zchktr.f

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*> \brief \b ZCHKTR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
*                          THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
*                          WORK, RWORK, NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NMAX, NN, NNB, NNS, NOUT
*       DOUBLE PRECISION   THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            NBVAL( * ), NSVAL( * ), NVAL( * )
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( * ), AINV( * ), B( * ), WORK( * ), X( * ),
*      $                   XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZCHKTR tests ZTRTRI, -TRS, -RFS, and -CON, and ZLATRS
*> \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 column dimension N.
*> \endverbatim
*>
*> \param[in] NNB
*> \verbatim
*>          NNB is INTEGER
*>          The number of values of NB contained in the vector NBVAL.
*> \endverbatim
*>
*> \param[in] NBVAL
*> \verbatim
*>          NBVAL is INTEGER array, dimension (NNB)
*>          The values of the blocksize NB.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*>          NNS is INTEGER
*>          The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*>          NSVAL is INTEGER array, dimension (NNS)
*>          The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is 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 leading dimension of the work arrays.
*>          NMAX >= the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A 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*NSMAX)
*>          where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension
*>                      (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension
*>                      (max(NMAX,2*NSMAX))
*> \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 complex16_lin
*
*  =====================================================================
      SUBROUTINE zchktr( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
     $                   THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
     $                   WORK, RWORK, 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, NNB, NNS, NOUT
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            NBVAL( * ), NSVAL( * ), NVAL( * )
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( * ), AINV( * ), B( * ), WORK( * ), X( * ),
     $                   xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NTYPE1, NTYPES
      PARAMETER          ( NTYPE1 = 10, ntypes = 18 )
      INTEGER            NTESTS
      parameter( ntests = 9 )
      INTEGER            NTRAN
      parameter( ntran = 3 )
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d0, zero = 0.0d0 )
*     ..
*     .. Local Scalars ..
      CHARACTER          DIAG, NORM, TRANS, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, IDIAG, IMAT, IN, INB, INFO, IRHS, ITRAN,
     $                   iuplo, k, lda, n, nb, nerrs, nfail, nrhs, nrun
      DOUBLE PRECISION   AINVNM, ANORM, DUMMY, RCOND, RCONDC, RCONDI,
     $                   RCONDO, SCALE
*     ..
*     .. Local Arrays ..
      CHARACTER          TRANSS( NTRAN ), UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      DOUBLE PRECISION   RESULT( NTESTS )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   ZLANTR
      EXTERNAL           lsame, zlantr
*     ..
*     .. External Subroutines ..
      EXTERNAL           alaerh, alahd, alasum, xlaenv, zcopy, zerrtr,
     $                   zget04, zlacpy, zlarhs, zlatrs, zlattr, ztrcon,
     $                   ztrrfs, ztrt01, ztrt02, ztrt03, ztrt05, ztrt06,
     $                   ztrtri, ztrtrs
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*32       SRNAMT
      INTEGER            INFOT, IOUNIT
*     ..
*     .. Common blocks ..
      COMMON             / infoc / infot, iounit, ok, lerr
      COMMON             / srnamc / srnamt
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Data statements ..
      DATA               iseedy / 1988, 1989, 1990, 1991 /
      DATA               uplos / 'U', 'L' / , transs / 'N', 'T', 'C' /
*     ..
*     .. Executable Statements ..
*
*     Initialize constants and the random number seed.
*
      path( 1: 1 ) = 'Zomplex precision'
      path( 2: 3 ) = 'TR'
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
*     Test the error exits
*
      IF( tsterr )
     $   CALL zerrtr( path, nout )
      infot = 0
*
      DO 120 in = 1, nn
*
*        Do for each value of N in NVAL
*
         n = nval( in )
         lda = max( 1, n )
         xtype = 'N'
*
         DO 80 imat = 1, ntype1
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
            IF( .NOT.dotype( imat ) )
     $         GO TO 80
*
            DO 70 iuplo = 1, 2
*
*              Do first for UPLO = 'U', then for UPLO = 'L'
*
               uplo = uplos( iuplo )
*
*              Call ZLATTR to generate a triangular test matrix.
*
               srnamt = 'ZLATTR'
               CALL zlattr( imat, uplo, 'No transpose', diag, iseed, n,
     $                      a, lda, x, work, rwork, info )
*
*              Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
               IF( lsame( diag, 'N' ) ) THEN
                  idiag = 1
               ELSE
                  idiag = 2
               END IF
*
               DO 60 inb = 1, nnb
*
*                 Do for each blocksize in NBVAL
*
                  nb = nbval( inb )
                  CALL xlaenv( 1, nb )
*
*+    TEST 1
*                 Form the inverse of A.
*
                  CALL zlacpy( uplo, n, n, a, lda, ainv, lda )
                  srnamt = 'ZTRTRI'
                  CALL ztrtri( uplo, diag, n, ainv, lda, info )
*
*                 Check error code from ZTRTRI.
*
                  IF( info.NE.0 )
     $               CALL alaerh( path, 'ZTRTRI', info, 0, uplo // diag,
     $                            n, n, -1, -1, nb, imat, nfail, nerrs,
     $                            nout )
*
*                 Compute the infinity-norm condition number of A.
*
                  anorm = zlantr( 'I', uplo, diag, n, n, a, lda, rwork )
                  ainvnm = zlantr( 'i', UPLO, DIAG, N, N, AINV, LDA,
     $                     RWORK )
.LE..OR..LE.                  IF( ANORMZERO  AINVNMZERO ) THEN
                     RCONDI = ONE
                  ELSE
                     RCONDI = ( ONE / ANORM ) / AINVNM
                  END IF
*
*                 Compute the residual for the triangular matrix times
*                 its inverse.  Also compute the 1-norm condition number
*                 of A.
*
                  CALL ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDA, RCONDO,
     $                         RWORK, RESULT( 1 ) )
*                 Print the test ratio if it is .GE. THRESH.
*
.GE.                  IF( RESULT( 1 )THRESH ) THEN
.EQ..AND..EQ.                     IF( NFAIL0  NERRS0 )
     $                  CALL ALAHD( NOUT, PATH )
                     WRITE( NOUT, FMT = 9999 )UPLO, DIAG, N, NB, IMAT,
     $                  1, RESULT( 1 )
                     NFAIL = NFAIL + 1
                  END IF
                  NRUN = NRUN + 1
*
*                 Skip remaining tests if not the first block size.
*
.NE.                  IF( INB1 )
     $               GO TO 60
*
                  DO 40 IRHS = 1, NNS
                     NRHS = NSVAL( IRHS )
                     XTYPE = 'n'
*
                     DO 30 ITRAN = 1, NTRAN
*
*                    Do for op(A) = A, A**T, or A**H.
*
                        TRANS = TRANSS( ITRAN )
.EQ.                        IF( ITRAN1 ) THEN
                           NORM = 'o'
                           RCONDC = RCONDO
                        ELSE
                           NORM = 'i'
                           RCONDC = RCONDI
                        END IF
*
*+    TEST 2
*                       Solve and compute residual for op(A)*x = b.
*
                        SRNAMT = 'zlarhs'
                        CALL ZLARHS( PATH, XTYPE, UPLO, TRANS, N, N, 0,
     $                               IDIAG, NRHS, A, LDA, XACT, LDA, B,
     $                               LDA, ISEED, INFO )
                        XTYPE = 'c'
                        CALL ZLACPY( 'full', N, NRHS, B, LDA, X, LDA )
*
                        SRNAMT = 'ztrtrs'
                        CALL ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
     $                               X, LDA, INFO )
*
*                       Check error code from ZTRTRS.
*
.NE.                        IF( INFO0 )
     $                     CALL ALAERH( PATH, 'ztrtrs', INFO, 0,
     $                                  UPLO // TRANS // DIAG, N, N, -1,
     $                                  -1, NRHS, IMAT, NFAIL, NERRS,
     $                                  NOUT )
*
*                       This line is needed on a Sun SPARCstation.
*
.GT.                        IF( N0 )
     $                     DUMMY = A( 1 )
*
                        CALL ZTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
     $                               X, LDA, B, LDA, WORK, RWORK,
     $                               RESULT( 2 ) )
*
*+    TEST 3
*                       Check solution from generated exact solution.
*
                        CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                               RESULT( 3 ) )
*
*+    TESTS 4, 5, and 6
*                       Use iterative refinement to improve the solution
*                       and compute error bounds.
*
                        SRNAMT = 'ztrrfs'
                        CALL ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
     $                               B, LDA, X, LDA, RWORK,
     $                               RWORK( NRHS+1 ), WORK,
     $                               RWORK( 2*NRHS+1 ), INFO )
*
*                       Check error code from ZTRRFS.
*
.NE.                        IF( INFO0 )
     $                     CALL ALAERH( PATH, 'ztrrfs', INFO, 0,
     $                                  UPLO // TRANS // DIAG, N, N, -1,
     $                                  -1, NRHS, IMAT, NFAIL, NERRS,
     $                                  NOUT )
*
                        CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                               RESULT( 4 ) )
                        CALL ZTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
     $                               B, LDA, X, LDA, XACT, LDA, RWORK,
     $                               RWORK( NRHS+1 ), RESULT( 5 ) )
*
*                       Print information about the tests that did not
*                       pass the threshold.
*
                        DO 20 K = 2, 6
.GE.                           IF( RESULT( K )THRESH ) THEN
.EQ..AND..EQ.                              IF( NFAIL0  NERRS0 )
     $                           CALL ALAHD( NOUT, PATH )
                              WRITE( NOUT, FMT = 9998 )UPLO, TRANS,
     $                           DIAG, N, NRHS, IMAT, K, RESULT( K )
                              NFAIL = NFAIL + 1
                           END IF
   20                   CONTINUE
                        NRUN = NRUN + 5
   30                CONTINUE
   40             CONTINUE
*
*+    TEST 7
*                       Get an estimate of RCOND = 1/CNDNUM.
*
                  DO 50 ITRAN = 1, 2
.EQ.                     IF( ITRAN1 ) THEN
                        NORM = 'o'
                        RCONDC = RCONDO
                     ELSE
                        NORM = 'i'
                        RCONDC = RCONDI
                     END IF
                     SRNAMT = 'ztrcon'
                     CALL ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND,
     $                            WORK, RWORK, INFO )
*
*                       Check error code from ZTRCON.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'ztrcon', INFO, 0,
     $                               NORM // UPLO // DIAG, N, N, -1, -1,
     $                               -1, IMAT, NFAIL, NERRS, NOUT )
*
                     CALL ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA,
     $                            RWORK, RESULT( 7 ) )
*
*                    Print the test ratio if it is .GE. THRESH.
*
.GE.                     IF( RESULT( 7 )THRESH ) THEN
.EQ..AND..EQ.                        IF( NFAIL0  NERRS0 )
     $                     CALL ALAHD( NOUT, PATH )
                        WRITE( NOUT, FMT = 9997 )NORM, UPLO, N, IMAT,
     $                     7, RESULT( 7 )
                        NFAIL = NFAIL + 1
                     END IF
                     NRUN = NRUN + 1
   50             CONTINUE
   60          CONTINUE
   70       CONTINUE
   80    CONTINUE
*
*        Use pathological test matrices to test ZLATRS.
*
         DO 110 IMAT = NTYPE1 + 1, NTYPES
*
*           Do the tests only if DOTYPE( IMAT ) is true.
*
.NOT.            IF( DOTYPE( IMAT ) )
     $         GO TO 110
*
            DO 100 IUPLO = 1, 2
*
*              Do first for UPLO = 'U', then for UPLO = 'L'
*
               UPLO = UPLOS( IUPLO )
               DO 90 ITRAN = 1, NTRAN
*
*                 Do for op(A) = A, A**T, and A**H.
*
                  TRANS = TRANSS( ITRAN )
*
*                 Call ZLATTR to generate a triangular test matrix.
*
                  SRNAMT = 'zlattr'
                  CALL ZLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A,
     $                         LDA, X, WORK, RWORK, INFO )
*
*+    TEST 8
*                 Solve the system op(A)*x = b.
*
                  SRNAMT = 'zlatrs'
                  CALL ZCOPY( N, X, 1, B, 1 )
                  CALL ZLATRS( UPLO, TRANS, DIAG, 'n', N, A, LDA, B,
     $                         SCALE, RWORK, INFO )
*
*                 Check error code from ZLATRS.
*
.NE.                  IF( INFO0 )
     $               CALL ALAERH( PATH, 'zlatrs', INFO, 0,
     $                            UPLO // TRANS // DIAG // 'n', N, N,
     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
                  CALL ZTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
     $                         RWORK, ONE, B, LDA, X, LDA, WORK,
     $                         RESULT( 8 ) )
*
*+    TEST 9
*                 Solve op(A)*X = b again with NORMIN = 'Y'.
*
                  CALL ZCOPY( N, X, 1, B( N+1 ), 1 )
                  CALL ZLATRS( UPLO, TRANS, DIAG, 'y', N, A, LDA,
     $                         B( N+1 ), SCALE, RWORK, INFO )
*
*                 Check error code from ZLATRS.
*
.NE.                  IF( INFO0 )
     $               CALL ALAERH( PATH, 'zlatrs', INFO, 0,
     $                            UPLO // TRANS // DIAG // 'y', N, N,
     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
*
                  CALL ZTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
     $                         RWORK, ONE, B( N+1 ), LDA, X, LDA, WORK,
     $                         RESULT( 9 ) )
*
*                 Print information about the tests that did not pass
*                 the threshold.
*
.GE.                  IF( RESULT( 8 )THRESH ) THEN
.EQ..AND..EQ.                     IF( NFAIL0  NERRS0 )
     $                  CALL ALAHD( NOUT, PATH )
                     WRITE( NOUT, FMT = 9996 )'zlatrs', UPLO, TRANS,
     $                  DIAG, 'n', N, IMAT, 8, RESULT( 8 )
                     NFAIL = NFAIL + 1
                  END IF
.GE.                  IF( RESULT( 9 )THRESH ) THEN
.EQ..AND..EQ.                     IF( NFAIL0  NERRS0 )
     $                  CALL ALAHD( NOUT, PATH )
                     WRITE( NOUT, FMT = 9996 )'zlatrs', UPLO, TRANS,
     $                  DIAG, 'y', N, IMAT, 9, RESULT( 9 )
                     NFAIL = NFAIL + 1
                  END IF
                  NRUN = NRUN + 2
   90          CONTINUE
  100       CONTINUE
  110    CONTINUE
  120 CONTINUE
*
*     Print a summary of the results.
*
      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
 9999 FORMAT( ' uplo=''', A1, ''', diag=''', A1, ''', n=', I5, ', nb=',
     $      I4, ', type ', I2, ', test(', I2, ')= ', G12.5 )
 9998 FORMAT( ' uplo=''', A1, ''', trans=''', A1, ''', diag=''', A1,
     $      ''', n=', I5, ', nb=', I4, ', type ', I2, ',
     $      test(', I2, ')= ', g12.5 )
 9997 FORMAT( ' NORM=''', a1, ''', UPLO =''', a1, ''', N=', i5, ',',
     $      11x, ' type ', i2, ', test(', i2, ')=', g12.5 )
 9996 FORMAT( 1x, a, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
     $      A1, ''',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
     $      G12.5 )
      RETURN
*
*     End of ZCHKTR
*
      END