NFAIL, NERRS, $ NOUT ) * * Compute the residual for a symmetric matrix times * its inverse. * CALL SPOT03( UPLO, N, A, LDA, AINV, LDA, 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, NB, IMAT, K, $ RESULT( K ) NFAIL = NFAIL + 1 END IF 110 CONTINUE NRUN = NRUN + NT * * Skip the other tests if this is not the first block * size. * IF( INB.GT.1 ) $ GO TO 150 * * 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 (Using DSYTRS) * Solve and compute residual for A * X = B. * * Choose a set of NRHS random solution vectors * stored in XACT and set up the right hand side 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 = 'SSYTRS' CALL SSYTRS( UPLO, N, NRHS, AFAC, LDA, IWORK, X, $ LDA, INFO ) * * Check error code from SSYTRS and handle error. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSYTRS', INFO, 0, UPLO, N, $ N, -1, -1, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) * * Compute the residual for the solution * CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, $ LDA, RWORK, RESULT( 3 ) ) * *+ TEST 4 (Using DSYTRS2) * Solve and compute residual for A * X = B. * * Choose a set of NRHS random solution vectors * stored in XACT and set up the right hand side 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 = 'DSYTRS2' CALL SSYTRS2( UPLO, N, NRHS, AFAC, LDA, IWORK, X, $ LDA, WORK, INFO ) * * Check error code from SSYTRS2 and handle error. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSYTRS2', INFO, 0, UPLO, N, $ N, -1, -1, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) * * Compute the residual for the solution * CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, $ LDA, RWORK, RESULT( 4 ) ) * *+ TEST 5 * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 5 ) ) * *+ TESTS 6, 7, and 8 * Use iterative refinement to improve the solution. * SRNAMT = 'SSYRFS' CALL SSYRFS( UPLO, N, NRHS, A, LDA, AFAC, LDA, $ IWORK, B, LDA, X, LDA, RWORK, $ RWORK( NRHS+1 ), WORK, IWORK( N+1 ), $ INFO ) * * Check error code from SSYRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSYRFS', INFO, 0, UPLO, N, $ N, -1, -1, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 6 ) ) CALL SPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA, $ XACT, LDA, RWORK, RWORK( NRHS+1 ), $ RESULT( 7 ) ) * * Print information about the tests that did not pass * the threshold. * DO 120 K = 3, 8 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 + 6 130 CONTINUE * *+ TEST 9 * Get an estimate of RCOND = 1/CNDNUM. * 140 CONTINUE ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) SRNAMT = 'SSYCON' CALL SSYCON( UPLO, N, AFAC, LDA, IWORK, ANORM, RCOND, $ WORK, IWORK( N+1 ), INFO ) * * Check error code from SSYCON and handle error. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SSYCON', INFO, 0, UPLO, N, N, $ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) * * Compute the test ratio to compare to values of RCOND * RESULT( 9 ) = SGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * IF( RESULT( 9 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 9, $ RESULT( 9 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 150 CONTINUE * 160 CONTINUE 170 CONTINUE 180 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 SCHKSY * END