schktb.f

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*> \brief \b SCHKTB
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
*                          NMAX, AB, AINV, B, X, XACT, WORK, RWORK, IWORK,
*                          NOUT )
*
*       .. Scalar Arguments ..
*       LOGICAL            TSTERR
*       INTEGER            NMAX, NN, NNS, NOUT
*       REAL               THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            DOTYPE( * )
*       INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
*       REAL               AB( * ), AINV( * ), B( * ), RWORK( * ),
*      $                   WORK( * ), X( * ), XACT( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SCHKTB tests STBTRS, -RFS, and -CON, and SLATBS.
*> \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] 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 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 leading dimension of the work arrays.
*>          NMAX >= the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] AB
*> \verbatim
*>          AB 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*NSMAX)
*>          where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*>          XACT is REAL array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension
*>                      (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension
*>                      (max(NMAX,2*NSMAX))
*> \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.
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE schktb( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
     $                   NMAX, AB, 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, NNS, NOUT
      REAL               THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
      REAL               AB( * ), AINV( * ), B( * ), RWORK( * ),
     $                   work( * ), x( * ), xact( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NTYPE1, NTYPES
      PARAMETER          ( NTYPE1 = 9, ntypes = 17 )
      INTEGER            NTESTS
      parameter( ntests = 8 )
      INTEGER            NTRAN
      parameter( ntran = 3 )
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      CHARACTER          DIAG, NORM, TRANS, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN,
     $                   iuplo, j, k, kd, lda, ldab, n, nerrs, nfail,
     $                   nimat, nimat2, nk, nrhs, nrun
      REAL               AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
     $                   SCALE
*     ..
*     .. Local Arrays ..
      CHARACTER          TRANSS( NTRAN ), UPLOS( 2 )
      INTEGER            ISEED( 4 ), ISEEDY( 4 )
      REAL               RESULT( NTESTS )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLANTB, SLANTR
      EXTERNAL           lsame, slantb, slantr
*     ..
*     .. External Subroutines ..
      EXTERNAL           alaerh, alahd, alasum, scopy, serrtr, sget04,
     $                   slacpy, slarhs, slaset, slatbs, slattb, stbcon,
     $                   stbrfs, stbsv, stbt02, stbt03, stbt05, stbt06,
     $                   stbtrs
*     ..
*     .. 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, min
*     ..
*     .. 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 ) = 'Single precision'
      path( 2: 3 ) = 'TB'
      nrun = 0
      nfail = 0
      nerrs = 0
      DO 10 i = 1, 4
         iseed( i ) = iseedy( i )
   10 CONTINUE
*
*     Test the error exits
*
      IF( tsterr )
     $   CALL serrtr( path, nout )
      infot = 0
*
      DO 140 in = 1, nn
*
*        Do for each value of N in NVAL
*
         n = nval( in )
         lda = max( 1, n )
         xtype = 'N'
         nimat = ntype1
         nimat2 = ntypes
         IF( n.LE.0 ) THEN
            nimat = 1
            nimat2 = ntype1 + 1
         END IF
*
         nk = min( n+1, 4 )
         DO 130 ik = 1, nk
*
*           Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes
*           it easier to skip redundant values for small values of N.
*
            IF( ik.EQ.1 ) THEN
               kd = 0
            ELSE IF( ik.EQ.2 ) THEN
               kd = max( n, 0 )
            ELSE IF( ik.EQ.3 ) THEN
               kd = ( 3*n-1 ) / 4
            ELSE IF( ik.EQ.4 ) THEN
               kd = ( n+1 ) / 4
            END IF
            ldab = kd + 1
*
            DO 90 imat = 1, nimat
*
*              Do the tests only if DOTYPE( IMAT ) is true.
*
               IF( .NOT.dotype( imat ) )
     $            GO TO 90
*
               DO 80 iuplo = 1, 2
*
*                 Do first for UPLO = 'U', then for UPLO = 'L'
*
                  uplo = uplos( iuplo )
*
*                 Call SLATTB to generate a triangular test matrix.
*
                  srnamt = 'SLATTB'
                  CALL slattb( imat, uplo, 'No transpose', diag, iseed,
     $                         n, kd, ab, ldab, x, work, info )
*
*                 Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
                  IF( lsame( diag, 'N' ) ) THEN
                     idiag = 1
                  ELSE
                     idiag = 2
                  END IF
*
*                 Form the inverse of A so we can get a good estimate
*                 of RCONDC = 1/(norm(A) * norm(inv(A))).
*
                  CALL slaset( 'Full', n, n, zero, one, ainv, lda )
                  IF( lsame( uplo, 'U' ) ) THEN
                     DO 20 j = 1, n
                        CALL stbsv( uplo, 'No transpose', diag, j, kd,
     $                              ab, ldab, ainv( ( j-1 )*lda+1 ), 1 )
   20                CONTINUE
                  ELSE
                     DO 30 j = 1, n
                        CALL stbsv( uplo, 'No transpose', diag, n-j+1,
     $                              kd, ab( ( j-1 )*ldab+1 ), ldab,
     $                              ainv( ( j-1 )*lda+j ), 1 )
   30                CONTINUE
                  END IF
*
*                 Compute the 1-norm condition number of A.
*
                  anorm = slantb( '1', uplo, diag, n, kd, ab, ldab,
     $                    rwork )
                  ainvnm = slantr( '1', uplo, diag, n, n, ainv, lda,
     $                     rwork )
                  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
                     rcondo = one
                  ELSE
                     rcondo = ( one / anorm ) / ainvnm
                  END IF
*
*                 Compute the infinity-norm condition number of A.
*
                  anorm = slantb( 'I', uplo, diag, n, kd, ab, ldab,
     $                    rwork )
                  ainvnm = slantr( 'i', UPLO, DIAG, N, N, AINV, LDA,
     $                     RWORK )
.LE..OR..LE.                  IF( ANORMZERO  AINVNMZERO ) THEN
                     RCONDI = ONE
                  ELSE
                     RCONDI = ( ONE / ANORM ) / AINVNM
                  END IF
*
                  DO 60 IRHS = 1, NNS
                     NRHS = NSVAL( IRHS )
                     XTYPE = 'n'
*
                     DO 50 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 1
*                    Solve and compute residual for op(A)*x = b.
*
                        SRNAMT = 'slarhs'
                        CALL SLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD,
     $                               IDIAG, NRHS, AB, LDAB, XACT, LDA,
     $                               B, LDA, ISEED, INFO )
                        XTYPE = 'c'
                        CALL SLACPY( 'full', N, NRHS, B, LDA, X, LDA )
*
                        SRNAMT = 'stbtrs'
                        CALL STBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
     $                               LDAB, X, LDA, INFO )
*
*                    Check error code from STBTRS.
*
.NE.                        IF( INFO0 )
     $                     CALL ALAERH( PATH, 'stbtrs', INFO, 0,
     $                                  UPLO // TRANS // DIAG, N, N, KD,
     $                                  KD, NRHS, IMAT, NFAIL, NERRS,
     $                                  NOUT )
*
                        CALL STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
     $                               LDAB, X, LDA, B, LDA, WORK,
     $                               RESULT( 1 ) )
*
*+    TEST 2
*                    Check solution from generated exact solution.
*
                        CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                               RESULT( 2 ) )
*
*+    TESTS 3, 4, and 5
*                    Use iterative refinement to improve the solution
*                    and compute error bounds.
*
                        SRNAMT = 'stbrfs'
                        CALL STBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
     $                               LDAB, B, LDA, X, LDA, RWORK,
     $                               RWORK( NRHS+1 ), WORK, IWORK,
     $                               INFO )
*
*                    Check error code from STBRFS.
*
.NE.                        IF( INFO0 )
     $                     CALL ALAERH( PATH, 'stbrfs', INFO, 0,
     $                                  UPLO // TRANS // DIAG, N, N, KD,
     $                                  KD, NRHS, IMAT, NFAIL, NERRS,
     $                                  NOUT )
*
                        CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
     $                               RESULT( 3 ) )
                        CALL STBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
     $                               LDAB, B, LDA, X, LDA, XACT, LDA,
     $                               RWORK, RWORK( NRHS+1 ),
     $                               RESULT( 4 ) )
*
*                       Print information about the tests that did not
*                       pass the threshold.
*
                        DO 40 K = 1, 5
.GE.                           IF( RESULT( K )THRESH ) THEN
.EQ..AND..EQ.                              IF( NFAIL0  NERRS0 )
     $                           CALL ALAHD( NOUT, PATH )
                              WRITE( NOUT, FMT = 9999 )UPLO, TRANS,
     $                           DIAG, N, KD, NRHS, IMAT, K, RESULT( K )
                              NFAIL = NFAIL + 1
                           END IF
   40                   CONTINUE
                        NRUN = NRUN + 5
   50                CONTINUE
   60             CONTINUE
*
*+    TEST 6
*                    Get an estimate of RCOND = 1/CNDNUM.
*
                  DO 70 ITRAN = 1, 2
.EQ.                     IF( ITRAN1 ) THEN
                        NORM = 'o'
                        RCONDC = RCONDO
                     ELSE
                        NORM = 'i'
                        RCONDC = RCONDI
                     END IF
                     SRNAMT = 'stbcon'
                     CALL STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB,
     $                            RCOND, WORK, IWORK, INFO )
*
*                    Check error code from STBCON.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'stbcon', INFO, 0,
     $                               NORM // UPLO // DIAG, N, N, KD, KD,
     $                               -1, IMAT, NFAIL, NERRS, NOUT )
*
                     CALL STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB,
     $                            LDAB, RWORK, RESULT( 6 ) )
*
*                    Print information about the tests that did not pass
*                    the threshold.
*
.GE.                     IF( RESULT( 6 )THRESH ) THEN
.EQ..AND..EQ.                        IF( NFAIL0  NERRS0 )
     $                     CALL ALAHD( NOUT, PATH )
                        WRITE( NOUT, FMT = 9998 ) 'stbcon', NORM, UPLO,
     $                     DIAG, N, KD, IMAT, 6, RESULT( 6 )
                        NFAIL = NFAIL + 1
                     END IF
                     NRUN = NRUN + 1
   70             CONTINUE
   80          CONTINUE
   90       CONTINUE
*
*           Use pathological test matrices to test SLATBS.
*
            DO 120 IMAT = NTYPE1 + 1, NIMAT2
*
*              Do the tests only if DOTYPE( IMAT ) is true.
*
.NOT.               IF( DOTYPE( IMAT ) )
     $            GO TO 120
*
               DO 110 IUPLO = 1, 2
*
*                 Do first for UPLO = 'U', then for UPLO = 'L'
*
                  UPLO = UPLOS( IUPLO )
                  DO 100 ITRAN = 1, NTRAN
*
*                    Do for op(A) = A, A**T, and A**H.
*
                     TRANS = TRANSS( ITRAN )
*
*                    Call SLATTB to generate a triangular test matrix.
*
                     SRNAMT = 'slattb'
                     CALL SLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD,
     $                            AB, LDAB, X, WORK, INFO )
*
*+    TEST 7
*                    Solve the system op(A)*x = b
*
                     SRNAMT = 'slatbs'
                     CALL SCOPY( N, X, 1, B, 1 )
                     CALL SLATBS( UPLO, TRANS, DIAG, 'n', N, KD, AB,
     $                            LDAB, B, SCALE, RWORK, INFO )
*
*                    Check error code from SLATBS.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'slatbs', INFO, 0,
     $                               UPLO // TRANS // DIAG // 'n', N, N,
     $                               KD, KD, -1, IMAT, NFAIL, NERRS,
     $                               NOUT )
*
                     CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
     $                            SCALE, RWORK, ONE, B, LDA, X, LDA,
     $                            WORK, RESULT( 7 ) )
*
*+    TEST 8
*                    Solve op(A)*x = b again with NORMIN = 'Y'.
*
                     CALL SCOPY( N, X, 1, B, 1 )
                     CALL SLATBS( UPLO, TRANS, DIAG, 'y', N, KD, AB,
     $                            LDAB, B, SCALE, RWORK, INFO )
*
*                    Check error code from SLATBS.
*
.NE.                     IF( INFO0 )
     $                  CALL ALAERH( PATH, 'slatbs', INFO, 0,
     $                               UPLO // TRANS // DIAG // 'y', N, N,
     $                               KD, KD, -1, IMAT, NFAIL, NERRS,
     $                               NOUT )
*
                     CALL STBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
     $                            SCALE, RWORK, ONE, B, LDA, X, LDA,
     $                            WORK, RESULT( 8 ) )
*
*                    Print information about the tests that did not pass
*                    the threshold.
*
.GE.                     IF( RESULT( 7 )THRESH ) THEN
.EQ..AND..EQ.                        IF( NFAIL0  NERRS0 )
     $                     CALL ALAHD( NOUT, PATH )
                        WRITE( NOUT, FMT = 9997 )'slatbs', UPLO, TRANS,
     $                     DIAG, 'n', N, KD, IMAT, 7, RESULT( 7 )
                        NFAIL = NFAIL + 1
                     END IF
.GE.                     IF( RESULT( 8 )THRESH ) THEN
.EQ..AND..EQ.                        IF( NFAIL0  NERRS0 )
     $                     CALL ALAHD( NOUT, PATH )
                        WRITE( NOUT, FMT = 9997 )'slatbs', UPLO, TRANS,
     $                     DIAG, 'y', N, KD, IMAT, 8, RESULT( 8 )
                        NFAIL = NFAIL + 1
                     END IF
                     NRUN = NRUN + 2
  100             CONTINUE
  110          CONTINUE
  120       CONTINUE
  130    CONTINUE
  140 CONTINUE
*
*     Print a summary of the results.
*
      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
 9999 FORMAT( ' uplo=''', A1, ''', trans=''', A1, ''',
     $      diag=''', A1, ''', n=', I5, ', kd=', I5, ', nrhs=', I5,
     $      ', type ', I2, ', test(', I2, ')=', G12.5 )
 9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',',
     $      I5, ',', I5, ',  ... ), type ', I2, ', test(', I2, ')=',
     $      G12.5 )
 9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
     $      A1, ''',', I5, ',', I5, ', ...  ),  type ', I2, ', test(',
     $      I1, ')=', G12.5 )
      RETURN
*
*     End of SCHKTB
*
      END