zdrvrfp.f

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*> \brief \b ZDRVRFP
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZDRVRFP( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
*      +              THRESH, A, ASAV, AFAC, AINV, B,
*      +              BSAV, XACT, X, ARF, ARFINV,
*      +              Z_WORK_ZLATMS, Z_WORK_ZPOT02,
*      +              Z_WORK_ZPOT03, D_WORK_ZLATMS, D_WORK_ZLANHE,
*      +              D_WORK_ZPOT01, D_WORK_ZPOT02, D_WORK_ZPOT03 )
*
*       .. Scalar Arguments ..
*       INTEGER            NN, NNS, NNT, NOUT
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       INTEGER            NVAL( NN ), NSVAL( NNS ), NTVAL( NNT )
*       COMPLEX*16         A( * )
*       COMPLEX*16         AINV( * )
*       COMPLEX*16         ASAV( * )
*       COMPLEX*16         B( * )
*       COMPLEX*16         BSAV( * )
*       COMPLEX*16         AFAC( * )
*       COMPLEX*16         ARF( * )
*       COMPLEX*16         ARFINV( * )
*       COMPLEX*16         XACT( * )
*       COMPLEX*16         X( * )
*       COMPLEX*16         Z_WORK_ZLATMS( * )
*       COMPLEX*16         Z_WORK_ZPOT02( * )
*       COMPLEX*16         Z_WORK_ZPOT03( * )
*       DOUBLE PRECISION   D_WORK_ZLATMS( * )
*       DOUBLE PRECISION   D_WORK_ZLANHE( * )
*       DOUBLE PRECISION   D_WORK_ZPOT01( * )
*       DOUBLE PRECISION   D_WORK_ZPOT02( * )
*       DOUBLE PRECISION   D_WORK_ZPOT03( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZDRVRFP tests the LAPACK RFP routines:
*>     ZPFTRF, ZPFTRS, and ZPFTRI.
*>
*> This testing routine follow the same tests as ZDRVPO (test for the full
*> format Symmetric Positive Definite solver).
*>
*> The tests are performed in Full Format, conversion back and forth from
*> full format to RFP format are performed using the routines ZTRTTF and
*> ZTFTTR.
*>
*> First, a specific matrix A of size N is created. There is nine types of
*> different matrixes possible.
*>  1. Diagonal                        6. Random, CNDNUM = sqrt(0.1/EPS)
*>  2. Random, CNDNUM = 2              7. Random, CNDNUM = 0.1/EPS
*> *3. First row and column zero       8. Scaled near underflow
*> *4. Last row and column zero        9. Scaled near overflow
*> *5. Middle row and column zero
*> (* - tests error exits from ZPFTRF, no test ratios are computed)
*> A solution XACT of size N-by-NRHS is created and the associated right
*> hand side B as well. Then ZPFTRF is called to compute L (or U), the
*> Cholesky factor of A. Then L (or U) is used to solve the linear system
*> of equations AX = B. This gives X. Then L (or U) is used to compute the
*> inverse of A, AINV. The following four tests are then performed:
*> (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*>     norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where EPS is the machine precision, RCOND the condition number of A, and
*> norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
*> Errors occur when INFO parameter is not as expected. Failures occur when
*> a test ratios is greater than THRES.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NOUT
*> \verbatim
*>          NOUT is INTEGER
*>                The unit number for output.
*> \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] NNT
*> \verbatim
*>          NNT is INTEGER
*>                The number of values of MATRIX TYPE contained in the vector NTVAL.
*> \endverbatim
*>
*> \param[in] NTVAL
*> \verbatim
*>          NTVAL is INTEGER array, dimension (NNT)
*>                The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
*> \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[out] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] ASAV
*> \verbatim
*>          ASAV 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*MAXRHS)
*> \endverbatim
*>
*> \param[out] BSAV
*> \verbatim
*>          BSAV is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (NMAX*MAXRHS)
*> \endverbatim
*>
*> \param[out] ARF
*> \verbatim
*>          ARF is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
*> \endverbatim
*>
*> \param[out] ARFINV
*> \verbatim
*>          ARFINV is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
*> \endverbatim
*>
*> \param[out] Z_WORK_ZLATMS
*> \verbatim
*>          Z_WORK_ZLATMS is COMPLEX*16 array, dimension ( 3*NMAX )
*> \endverbatim
*>
*> \param[out] Z_WORK_ZPOT02
*> \verbatim
*>          Z_WORK_ZPOT02 is COMPLEX*16 array, dimension ( NMAX*MAXRHS )
*> \endverbatim
*>
*> \param[out] Z_WORK_ZPOT03
*> \verbatim
*>          Z_WORK_ZPOT03 is COMPLEX*16 array, dimension ( NMAX*NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZLATMS
*> \verbatim
*>          D_WORK_ZLATMS is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZLANHE
*> \verbatim
*>          D_WORK_ZLANHE is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT01
*> \verbatim
*>          D_WORK_ZPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT02
*> \verbatim
*>          D_WORK_ZPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*>
*> \param[out] D_WORK_ZPOT03
*> \verbatim
*>          D_WORK_ZPOT03 is DOUBLE PRECISION array, dimension ( NMAX )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE zdrvrfp( NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL,
     +              THRESH, A, ASAV, AFAC, AINV, B,
     +              BSAV, XACT, X, ARF, ARFINV,
     +              Z_WORK_ZLATMS, Z_WORK_ZPOT02,
     +              Z_WORK_ZPOT03, D_WORK_ZLATMS, D_WORK_ZLANHE,
     +              D_WORK_ZPOT01, D_WORK_ZPOT02, D_WORK_ZPOT03 )
*
*  -- 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 ..
      INTEGER            NN, NNS, NNT, NOUT
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      INTEGER            NVAL( NN ), NSVAL( NNS ), NTVAL( NNT )
      COMPLEX*16         A( * )
      COMPLEX*16         AINV( * )
      COMPLEX*16         ASAV( * )
      COMPLEX*16         B( * )
      COMPLEX*16         BSAV( * )
      COMPLEX*16         AFAC( * )
      COMPLEX*16         ARF( * )
      COMPLEX*16         ARFINV( * )
      COMPLEX*16         XACT( * )
      COMPLEX*16         X( * )
      COMPLEX*16         Z_WORK_ZLATMS( * )
      COMPLEX*16         Z_WORK_ZPOT02( * )
      COMPLEX*16         Z_WORK_ZPOT03( * )
      DOUBLE PRECISION   D_WORK_ZLATMS( * )
      DOUBLE PRECISION   D_WORK_ZLANHE( * )
      DOUBLE PRECISION   D_WORK_ZPOT01( * )
      DOUBLE PRECISION   D_WORK_ZPOT02( * )
      DOUBLE PRECISION   D_WORK_ZPOT03( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0d+0, zero = 0.0d+0 )
      INTEGER            NTESTS
      PARAMETER          ( NTESTS = 4 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ZEROT
      INTEGER            I, INFO, IUPLO, LDA, LDB, IMAT, NERRS, NFAIL,
     +                   nrhs, nrun, izero, ioff, k, nt, n, iform, iin,
     +                   iit, iis
      CHARACTER          DIST, CTYPE, UPLO, CFORM
      INTEGER            KL, KU, MODE
      DOUBLE PRECISION   ANORM, AINVNM, CNDNUM, RCONDC
*     ..
*     .. Local Arrays ..
      CHARACTER          UPLOS( 2 ), FORMS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      DOUBLE PRECISION   RESULT( NTESTS )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   ZLANHE
      EXTERNAL           zlanhe
*     ..
*     .. External Subroutines ..
      EXTERNAL           aladhd, alaerh, alasvm, zget04, ztfttr, zlacpy,
     +                   zlaipd, zlarhs, zlatb4, zlatms, zpftri, zpftrf,
     +                   zpftrs, zpot01, zpot02, zpot03, zpotri, zpotrf,
     +                   ztrttf
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / SRNAMC / SRNAMT
*     ..
*     .. Data statements ..
      DATA               iseedy / 1988, 1989, 1990, 1991 /
      DATA               uplos / 'U', 'L' /
      DATA               forms / 'N', 'C' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
      DO 130 iin = 1, nn
*
         n = nval( iin )
         lda = max( n, 1 )
         ldb = max( n, 1 )
*
         DO 980 iis = 1, nns
*
            nrhs = nsval( iis )
*
            DO 120 iit = 1, nnt
*
               imat = ntval( iit )
*
*              If N.EQ.0, only consider the first type
*
               IF( n.EQ.0 .AND. iit.GE.1 ) GO TO 120
*
*              Skip types 3, 4, or 5 if the matrix size is too small.
*
               IF( imat.EQ.4 .AND. n.LE.1 ) GO TO 120
               IF( imat.EQ.5 .AND. n.LE.2 ) GO TO 120
*
*              Do first for UPLO = 'U', then for UPLO = 'L'
*
               DO 110 iuplo = 1, 2
                  uplo = uplos( iuplo )
*
*                 Do first for CFORM = 'N', then for CFORM = 'C'
*
                  DO 100 iform = 1, 2
                     cform = forms( iform )
*
*                    Set up parameters with ZLATB4 and generate a test
*                    matrix with ZLATMS.
*
                     CALL zlatb4( 'ZPO', imat, n, n, ctype, kl, ku,
     +                            anorm, mode, cndnum, dist )
*
                     srnamt = 'ZLATMS'
                     CALL zlatms( n, n, dist, iseed, ctype,
     +                            d_work_zlatms,
     +                            mode, cndnum, anorm, kl, ku, uplo, a,
     +                            lda, z_work_zlatms, info )
*
*                    Check error code from ZLATMS.
*
                     IF( info.NE.0 ) THEN
                        CALL alaerh( 'ZPF', 'ZLATMS', info, 0, uplo, n,
     +                               n, -1, -1, -1, iit, nfail, nerrs,
     +                               nout )
                        GO TO 100
                     END IF
*
*                    For types 3-5, zero one row and column of the matrix to
*                    test that INFO is returned correctly.
*
                     zerot = imat.GE.3 .AND. imat.LE.5
                     IF( zerot ) THEN
                        IF( iit.EQ.3 ) THEN
                           izero = 1
                        ELSE IF( iit.EQ.4 ) THEN
                           izero = n
                        ELSE
                           izero = n / 2 + 1
                        END IF
                        ioff = ( izero-1 )*lda
*
*                       Set row and column IZERO of A to 0.
*
                        IF( iuplo.EQ.1 ) THEN
                           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
                        izero = 0
                     END IF
*
*                    Set the imaginary part of the diagonals.
*
                     CALL zlaipd( n, a, lda+1, 0 )
*
*                    Save a copy of the matrix A in ASAV.
*
                     CALL zlacpy( uplo, n, n, a, lda, asav, lda )
*
*                    Compute the condition number of A (RCONDC).
*
                     IF( zerot ) THEN
                        rcondc = zero
                     ELSE
*
*                       Compute the 1-norm of A.
*
                        anorm = zlanhe( '1', uplo, n, a, lda,
     +                         d_work_zlanhe )
*
*                       Factor the matrix A.
*
                        CALL zpotrf( uplo, n, a, lda, info )
*
*                       Form the inverse of A.
*
                        CALL zpotri( uplo, n, a, lda, info )
 
                        IF ( n .NE. 0 ) THEN
*
*                          Compute the 1-norm condition number of A.
*
                           ainvnm = zlanhe( '1', uplo, n, a, lda,
     +                           d_work_zlanhe )
                           rcondc = ( one / anorm ) / ainvnm
*
*                          Restore the matrix A.
*
                           CALL zlacpy( uplo, n, n, asav, lda, a, lda )
                        END IF
*
                     END IF
*
*                    Form an exact solution and set the right hand side.
*
                     srnamt = 'ZLARHS'
                     CALL zlarhs( 'ZPO', 'N', uplo, ' ', n, n, kl, ku,
     +                            nrhs, a, lda, xact, lda, b, lda,
     +                            iseed, info )
                     CALL zlacpy( 'Full', n, nrhs, b, lda, bsav, lda )
*
*                    Compute the L*L' or U'*U factorization of the
*                    matrix and solve the system.
*
                     CALL zlacpy( uplo, n, n, a, lda, afac, lda )
                     CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldb )
*
                     srnamt = 'ZTRTTF'
                     CALL ztrttf( cform, uplo, n, afac, lda, arf, info )
                     srnamt = 'ZPFTRF'
                     CALL zpftrf( cform, uplo, n, arf, info )
*
*                    Check error code from ZPFTRF.
*
                     IF( info.NE.izero ) THEN
*
*                       LANGOU: there is a small hick here: IZERO should
*                       always be INFO however if INFO is ZERO, ALAERH does not
*                       complain.
*
                         CALL alaerh( 'ZPF', 'ZPFSV ', info, izero,
     +                                uplo, n, n, -1, -1, nrhs, iit,
     +                                nfail, nerrs, nout )
                         GO TO 100
                      END IF
*
*                     Skip the tests if INFO is not 0.
*
                     IF( info.NE.0 ) THEN
                        GO TO 100
                     END IF
*
                     srnamt = 'ZPFTRS'
                     CALL zpftrs( cform, uplo, n, nrhs, arf, x, ldb,
     +                            info )
*
                     srnamt = 'ZTFTTR'
                     CALL ztfttr( cform, uplo, n, arf, afac, lda, info )
*
*                    Reconstruct matrix from factors and compute
*                    residual.
*
                     CALL zlacpy( uplo, n, n, afac, lda, asav, lda )
                     CALL zpot01( uplo, n, a, lda, afac, lda,
     +                             d_work_zpot01, result( 1 ) )
                     CALL zlacpy( uplo, n, n, asav, lda, afac, lda )
*
*                    Form the inverse and compute the residual.
*
                    IF(mod(n,2).EQ.0)THEN
                       CALL zlacpy( 'A', n+1, n/2, arf, n+1, arfinv,
     +                               n+1 )
                    ELSE
                       CALL zlacpy( 'A', n, (n+1)/2, arf, n, arfinv,
     +                               n )
                    END IF
*
                     srnamt = 'ZPFTRI'
                     CALL zpftri( cform, uplo, n, arfinv , info )
*
                     srnamt = 'ZTFTTR'
                     CALL ztfttr( cform, uplo, n, arfinv, ainv, lda,
     +                            info )
*
*                    Check error code from ZPFTRI.
*
                     IF( info.NE.0 )
     +                  CALL alaerh( 'ZPO', 'ZPFTRI', info, 0, uplo, n,
     +                               n, -1, -1, -1, imat, nfail, nerrs,
     +                               nout )
*
                     CALL zpot03( uplo, n, a, lda, ainv, lda,
     +                            z_work_zpot03, lda, d_work_zpot03,
     +                            rcondc, result( 2 ) )
*
*                    Compute residual of the computed solution.
*
                     CALL zlacpy( 'Full', n, nrhs, b, lda,
     +                            z_work_zpot02, lda )
                     CALL zpot02( uplo, n, nrhs, a, lda, x, lda,
     +                            z_work_zpot02, lda, d_work_zpot02,
     +                            result( 3 ) )
*
*                    Check solution from generated exact solution.
*
                     CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
     +                         result( 4 ) )
                     nt = 4
*
*                    Print information about the tests that did not
*                    pass the threshold.
*
                     DO 60 k = 1, nt
                        IF( result( k ).GE.thresh ) THEN
                           IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
     +                        CALL aladhd( nout, 'ZPF' )
                           WRITE( nout, fmt = 9999 )'ZPFSV ', uplo,
     +                            n, iit, k, result( k )
                           nfail = nfail + 1
                        END IF
   60                CONTINUE
                     nrun = nrun + nt
  100             CONTINUE
  110          CONTINUE
  120       CONTINUE
  980    CONTINUE
  130 CONTINUE
*
*     Print a summary of the results.
*
      CALL alasvm( 'ZPF', nout, nfail, nrun, nerrs )
*
 9999 FORMAT( 1x, a6, ', UPLO=''', a1, ''', N =', i5, ', type ', i1,
     +      ', test(', i1, ')=', g12.5 )
*
      RETURN
*
*     End of ZDRVRFP
*
      END