ddrvpb.f

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*> \brief \b DDRVPB
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
*                          A, AFAC, ASAV, B, BSAV, X, XACT, S, 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   A( * ), AFAC( * ), ASAV( * ), B( * ),
*      $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
*      $                   X( * ), XACT( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DDRVPB tests the driver routines DPBSV and -SVX.
*> \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 DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AFAC
*> \verbatim
*>          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] ASAV
*> \verbatim
*>          ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] BSAV
*> \verbatim
*>          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*>          S is DOUBLE PRECISION array, dimension (NMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension
*>                      (NMAX*max(3,NRHS))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (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 November 2011
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE ddrvpb( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
     $                   a, afac, asav, b, bsav, x, xact, s, work,
     $                   rwork, iwork, nout )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      LOGICAL            TSTERR
      INTEGER            NMAX, NN, NOUT, NRHS
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NVAL( * )
      DOUBLE PRECISION   A( * ), AFAC( * ), ASAV( * ), B( * ),
     $                   bsav( * ), rwork( * ), s( * ), work( * ),
     $                   x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter                ( one = 1.0d+0, zero = 0.0d+0 )
      INTEGER            NTYPES, NTESTS
      parameter                ( ntypes = 8, ntests = 6 )
      INTEGER            NBW
      parameter                ( nbw = 4 )
*     ..
*     .. Local Scalars ..
      LOGICAL            EQUIL, NOFACT, PREFAC, ZEROT
      CHARACTER          DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, I1, I2, IEQUED, IFACT, IKD, IMAT, IN, INFO,
     $                   ioff, iuplo, iw, izero, k, k1, kd, kl, koff,
     $                   ku, lda, ldab, mode, n, nb, nbmin, nerrs,
     $                   nfact, nfail, nimat, nkd, nrun, nt
      DOUBLE PRECISION   AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
     $                   roldc, scond
*     ..
*     .. Local Arrays ..
      CHARACTER          EQUEDS( 2 ), FACTS( 3 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 ), KDVAL( nbw )
      DOUBLE PRECISION   RESULT( ntests )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DGET06, DLANGE, DLANSB
      EXTERNAL           lsame, dget06, dlange, dlansb
*     ..
*     .. External Subroutines ..
      EXTERNAL           aladhd, alaerh, alasvm, dcopy, derrvx, dget04,
     $                   dlacpy, dlaqsb, dlarhs, dlaset, dlatb4, dlatms,
     $                   dpbequ, dpbsv, dpbsvx, dpbt01, dpbt02, dpbt05,
     $                   dpbtrf, dpbtrs, dswap, 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               facts / 'F', 'N', 'E' /
      DATA               equeds / 'N', 'Y' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      path( 1: 1 ) = 'Double precision'
      path( 2: 3 ) = 'PB'
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
*     Test the error exits
*
      IF( tsterr )
     $   CALL derrvx( path, nout )
      infot = 0
      kdval( 1 ) = 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 110 in = 1, nn
         n = nval( in )
         lda = max( n, 1 )
         xtype = 'N'
*
*        Set limits on the number of loop iterations.
*
         nkd = max( 1, min( n, 4 ) )
         nimat = ntypes
         IF( n.EQ.0 )
     $      nimat = 1
*
         kdval( 2 ) = n + ( n+1 ) / 4
         kdval( 3 ) = ( 3*n-1 ) / 4
         kdval( 4 ) = ( n+1 ) / 4
*
         DO 100 ikd = 1, nkd
*
*           Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
*           makes it easier to skip redundant values for small values
*           of N.
*
            kd = kdval( ikd )
            ldab = kd + 1
*
*           Do first for UPLO = 'U', then for UPLO = 'L'
*
            DO 90 iuplo = 1, 2
               koff = 1
               IF( iuplo.EQ.1 ) THEN
                  uplo = 'U'
                  packit = 'Q'
                  koff = max( 1, kd+2-n )
               ELSE
                  uplo = 'L'
                  packit = 'B'
               END IF
*
               DO 80 imat = 1, nimat
*
*                 Do the tests only if DOTYPE( IMAT ) is true.
*
                  IF( .NOT.dotype( imat ) )
     $               GO TO 80
*
*                 Skip types 2, 3, or 4 if the matrix size is too small.
*
                  zerot = imat.GE.2 .AND. imat.LE.4
                  IF( zerot .AND. n.LT.imat-1 )
     $               GO TO 80
*
                  IF( .NOT.zerot .OR. .NOT.dotype( 1 ) ) THEN
*
*                    Set up parameters with DLATB4 and generate a test
*                    matrix with DLATMS.
*
                     CALL dlatb4( path, imat, n, n, TYPE, KL, KU, ANORM,
     $                            mode, cndnum, dist )
*
                     srnamt = 'DLATMS'
                     CALL dlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
     $                            cndnum, anorm, kd, kd, packit,
     $                            a( koff ), ldab, work, info )
*
*                    Check error code from DLATMS.
*
                     IF( info.NE.0 ) THEN
                        CALL alaerh( path, 'DLATMS', info, 0, uplo, n,
     $                               n, -1, -1, -1, imat, nfail, nerrs,
     $                               nout )
                        GO TO 80
                     END IF
                  ELSE IF( izero.GT.0 ) THEN
*
*                    Use the same matrix for types 3 and 4 as for type
*                    2 by copying back the zeroed out column,
*
                     iw = 2*lda + 1
                     IF( iuplo.EQ.1 ) THEN
                        ioff = ( izero-1 )*ldab + kd + 1
                        CALL dcopy( izero-i1, work( iw ), 1,
     $                              a( ioff-izero+i1 ), 1 )
                        iw = iw + izero - i1
                        CALL dcopy( i2-izero+1, work( iw ), 1,
     $                              a( ioff ), max( ldab-1, 1 ) )
                     ELSE
                        ioff = ( i1-1 )*ldab + 1
                        CALL dcopy( izero-i1, work( iw ), 1,
     $                              a( ioff+izero-i1 ),
     $                              max( ldab-1, 1 ) )
                        ioff = ( izero-1 )*ldab + 1
                        iw = iw + izero - i1
                        CALL dcopy( i2-izero+1, work( iw ), 1,
     $                              a( ioff ), 1 )
                     END IF
                  END IF
*
*                 For types 2-4, zero one row and column of the matrix
*                 to test that INFO is returned correctly.
*
                  izero = 0
                  IF( zerot ) THEN
                     IF( imat.EQ.2 ) THEN
                        izero = 1
                     ELSE IF( imat.EQ.3 ) THEN
                        izero = n
                     ELSE
                        izero = n / 2 + 1
                     END IF
*
*                    Save the zeroed out row and column in WORK(*,3)
*
                     iw = 2*lda
                     DO 20 i = 1, min( 2*kd+1, n )
                        work( iw+i ) = zero
   20                CONTINUE
                     iw = iw + 1
                     i1 = max( izero-kd, 1 )
                     i2 = min( izero+kd, n )
*
                     IF( iuplo.EQ.1 ) THEN
                        ioff = ( izero-1 )*ldab + kd + 1
                        CALL dswap( izero-i1, a( ioff-izero+i1 ), 1,
     $                              work( iw ), 1 )
                        iw = iw + izero - i1
                        CALL dswap( i2-izero+1, a( ioff ),
     $                              max( ldab-1, 1 ), work( iw ), 1 )
                     ELSE
                        ioff = ( i1-1 )*ldab + 1
                        CALL dswap( izero-i1, a( ioff+izero-i1 ),
     $                              max( ldab-1, 1 ), work( iw ), 1 )
                        ioff = ( izero-1 )*ldab + 1
                        iw = iw + izero - i1
                        CALL dswap( i2-izero+1, a( ioff ), 1,
     $                              work( iw ), 1 )
                     END IF
                  END IF
*
*                 Save a copy of the matrix A in ASAV.
*
                  CALL dlacpy( 'Full', kd+1, n, a, ldab, asav, ldab )
*
                  DO 70 iequed = 1, 2
                     equed = equeds( iequed )
                     IF( iequed.EQ.1 ) THEN
                        nfact = 3
                     ELSE
                        nfact = 1
                     END IF
*
                     DO 60 ifact = 1, nfact
                        fact = facts( ifact )
                        prefac = lsame( fact, 'F' )
                        nofact = lsame( fact, 'N' )
                        equil = lsame( fact, 'E' )
*
                        IF( zerot ) THEN
                           IF( prefac )
     $                        GO TO 60
                           rcondc = zero
*
                        ELSE IF( .NOT.lsame( fact, 'N' ) ) THEN
*
*                          Compute the condition number for comparison
*                          with the value returned by DPBSVX (FACT =
*                          'N' reuses the condition number from the
*                          previous iteration with FACT = 'F').
*
                           CALL dlacpy( 'Full', kd+1, n, asav, ldab,
     $                                  afac, ldab )
                           IF( equil .OR. iequed.GT.1 ) THEN
*
*                             Compute row and column scale factors to
*                             equilibrate the matrix A.
*
                              CALL dpbequ( uplo, n, kd, afac, ldab, s,
     $                                     scond, amax, info )
                              IF( info.EQ.0 .AND. n.GT.0 ) THEN
                                 IF( iequed.GT.1 )
     $                              scond = zero
*
*                                Equilibrate the matrix.
*
                                 CALL dlaqsb( uplo, n, kd, afac, ldab,
     $                                        s, scond, amax, equed )
                              END IF
                           END IF
*
*                          Save the condition number of the
*                          non-equilibrated system for use in DGET04.
*
                           IF( equil )
     $                        roldc = rcondc
*
*                          Compute the 1-norm of A.
*
                           anorm = dlansb( '1', uplo, n, kd, afac, ldab,
     $                             rwork )
*
*                          Factor the matrix A.
*
                           CALL dpbtrf( uplo, n, kd, afac, ldab, info )
*
*                          Form the inverse of A.
*
                           CALL dlaset( 'Full', n, n, zero, one, a,
     $                                  lda )
                           srnamt = 'DPBTRS'
                           CALL dpbtrs( uplo, n, kd, n, afac, ldab, a,
     $                                  lda, info )
*
*                          Compute the 1-norm condition number of A.
*
                           ainvnm = dlange( '1', n, n, a, lda, rwork )
                           IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
                              rcondc = one
                           ELSE
                              rcondc = ( one / anorm ) / ainvnm
                           END IF
                        END IF
*
*                       Restore the matrix A.
*
                        CALL dlacpy( 'Full', kd+1, n, asav, ldab, a,
     $                               ldab )
*
*                       Form an exact solution and set the right hand
*                       side.
*
                        srnamt = 'DLARHS'
                        CALL dlarhs( path, xtype, uplo, ' ', n, n, kd,
     $                               kd, nrhs, a, ldab, xact, lda, b,
     $                               lda, iseed, info )
                        xtype = 'C'
                        CALL dlacpy( 'Full', n, nrhs, b, lda, bsav,
     $                               lda )
*
                        IF( nofact ) THEN
*
*                          --- Test DPBSV  ---
*
*                          Compute the L*L' or U'*U factorization of the
*                          matrix and solve the system.
*
                           CALL dlacpy( 'Full', kd+1, n, a, ldab, afac,
     $                                  ldab )
                           CALL dlacpy( 'Full', n, nrhs, b, lda, x,
     $                                  lda )
*
                           srnamt = 'DPBSV '
                           CALL dpbsv( uplo, n, kd, nrhs, afac, ldab, x,
     $                                 lda, info )
*
*                          Check error code from DPBSV .
*
                           IF( info.NE.izero ) THEN
                              CALL alaerh( path, 'DPBSV ', info, izero,
     $                                     uplo, n, n, kd, kd, nrhs,
     $                                     imat, nfail, nerrs, nout )
                              GO TO 40
                           ELSE IF( info.NE.0 ) THEN
                              GO TO 40
                           END IF
*
*                          Reconstruct matrix from factors and compute
*                          residual.
*
                           CALL dpbt01( uplo, n, kd, a, ldab, afac,
     $                                  ldab, rwork, result( 1 ) )
*
*                          Compute residual of the computed solution.
*
                           CALL dlacpy( 'Full', n, nrhs, b, lda, work,
     $                                  lda )
                           CALL dpbt02( uplo, n, kd, nrhs, a, ldab, x,
     $                                  lda, work, lda, rwork,
     $                                  result( 2 ) )
*
*                          Check solution from generated exact solution.
*
                           CALL dget04( n, nrhs, x, lda, xact, lda,
     $                                  rcondc, result( 3 ) )
                           nt = 3
*
*                          Print information about the tests that did
*                          not pass the threshold.
*
                           DO 30 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 )'DPBSV ',
     $                              uplo, n, kd, imat, k, result( k )
                                 nfail = nfail + 1
                              END IF
   30                      CONTINUE
                           nrun = nrun + nt
   40                      CONTINUE
                        END IF
*
*                       --- Test DPBSVX ---
*
                        IF( .NOT.prefac )
     $                     CALL dlaset( 'Full', kd+1, n, zero, zero,
     $                                  afac, ldab )
                        CALL dlaset( 'Full', n, nrhs, zero, zero, x,
     $                               lda )
                        IF( iequed.GT.1 .AND. n.GT.0 ) THEN
*
*                          Equilibrate the matrix if FACT='F' and
*                          EQUED='Y'
*
                           CALL dlaqsb( uplo, n, kd, a, ldab, s, scond,
     $                                  amax, equed )
                        END IF
*
*                       Solve the system and compute the condition
*                       number and error bounds using DPBSVX.
*
                        srnamt = 'DPBSVX'
                        CALL dpbsvx( fact, uplo, n, kd, nrhs, a, ldab,
     $                               afac, ldab, equed, s, b, lda, x,
     $                               lda, rcond, rwork, rwork( nrhs+1 ),
     $                               work, iwork, info )
*
*                       Check the error code from DPBSVX.
*
                        IF( info.NE.izero ) THEN
                           CALL alaerh( path, 'DPBSVX', info, izero,
     $                                  fact // uplo, n, n, kd, kd,
     $                                  nrhs, imat, nfail, nerrs, nout )
                           GO TO 60
                        END IF
*
                        IF( info.EQ.0 ) THEN
                           IF( .NOT.prefac ) THEN
*
*                             Reconstruct matrix from factors and
*                             compute residual.
*
                              CALL dpbt01( uplo, n, kd, a, ldab, afac,
     $                                     ldab, rwork( 2*nrhs+1 ),
     $                                     result( 1 ) )
                              k1 = 1
                           ELSE
                              k1 = 2
                           END IF
*
*                          Compute residual of the computed solution.
*
                           CALL dlacpy( 'Full', n, nrhs, bsav, lda,
     $                                  work, lda )
                           CALL dpbt02( uplo, n, kd, nrhs, asav, ldab,
     $                                  x, lda, work, lda,
     $                                  rwork( 2*nrhs+1 ), result( 2 ) )
*
*                          Check solution from generated exact solution.
*
                           IF( nofact .OR. ( prefac .AND. lsame( equed,
     $                         'N' ) ) ) THEN
                              CALL dget04( n, nrhs, x, lda, xact, lda,
     $                                     rcondc, result( 3 ) )
                           ELSE
                              CALL dget04( n, nrhs, x, lda, xact, lda,
     $                                     roldc, result( 3 ) )
                           END IF
*
*                          Check the error bounds from iterative
*                          refinement.
*
                           CALL dpbt05( uplo, n, kd, nrhs, asav, ldab,
     $                                  b, lda, x, lda, xact, lda,
     $                                  rwork, rwork( nrhs+1 ),
     $                                  result( 4 ) )
                        ELSE
                           k1 = 6
                        END IF
*
*                       Compare RCOND from DPBSVX with the computed
*                       value in RCONDC.
*
                        result( 6 ) = dget06( rcond, rcondc )
*
*                       Print information about the tests that did not
*                       pass the threshold.
*
                        DO 50 k = k1, 6
                           IF( result( k ).GE.thresh ) THEN
                              IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     $                           CALL aladhd( nout, path )
                              IF( prefac ) THEN
                                 WRITE( nout, fmt = 9997 )'DPBSVX',
     $                              fact, uplo, n, kd, equed, imat, k,
     $                              result( k )
                              ELSE
                                 WRITE( nout, fmt = 9998 )'DPBSVX',
     $                              fact, uplo, n, kd, imat, k,
     $                              result( k )
                              END IF
                              nfail = nfail + 1
                           END IF
   50                   CONTINUE
                        nrun = nrun + 7 - k1
   60                CONTINUE
   70             CONTINUE
   80          CONTINUE
   90       CONTINUE
  100    CONTINUE
  110 CONTINUE
*
*     Print a summary of the results.
*
      CALL alasvm( path, nout, nfail, nrun, nerrs )
*
 9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', KD =', i5,
     $      ', type ', i1, ', test(', i1, ')=', g12.5 )
 9998 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ', i5, ', ', i5,
     $      ', ... ), type ', i1, ', test(', i1, ')=', g12.5 )
 9997 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ', i5, ', ', i5,
     $      ', ... ), EQUED=''', a1, ''', type ', i1, ', test(', i1,
     $      ')=', g12.5 )
      RETURN
*
*     End of DDRVPB
*
      END