zdrvsyx.f

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*> \brief \b ZDRVSYX
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZDRVSY( 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
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), NVAL( * )
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
*      $                   WORK( * ), X( * ), XACT( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZDRVSY tests the driver routines ZSYSV, -SVX, and -SVXX.
*>
*> Note that this file is used only when the XBLAS are available,
*> otherwise zdrvsy.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 DOUBLE PRECISION
*>          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 COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*>          AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*>          AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension
*>                      (NMAX*max(2,NRHS))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (2*NMAX+2*NRHS)
*> \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 April 2012
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE zdrvsy( DOTYPE, NN, NVAL, NRHS, 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, nout, nrhs
      DOUBLE PRECISION   thresh
*     ..
*     .. Array Arguments ..
      LOGICAL            dotype( * )
      INTEGER            iwork( * ), nval( * )
      DOUBLE PRECISION   rwork( * )
      COMPLEX*16         a( * ), afac( * ), ainv( * ), b( * ),
     $                   work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   one, zero
      parameter                ( one = 1.0d+0, zero = 0.0d+0 )
      INTEGER            ntypes, ntests
      parameter                ( ntypes = 11, 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
      DOUBLE PRECISION   ainvnm, anorm, cndnum, rcond, rcondc,
     $                   rpvgrw_svxx
*     ..
*     .. Local Arrays ..
      CHARACTER          facts( nfact ), uplos( 2 )
      INTEGER            iseed( 4 ), iseedy( 4 )
      DOUBLE PRECISION   result( ntests ), berr( nrhs ),
     $                   errbnds_n( nrhs, 3 ), errbnds_c( nrhs, 3 )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   dget06, zlansy
      EXTERNAL           dget06, zlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
     $                   zlacpy, zlarhs, zlaset, zlatb4, zlatms, zlatsy,
     $                   zpot05, zsysv, zsysvx, zsyt01, zsyt02, zsytrf,
     $                   zsytri2, zsysvxx
*     ..
*     .. 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          dcmplx, 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 ) = 'Zomplex 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 zerrvx( 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
         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 )
*
               IF( imat.NE.ntypes ) THEN
*
*                 Set up parameters with ZLATB4 and generate a test
*                 matrix with ZLATMS.
*
                  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm,
     $                         mode, cndnum, dist )
*
                  srnamt = 'ZLATMS'
                  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
     $                         cndnum, anorm, kl, ku, uplo, a, lda,
     $                         work, info )
*
*                 Check error code from ZLATMS.
*
                  IF( info.NE.0 ) THEN
                     CALL alaerh( path, 'ZLATMS', 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
                     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
                        IF( iuplo.EQ.1 ) THEN
*
*                          Set the first IZERO rows to zero.
*
                           ioff = 0
                           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 to zero.
*
                           ioff = 0
                           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
               ELSE
*
*                 IMAT = NTYPES:  Use a special block diagonal matrix to
*                 test alternate code for the 2-by-2 blocks.
*
                  CALL zlatsy( uplo, n, a, lda, iseed )
               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 ZSYSVX.
*
                  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 = zlansy( '1', uplo, n, a, lda, rwork )
*
*                    Factor the matrix A.
*
                     CALL zlacpy( uplo, n, n, a, lda, afac, lda )
                     CALL zsytrf( uplo, n, afac, lda, iwork, work,
     $                            lwork, info )
*
*                    Compute inv(A) and take its norm.
*
                     CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
                     lwork = (n+nb+1)*(nb+3)
                     CALL zsytri2( uplo, n, ainv, lda, iwork, work,
     $                            lwork, info )
                     ainvnm = zlansy( '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 = 'ZLARHS'
                  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
     $                         nrhs, a, lda, xact, lda, b, lda, iseed,
     $                         info )
                  xtype = 'C'
*
*                 --- Test ZSYSV  ---
*
                  IF( ifact.EQ.2 ) THEN
                     CALL zlacpy( uplo, n, n, a, lda, afac, lda )
                     CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
*
*                    Factor the matrix and solve the system using ZSYSV.
*
                     srnamt = 'ZSYSV '
                     CALL zsysv( 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 ZSYSV .
*
                     IF( info.NE.k ) THEN
                        CALL alaerh( path, 'ZSYSV ', 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 zsyt01( uplo, n, a, lda, afac, lda, iwork,
     $                            ainv, lda, rwork, result( 1 ) )
*
*                    Compute residual of the computed solution.
*
                     CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
                     CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
     $                            lda, rwork, result( 2 ) )
*
*                    Check solution from generated exact solution.
*
                     CALL zget04( 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 )'ZSYSV ', uplo, n,
     $                        imat, k, result( k )
                           nfail = nfail + 1
                        END IF
  110                CONTINUE
                     nrun = nrun + nt
  120                CONTINUE
                  END IF
*
*                 --- Test ZSYSVX ---
*
                  IF( ifact.EQ.2 )
     $               CALL zlaset( uplo, n, n, dcmplx( zero ),
     $                            dcmplx( zero ), afac, lda )
                  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
     $                         dcmplx( zero ), x, lda )
*
*                 Solve the system and compute the condition number and
*                 error bounds using ZSYSVX.
*
                  srnamt = 'ZSYSVX'
                  CALL zsysvx( fact, uplo, n, nrhs, a, lda, afac, lda,
     $                         iwork, b, lda, x, lda, rcond, rwork,
     $                         rwork( nrhs+1 ), work, lwork,
     $                         rwork( 2*nrhs+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 ZSYSVX.
*
                  IF( info.NE.k ) THEN
                     CALL alaerh( path, 'ZSYSVX', 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 zsyt01( 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 zlacpy( 'Full', n, nrhs, b, lda, work, lda )
                     CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
     $                            lda, rwork( 2*nrhs+1 ), result( 2 ) )
*
*                    Check solution from generated exact solution.
*
                     CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                            result( 3 ) )
*
*                    Check the error bounds from iterative refinement.
*
                     CALL zpot05( 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 ZSYSVX with the computed value
*                 in RCONDC.
*
                  result( 6 ) = dget06( 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 )'ZSYSVX', fact, uplo,
     $                     n, imat, k, result( k )
                        nfail = nfail + 1
                     END IF
  140             CONTINUE
                  nrun = nrun + 7 - k1
*
*                 --- Test ZSYSVXX ---
*
*                 Restore the matrices A and B.
*
                  IF( ifact.EQ.2 )
     $               CALL zlaset( uplo, n, n, cmplx( zero ),
     $                 cmplx( zero ), afac, lda )
                  CALL zlaset( 'Full', n, nrhs, cmplx( zero ),
     $                 cmplx( zero ), x, lda )
*
*                 Solve the system and compute the condition number
*                 and error bounds using ZSYSVXX.
*
                  srnamt = 'ZSYSVXX'
                  n_err_bnds = 3
                  equed = 'N'
                  CALL zsysvxx( 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,
     $                 rwork, 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 ZSYSVXX.
*
                  IF( info.NE.k .AND. info.LE.n ) THEN
                     CALL alaerh( path, 'ZSYSVXX', 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 zsyt01( 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 zlacpy( 'Full', n, nrhs, b, lda, work, lda )
                     CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
     $                    lda, rwork( 2*nrhs+1 ), result( 2 ) )
                     result( 2 ) = 0.0
*
*                 Check solution from generated exact solution.
*
                     CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
     $                    result( 3 ) )
*
*                 Check the error bounds from iterative refinement.
*
                     CALL zpot05( 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 ZSYSVXX with the computed value
*                 in RCONDC.
*
                  result( 6 ) = dget06( 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 )'ZSYSVXX',
     $                       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 ZSYSVXX

      CALL zebchvxx(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 ZDRVSY
*
      END