sdrvsyx.f

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*> \brief \b SDRVSYX
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
*                          A, AFAC, 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( * ), AINV( * ), B( * ),
*      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SDRVSY tests the driver routines SSYSV, -SVX, and -SVXX
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise sdrvsy.f defines this subroutine.
*> \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] 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( DOTYPE, NN, NVAL, NRHS, 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, NOUT, NRHS
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NVAL( * )
      REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
     $                   rwork( * ), work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0e+0, zero = 0.0e+0 )
      INTEGER            NTYPES, NTESTS
      parameter( ntypes = 10, ntests = 6 )
      INTEGER            NFACT
      parameter( nfact = 2 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ZEROT
      CHARACTER          DIST, EQUED, FACT, TYPE, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
     $                   izero, j, k, k1, kl, ku, lda, lwork, mode, n,
     $                   nb, nbmin, nerrs, nfail, nimat, nrun, nt,
     $                   n_err_bnds
      REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC,
     $                   RPVGRW_SVXX
*     ..
*     .. Local Arrays ..
      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      REAL               RESULT( NTESTS ), BERR( NRHS ),
     $                   errbnds_n( nrhs, 3 ), errbnds_c( nrhs, 3 )
*     ..
*     .. External Functions ..
      REAL               SGET06, SLANSY
      EXTERNAL           SGET06, SLANSY
*     ..
*     .. External Subroutines ..
      EXTERNAL           aladhd, alaerh, alasvm, serrvx, sget04, slacpy,
     $                   slarhs, slaset, slatb4, slatms, spot02, spot05,
     $                   ssysv, ssysvx, ssyt01, ssytrf, ssytri2, xlaenv,
     $                   ssysvxx
*     ..
*     .. 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.
*
      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
      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 testing.
*
      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
.LE.         IF( N0 )
     $      NIMAT = 1
*
         DO 170 IMAT = 1, NIMAT
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
.NOT.            IF( DOTYPE( IMAT ) )
     $         GO TO 170
*
*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
*
.GE..AND..LE.            ZEROT = IMAT3  IMAT6
.AND..LT.            IF( ZEROT  NIMAT-2 )
     $         GO TO 170
*
*           Do first for UPLO = 'U', then for UPLO = 'L'
*
            DO 160 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.
*
.NE.               IF( INFO0 ) THEN
                  CALL ALAERH( PATH, 'slatms', INFO, 0, UPLO, N, N, -1,
     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
                  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
.EQ.                  IF( IMAT3 ) THEN
                     IZERO = 1
.EQ.                  ELSE IF( IMAT4 ) THEN
                     IZERO = N
                  ELSE
                     IZERO = N / 2 + 1
                  END IF
*
.LT.                  IF( IMAT6 ) THEN
*
*                    Set row and column IZERO to zero.
*
.EQ.                     IF( IUPLO1 ) 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
.EQ.                     IF( IUPLO1 ) 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
*
               DO 150 IFACT = 1, NFACT
*
*                 Do first for FACT = 'F', then for other values.
*
                  FACT = FACTS( IFACT )
*
*                 Compute the condition number for comparison with
*                 the value returned by SSYSVX.
*
                  IF( ZEROT ) THEN
.EQ.                     IF( IFACT1 )
     $                  GO TO 150
                     RCONDC = ZERO
*
.EQ.                  ELSE IF( IFACT1 ) 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( UPLO, N, AFAC, LDA, 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)
                     CALL SSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
     $                            LWORK, INFO )
                     AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK )
*
*                    Compute the 1-norm condition number of A.
*
.LE..OR..LE.                     IF( ANORMZERO  AINVNMZERO ) 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( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
     $                         INFO )
                  XTYPE = 'c'
*
*                 --- Test SSYSV  ---
*
.EQ.                  IF( IFACT2 ) 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.
*
                     srnamt = 'SSYSV '
                     CALL ssysv( uplo, n, nrhs, afac, lda, 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 .
*
                     IF( info.NE.k ) THEN
                        CALL alaerh( path, 'SSYSV ', 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
*
*                    Reconstruct matrix from factors and compute
*                    residual.
*
                     CALL ssyt01( uplo, n, a, lda, afac, lda, iwork,
     $                            ainv, lda, rwork, result( 1 ) )
*
*                    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 ) )
*
*                    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 ', uplo, n,
     $                        imat, k, result( k )
                           nfail = nfail + 1
                        END IF
  110                CONTINUE
                     nrun = nrun + nt
  120                CONTINUE
                  END IF
*
*                 --- Test SSYSVX ---
*
                  IF( ifact.EQ.2 )
     $               CALL slaset( uplo, n, n, zero, zero, afac, lda )
                  CALL slaset( 'Full', n, nrhs, zero, zero, x, lda )
*
*                 Solve the system and compute the condition number and
*                 error bounds using SSYSVX.
*
                  srnamt = 'SSYSVX'
                  CALL ssysvx( fact, uplo, n, nrhs, a, lda, afac, lda,
     $                         iwork, b, lda, x, lda, rcond, rwork,
     $                         rwork( nrhs+1 ), work, lwork,
     $                         iwork( n+1 ), info )
*
*                 Adjust the expected value of INFO to account for
*                 pivoting.
*
                  k = izero
                  IF( k.GT.0 ) THEN
  130                CONTINUE
                     IF( iwork( k ).LT.0 ) THEN
                        IF( iwork( k ).NE.-k ) THEN
                           k = -iwork( k )
                           GO TO 130
                        END IF
                     ELSE IF( iwork( k ).NE.k ) THEN
                        k = iwork( k )
                        GO TO 130
                     END IF
                  END IF
*
*                 Check the error code from SSYSVX.
*
                  IF( info.NE.k ) THEN
                     CALL alaerh( path, 'SSYSVX', info, k, fact // uplo,
     $                            n, n, -1, -1, nrhs, imat, nfail,
     $                            nerrs, nout )
                     GO TO 150
                  END IF
*
                  IF( info.EQ.0 ) THEN
                     IF( ifact.GE.2 ) THEN
*
*                       Reconstruct matrix from factors and compute
*                       residual.
*
                        CALL ssyt01( uplo, n, a, lda, afac, lda, iwork,
     $                               ainv, lda, rwork( 2*nrhs+1 ),
     $                               result( 1 ) )
                        k1 = 1
                     ELSE
                        k1 = 2
                     END IF
*
*                    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( 2*nrhs+1 ), result( 2 ) )
*
*                    Check solution from generated exact solution.
*
                     CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                            result( 3 ) )
*
*                    Check the error bounds from iterative refinement.
*
                     CALL spot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
     $                            xact, lda, rwork, rwork( nrhs+1 ),
     $                            result( 4 ) )
                  ELSE
                     k1 = 6
                  END IF
*
*                 Compare RCOND from SSYSVX with the computed value
*                 in RCONDC.
*
                  result( 6 ) = sget06( rcond, rcondc )
*
*                 Print information about the tests that did not pass
*                 the threshold.
*
                  DO 140 k = k1, 6
                     IF( result( k ).GE.thresh ) THEN
                        IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                     CALL aladhd( nout, path )
                        WRITE( nout, fmt = 9998 )'SSYSVX', fact, uplo,
     $                     n, imat, k, result( k )
                        nfail = nfail + 1
                     END IF
  140             CONTINUE
                  nrun = nrun + 7 - k1
*
*                 --- Test SSYSVXX ---
*
*                 Restore the matrices A and B.
*
                  IF( ifact.EQ.2 )
     $               CALL slaset( uplo, n, n, zero, zero, afac, lda )
                  CALL slaset( 'Full', n, nrhs, zero, zero, x, lda )
*
*                 Solve the system and compute the condition number
*                 and error bounds using SSYSVXX.
*
                  srnamt = 'SSYSVXX'
                  n_err_bnds = 3
                  equed = 'N'
                  CALL ssysvxx( fact, uplo, n, nrhs, a, lda, afac,
     $                 lda, iwork, equed, work( n+1 ), b, lda, x,
     $                 lda, rcond, rpvgrw_svxx, berr, n_err_bnds,
     $                 errbnds_n, errbnds_c, 0, zero, work,
     $                 iwork( n+1 ), info )
*
*                 Adjust the expected value of INFO to account for
*                 pivoting.
*
                  k = izero
                  IF( k.GT.0 ) THEN
 135                 CONTINUE
                     IF( iwork( k ).LT.0 ) THEN
                        IF( iwork( k ).NE.-k ) THEN
                           k = -iwork( k )
                           GO TO 135
                        END IF
                     ELSE IF( iwork( k ).NE.k ) THEN
                        k = iwork( k )
                        GO TO 135
                     END IF
                  END IF
*
*                 Check the error code from SSYSVXX.
*
                  IF( info.NE.k .AND. info.LE.n ) THEN
                     CALL alaerh( path, 'SSYSVXX', info, k,
     $                    fact // uplo, n, n, -1, -1, nrhs, imat, nfail,
     $                    nerrs, nout )
                     GO TO 150
                  END IF
*
                  IF( info.EQ.0 ) THEN
                     IF( ifact.GE.2 ) THEN
*
*                 Reconstruct matrix from factors and compute
*                 residual.
*
                        CALL ssyt01( uplo, n, a, lda, afac, lda, iwork,
     $                       ainv, lda, rwork(2*nrhs+1),
     $                       result( 1 ) )
                        k1 = 1
                     ELSE
                        k1 = 2
                     END IF
*
*                 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( 2*nrhs+1 ), result( 2 ) )
*
*                 Check solution from generated exact solution.
*
                     CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                    result( 3 ) )
*
*                 Check the error bounds from iterative refinement.
*
                     CALL spot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
     $                    xact, lda, rwork, rwork( nrhs+1 ),
     $                    result( 4 ) )
                  ELSE
                     k1 = 6
                  END IF
*
*                 Compare RCOND from SSYSVXX with the computed value
*                 in RCONDC.
*
                  result( 6 ) = sget06( rcond, rcondc )
*
*                 Print information about the tests that did not pass
*                 the threshold.
*
                  DO 85 k = k1, 6
                     IF( result( k ).GE.thresh ) THEN
                        IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                       CALL aladhd( nout, path )
                        WRITE( nout, fmt = 9998 )'SSYSVXX',
     $                       fact, uplo, n, imat, k,
     $                       result( k )
                        nfail = nfail + 1
                     END IF
 85               CONTINUE
                  nrun = nrun + 7 - k1
*
  150          CONTINUE
*
  160       CONTINUE
  170    CONTINUE
  180 CONTINUE
*
*     Print a summary of the results.
*
      CALL alasvm( path, nout, nfail, nrun, nerrs )
*
 
*     Test Error Bounds from SSYSVXX
 
      CALL sebchvxx(thresh, path)
 
 9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
     $      ', test ', I2, ', ratio =', G12.5 )
 9998 FORMAT( 1X, A, ', fact=''', A1, ''', uplo=''', A1, ''', n =', I5,
     $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
      RETURN
*
*     End of SDRVSYX
*
      END