OpenBLAS/lapack-netlib/TESTING/EIG/dget24.f

*> \brief \b DGET24
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
*                          H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS,
*                          LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT,
*                          RESULT, WORK, LWORK, IWORK, BWORK, INFO )
*
*       .. Scalar Arguments ..
*       LOGICAL            COMP
*       INTEGER            INFO, JTYPE, LDA, LDVS, LWORK, N, NOUNIT, NSLCT
*       DOUBLE PRECISION   RCDEIN, RCDVIN, THRESH
*       ..
*       .. Array Arguments ..
*       LOGICAL            BWORK( * )
*       INTEGER            ISEED( 4 ), ISLCT( * ), IWORK( * )
*       DOUBLE PRECISION   A( LDA, * ), H( LDA, * ), HT( LDA, * ),
*      $                   RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
*      $                   WI( * ), WIT( * ), WITMP( * ), WORK( * ),
*      $                   WR( * ), WRT( * ), WRTMP( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    DGET24 checks the nonsymmetric eigenvalue (Schur form) problem
*>    expert driver DGEESX.
*>
*>    If COMP = .FALSE., the first 13 of the following tests will be
*>    be performed on the input matrix A, and also tests 14 and 15
*>    if LWORK is sufficiently large.
*>    If COMP = .TRUE., all 17 test will be performed.
*>
*>    (1)     0 if T is in Schur form, 1/ulp otherwise
*>           (no sorting of eigenvalues)
*>
*>    (2)     | A - VS T VS' | / ( n |A| ulp )
*>
*>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
*>      form  (no sorting of eigenvalues).
*>
*>    (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
*>
*>    (4)     0     if WR+sqrt(-1)*WI are eigenvalues of T
*>            1/ulp otherwise
*>            (no sorting of eigenvalues)
*>
*>    (5)     0     if T(with VS) = T(without VS),
*>            1/ulp otherwise
*>            (no sorting of eigenvalues)
*>
*>    (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
*>            1/ulp otherwise
*>            (no sorting of eigenvalues)
*>
*>    (7)     0 if T is in Schur form, 1/ulp otherwise
*>            (with sorting of eigenvalues)
*>
*>    (8)     | A - VS T VS' | / ( n |A| ulp )
*>
*>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
*>      form  (with sorting of eigenvalues).
*>
*>    (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
*>
*>    (10)    0     if WR+sqrt(-1)*WI are eigenvalues of T
*>            1/ulp otherwise
*>            If workspace sufficient, also compare WR, WI with and
*>            without reciprocal condition numbers
*>            (with sorting of eigenvalues)
*>
*>    (11)    0     if T(with VS) = T(without VS),
*>            1/ulp otherwise
*>            If workspace sufficient, also compare T with and without
*>            reciprocal condition numbers
*>            (with sorting of eigenvalues)
*>
*>    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
*>            1/ulp otherwise
*>            If workspace sufficient, also compare VS with and without
*>            reciprocal condition numbers
*>            (with sorting of eigenvalues)
*>
*>    (13)    if sorting worked and SDIM is the number of
*>            eigenvalues which were SELECTed
*>            If workspace sufficient, also compare SDIM with and
*>            without reciprocal condition numbers
*>
*>    (14)    if RCONDE the same no matter if VS and/or RCONDV computed
*>
*>    (15)    if RCONDV the same no matter if VS and/or RCONDE computed
*>
*>    (16)  |RCONDE - RCDEIN| / cond(RCONDE)
*>
*>       RCONDE is the reciprocal average eigenvalue condition number
*>       computed by DGEESX and RCDEIN (the precomputed true value)
*>       is supplied as input.  cond(RCONDE) is the condition number
*>       of RCONDE, and takes errors in computing RCONDE into account,
*>       so that the resulting quantity should be O(ULP). cond(RCONDE)
*>       is essentially given by norm(A)/RCONDV.
*>
*>    (17)  |RCONDV - RCDVIN| / cond(RCONDV)
*>
*>       RCONDV is the reciprocal right invariant subspace condition
*>       number computed by DGEESX and RCDVIN (the precomputed true
*>       value) is supplied as input. cond(RCONDV) is the condition
*>       number of RCONDV, and takes errors in computing RCONDV into
*>       account, so that the resulting quantity should be O(ULP).
*>       cond(RCONDV) is essentially given by norm(A)/RCONDE.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] COMP
*> \verbatim
*>          COMP is LOGICAL
*>          COMP describes which input tests to perform:
*>            = .FALSE. if the computed condition numbers are not to
*>                      be tested against RCDVIN and RCDEIN
*>            = .TRUE.  if they are to be compared
*> \endverbatim
*>
*> \param[in] JTYPE
*> \verbatim
*>          JTYPE is INTEGER
*>          Type of input matrix. Used to label output if error occurs.
*> \endverbatim
*>
*> \param[in] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          If COMP = .FALSE., the random number generator seed
*>          used to produce matrix.
*>          If COMP = .TRUE., ISEED(1) = the number of the example.
*>          Used to label output if error occurs.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*>          THRESH is DOUBLE PRECISION
*>          A test will count as "failed" if the "error", computed as
*>          described above, exceeds THRESH.  Note that the error
*>          is scaled to be O(1), so THRESH should be a reasonably
*>          small multiple of 1, e.g., 10 or 100.  In particular,
*>          it should not depend on the precision (single vs. double)
*>          or the size of the matrix.  It must be at least zero.
*> \endverbatim
*>
*> \param[in] NOUNIT
*> \verbatim
*>          NOUNIT is INTEGER
*>          The FORTRAN unit number for printing out error messages
*>          (e.g., if a routine returns INFO not equal to 0.)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The dimension of A. N must be at least 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA, N)
*>          Used to hold the matrix whose eigenvalues are to be
*>          computed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of A, and H. LDA must be at
*>          least 1 and at least N.
*> \endverbatim
*>
*> \param[out] H
*> \verbatim
*>          H is DOUBLE PRECISION array, dimension (LDA, N)
*>          Another copy of the test matrix A, modified by DGEESX.
*> \endverbatim
*>
*> \param[out] HT
*> \verbatim
*>          HT is DOUBLE PRECISION array, dimension (LDA, N)
*>          Yet another copy of the test matrix A, modified by DGEESX.
*> \endverbatim
*>
*> \param[out] WR
*> \verbatim
*>          WR is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] WI
*> \verbatim
*>          WI is DOUBLE PRECISION array, dimension (N)
*>
*>          The real and imaginary parts of the eigenvalues of A.
*>          On exit, WR + WI*i are the eigenvalues of the matrix in A.
*> \endverbatim
*>
*> \param[out] WRT
*> \verbatim
*>          WRT is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] WIT
*> \verbatim
*>          WIT is DOUBLE PRECISION array, dimension (N)
*>
*>          Like WR, WI, these arrays contain the eigenvalues of A,
*>          but those computed when DGEESX only computes a partial
*>          eigendecomposition, i.e. not Schur vectors
*> \endverbatim
*>
*> \param[out] WRTMP
*> \verbatim
*>          WRTMP is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] WITMP
*> \verbatim
*>          WITMP is DOUBLE PRECISION array, dimension (N)
*>
*>          Like WR, WI, these arrays contain the eigenvalues of A,
*>          but sorted by increasing real part.
*> \endverbatim
*>
*> \param[out] VS
*> \verbatim
*>          VS is DOUBLE PRECISION array, dimension (LDVS, N)
*>          VS holds the computed Schur vectors.
*> \endverbatim
*>
*> \param[in] LDVS
*> \verbatim
*>          LDVS is INTEGER
*>          Leading dimension of VS. Must be at least max(1, N).
*> \endverbatim
*>
*> \param[out] VS1
*> \verbatim
*>          VS1 is DOUBLE PRECISION array, dimension (LDVS, N)
*>          VS1 holds another copy of the computed Schur vectors.
*> \endverbatim
*>
*> \param[in] RCDEIN
*> \verbatim
*>          RCDEIN is DOUBLE PRECISION
*>          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
*>          condition number for the average of selected eigenvalues.
*> \endverbatim
*>
*> \param[in] RCDVIN
*> \verbatim
*>          RCDVIN is DOUBLE PRECISION
*>          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
*>          condition number for the selected right invariant subspace.
*> \endverbatim
*>
*> \param[in] NSLCT
*> \verbatim
*>          NSLCT is INTEGER
*>          When COMP = .TRUE. the number of selected eigenvalues
*>          corresponding to the precomputed values RCDEIN and RCDVIN.
*> \endverbatim
*>
*> \param[in] ISLCT
*> \verbatim
*>          ISLCT is INTEGER array, dimension (NSLCT)
*>          When COMP = .TRUE. ISLCT selects the eigenvalues of the
*>          input matrix corresponding to the precomputed values RCDEIN
*>          and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the
*>          eigenvalue with the J-th largest real part is selected.
*>          Not referenced if COMP = .FALSE.
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*>          RESULT is DOUBLE PRECISION array, dimension (17)
*>          The values computed by the 17 tests described above.
*>          The values are currently limited to 1/ulp, to avoid
*>          overflow.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The number of entries in WORK to be passed to DGEESX. This
*>          must be at least 3*N, and N+N**2 if tests 14--16 are to
*>          be performed.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (N*N)
*> \endverbatim
*>
*> \param[out] BWORK
*> \verbatim
*>          BWORK is LOGICAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          If 0,  successful exit.
*>          If <0, input parameter -INFO had an incorrect value.
*>          If >0, DGEESX returned an error code, the absolute
*>                 value of which is returned.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE DGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
     $                   H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS,
     $                   LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT,
     $                   RESULT, WORK, LWORK, IWORK, BWORK, INFO )
*
*  -- 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            COMP
      INTEGER            INFO, JTYPE, LDA, LDVS, LWORK, N, NOUNIT, NSLCT
      DOUBLE PRECISION   RCDEIN, RCDVIN, THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            BWORK( * )
      INTEGER            ISEED( 4 ), ISLCT( * ), IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), H( LDA, * ), HT( LDA, * ),
     $                   RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
     $                   WI( * ), WIT( * ), WITMP( * ), WORK( * ),
     $                   WR( * ), WRT( * ), WRTMP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      DOUBLE PRECISION   EPSIN
      PARAMETER          ( EPSIN = 5.9605D-8 )
*     ..
*     .. Local Scalars ..
      CHARACTER          SORT
      INTEGER            I, IINFO, ISORT, ITMP, J, KMIN, KNTEIG, LIWORK,
     $                   RSUB, SDIM, SDIM1
      DOUBLE PRECISION   ANORM, EPS, RCNDE1, RCNDV1, RCONDE, RCONDV,
     $                   SMLNUM, TMP, TOL, TOLIN, ULP, ULPINV, V, VIMIN,
     $                   VRMIN, WNORM
*     ..
*     .. Local Arrays ..
      INTEGER            IPNT( 20 )
*     ..
*     .. Arrays in Common ..
      LOGICAL            SELVAL( 20 )
      DOUBLE PRECISION   SELWI( 20 ), SELWR( 20 )
*     ..
*     .. Scalars in Common ..
      INTEGER            SELDIM, SELOPT
*     ..
*     .. Common blocks ..
      COMMON             / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
*     ..
*     .. External Functions ..
      LOGICAL            DSLECT
      DOUBLE PRECISION   DLAMCH, DLANGE
      EXTERNAL           DSLECT, DLAMCH, DLANGE
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DGEESX, DGEMM, DLACPY, DORT01, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX, MIN, SIGN, SQRT
*     ..
*     .. Executable Statements ..
*
*     Check for errors
*
      INFO = 0
      IF( THRESH.LT.ZERO ) THEN
         INFO = -3
      ELSE IF( NOUNIT.LE.0 ) THEN
         INFO = -5
      ELSE IF( N.LT.0 ) THEN
         INFO = -6
      ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN
         INFO = -8
      ELSE IF( LDVS.LT.1 .OR. LDVS.LT.N ) THEN
         INFO = -18
      ELSE IF( LWORK.LT.3*N ) THEN
         INFO = -26
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DGET24', -INFO )
         RETURN
      END IF
*
*     Quick return if nothing to do
*
      DO 10 I = 1, 17
         RESULT( I ) = -ONE
   10 CONTINUE
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Important constants
*
      SMLNUM = DLAMCH( 'Safe minimum' )
      ULP = DLAMCH( 'Precision' )
      ULPINV = ONE / ULP
*
*     Perform tests (1)-(13)
*
      SELOPT = 0
      LIWORK = N*N
      DO 120 ISORT = 0, 1
         IF( ISORT.EQ.0 ) THEN
            SORT = 'N'
            RSUB = 0
         ELSE
            SORT = 'S'
            RSUB = 6
         END IF
*
*        Compute Schur form and Schur vectors, and test them
*
         CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
         CALL DGEESX( 'V', SORT, DSLECT, 'N', N, H, LDA, SDIM, WR, WI,
     $                VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK,
     $                LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 1+RSUB ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX1', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX1', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            RETURN
         END IF
         IF( ISORT.EQ.0 ) THEN
            CALL DCOPY( N, WR, 1, WRTMP, 1 )
            CALL DCOPY( N, WI, 1, WITMP, 1 )
         END IF
*
*        Do Test (1) or Test (7)
*
         RESULT( 1+RSUB ) = ZERO
         DO 30 J = 1, N - 2
            DO 20 I = J + 2, N
               IF( H( I, J ).NE.ZERO )
     $            RESULT( 1+RSUB ) = ULPINV
   20       CONTINUE
   30    CONTINUE
         DO 40 I = 1, N - 2
            IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.ZERO )
     $         RESULT( 1+RSUB ) = ULPINV
   40    CONTINUE
         DO 50 I = 1, N - 1
            IF( H( I+1, I ).NE.ZERO ) THEN
               IF( H( I, I ).NE.H( I+1, I+1 ) .OR. H( I, I+1 ).EQ.
     $             ZERO .OR. SIGN( ONE, H( I+1, I ) ).EQ.
     $             SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB ) = ULPINV
            END IF
   50    CONTINUE
*
*        Test (2) or (8): Compute norm(A - Q*H*Q') / (norm(A) * N * ULP)
*
*        Copy A to VS1, used as workspace
*
         CALL DLACPY( ' ', N, N, A, LDA, VS1, LDVS )
*
*        Compute Q*H and store in HT.
*
         CALL DGEMM( 'No transpose', 'No transpose', N, N, N, ONE, VS,
     $               LDVS, H, LDA, ZERO, HT, LDA )
*
*        Compute A - Q*H*Q'
*
         CALL DGEMM( 'No transpose', 'Transpose', N, N, N, -ONE, HT,
     $               LDA, VS, LDVS, ONE, VS1, LDVS )
*
         ANORM = MAX( DLANGE( '1', N, N, A, LDA, WORK ), SMLNUM )
         WNORM = DLANGE( '1', N, N, VS1, LDVS, WORK )
*
         IF( ANORM.GT.WNORM ) THEN
            RESULT( 2+RSUB ) = ( WNORM / ANORM ) / ( N*ULP )
         ELSE
            IF( ANORM.LT.ONE ) THEN
               RESULT( 2+RSUB ) = ( MIN( WNORM, N*ANORM ) / ANORM ) /
     $                            ( N*ULP )
            ELSE
               RESULT( 2+RSUB ) = MIN( WNORM / ANORM, DBLE( N ) ) /
     $                            ( N*ULP )
            END IF
         END IF
*
*        Test (3) or (9):  Compute norm( I - Q'*Q ) / ( N * ULP )
*
         CALL DORT01( 'Columns', N, N, VS, LDVS, WORK, LWORK,
     $                RESULT( 3+RSUB ) )
*
*        Do Test (4) or Test (10)
*
         RESULT( 4+RSUB ) = ZERO
         DO 60 I = 1, N
            IF( H( I, I ).NE.WR( I ) )
     $         RESULT( 4+RSUB ) = ULPINV
   60    CONTINUE
         IF( N.GT.1 ) THEN
            IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO )
     $         RESULT( 4+RSUB ) = ULPINV
            IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO )
     $         RESULT( 4+RSUB ) = ULPINV
         END IF
         DO 70 I = 1, N - 1
            IF( H( I+1, I ).NE.ZERO ) THEN
               TMP = SQRT( ABS( H( I+1, I ) ) )*
     $               SQRT( ABS( H( I, I+1 ) ) )
               RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
     $                            ABS( WI( I )-TMP ) /
     $                            MAX( ULP*TMP, SMLNUM ) )
               RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
     $                            ABS( WI( I+1 )+TMP ) /
     $                            MAX( ULP*TMP, SMLNUM ) )
            ELSE IF( I.GT.1 ) THEN
               IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.ZERO .AND.
     $             WI( I ).NE.ZERO )RESULT( 4+RSUB ) = ULPINV
            END IF
   70    CONTINUE
*
*        Do Test (5) or Test (11)
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'N', SORT, DSLECT, 'N', N, HT, LDA, SDIM, WRT,
     $                WIT, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK,
     $                LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 5+RSUB ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX2', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX2', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
         RESULT( 5+RSUB ) = ZERO
         DO 90 J = 1, N
            DO 80 I = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 5+RSUB ) = ULPINV
   80       CONTINUE
   90    CONTINUE
*
*        Do Test (6) or Test (12)
*
         RESULT( 6+RSUB ) = ZERO
         DO 100 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 6+RSUB ) = ULPINV
  100    CONTINUE
*
*        Do Test (13)
*
         IF( ISORT.EQ.1 ) THEN
            RESULT( 13 ) = ZERO
            KNTEIG = 0
            DO 110 I = 1, N
               IF( DSLECT( WR( I ), WI( I ) ) .OR.
     $             DSLECT( WR( I ), -WI( I ) ) )KNTEIG = KNTEIG + 1
               IF( I.LT.N ) THEN
                  IF( ( DSLECT( WR( I+1 ), WI( I+1 ) ) .OR.
     $                DSLECT( WR( I+1 ), -WI( I+1 ) ) ) .AND.
     $                ( .NOT.( DSLECT( WR( I ),
     $                WI( I ) ) .OR. DSLECT( WR( I ),
     $                -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )RESULT( 13 )
     $                = ULPINV
               END IF
  110       CONTINUE
            IF( SDIM.NE.KNTEIG )
     $         RESULT( 13 ) = ULPINV
         END IF
*
  120 CONTINUE
*
*     If there is enough workspace, perform tests (14) and (15)
*     as well as (10) through (13)
*
      IF( LWORK.GE.N+( N*N ) / 2 ) THEN
*
*        Compute both RCONDE and RCONDV with VS
*
         SORT = 'S'
         RESULT( 14 ) = ZERO
         RESULT( 15 ) = ZERO
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'V', SORT, DSLECT, 'B', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCONDE, RCONDV, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 14 ) = ULPINV
            RESULT( 15 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX3', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX3', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 140 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 130 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  130       CONTINUE
  140    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
*        Compute both RCONDE and RCONDV without VS, and compare
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'N', SORT, DSLECT, 'B', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 14 ) = ULPINV
            RESULT( 15 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX4', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX4', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform tests (14) and (15)
*
         IF( RCNDE1.NE.RCONDE )
     $      RESULT( 14 ) = ULPINV
         IF( RCNDV1.NE.RCONDV )
     $      RESULT( 15 ) = ULPINV
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 160 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 150 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  150       CONTINUE
  160    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
*        Compute RCONDE with VS, and compare
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'V', SORT, DSLECT, 'E', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 14 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX5', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX5', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform test (14)
*
         IF( RCNDE1.NE.RCONDE )
     $      RESULT( 14 ) = ULPINV
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 180 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 170 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  170       CONTINUE
  180    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
*        Compute RCONDE without VS, and compare
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'N', SORT, DSLECT, 'E', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 14 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX6', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX6', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform test (14)
*
         IF( RCNDE1.NE.RCONDE )
     $      RESULT( 14 ) = ULPINV
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 200 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 190 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  190       CONTINUE
  200    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
*        Compute RCONDV with VS, and compare
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'V', SORT, DSLECT, 'V', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 15 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX7', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX7', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform test (15)
*
         IF( RCNDV1.NE.RCONDV )
     $      RESULT( 15 ) = ULPINV
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 220 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 210 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  210       CONTINUE
  220    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
*        Compute RCONDV without VS, and compare
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'N', SORT, DSLECT, 'V', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 15 ) = ULPINV
            IF( JTYPE.NE.22 ) THEN
               WRITE( NOUNIT, FMT = 9998 )'DGEESX8', IINFO, N, JTYPE,
     $            ISEED
            ELSE
               WRITE( NOUNIT, FMT = 9999 )'DGEESX8', IINFO, N,
     $            ISEED( 1 )
            END IF
            INFO = ABS( IINFO )
            GO TO 250
         END IF
*
*        Perform test (15)
*
         IF( RCNDV1.NE.RCONDV )
     $      RESULT( 15 ) = ULPINV
*
*        Perform tests (10), (11), (12), and (13)
*
         DO 240 I = 1, N
            IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
     $         RESULT( 10 ) = ULPINV
            DO 230 J = 1, N
               IF( H( I, J ).NE.HT( I, J ) )
     $            RESULT( 11 ) = ULPINV
               IF( VS( I, J ).NE.VS1( I, J ) )
     $            RESULT( 12 ) = ULPINV
  230       CONTINUE
  240    CONTINUE
         IF( SDIM.NE.SDIM1 )
     $      RESULT( 13 ) = ULPINV
*
      END IF
*
  250 CONTINUE
*
*     If there are precomputed reciprocal condition numbers, compare
*     computed values with them.
*
      IF( COMP ) THEN
*
*        First set up SELOPT, SELDIM, SELVAL, SELWR, and SELWI so that
*        the logical function DSLECT selects the eigenvalues specified
*        by NSLCT and ISLCT.
*
         SELDIM = N
         SELOPT = 1
         EPS = MAX( ULP, EPSIN )
         DO 260 I = 1, N
            IPNT( I ) = I
            SELVAL( I ) = .FALSE.
            SELWR( I ) = WRTMP( I )
            SELWI( I ) = WITMP( I )
  260    CONTINUE
         DO 280 I = 1, N - 1
            KMIN = I
            VRMIN = WRTMP( I )
            VIMIN = WITMP( I )
            DO 270 J = I + 1, N
               IF( WRTMP( J ).LT.VRMIN ) THEN
                  KMIN = J
                  VRMIN = WRTMP( J )
                  VIMIN = WITMP( J )
               END IF
  270       CONTINUE
            WRTMP( KMIN ) = WRTMP( I )
            WITMP( KMIN ) = WITMP( I )
            WRTMP( I ) = VRMIN
            WITMP( I ) = VIMIN
            ITMP = IPNT( I )
            IPNT( I ) = IPNT( KMIN )
            IPNT( KMIN ) = ITMP
  280    CONTINUE
         DO 290 I = 1, NSLCT
            SELVAL( IPNT( ISLCT( I ) ) ) = .TRUE.
  290    CONTINUE
*
*        Compute condition numbers
*
         CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
         CALL DGEESX( 'N', 'S', DSLECT, 'B', N, HT, LDA, SDIM1, WRT,
     $                WIT, VS1, LDVS, RCONDE, RCONDV, WORK, LWORK,
     $                IWORK, LIWORK, BWORK, IINFO )
         IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
            RESULT( 16 ) = ULPINV
            RESULT( 17 ) = ULPINV
            WRITE( NOUNIT, FMT = 9999 )'DGEESX9', IINFO, N, ISEED( 1 )
            INFO = ABS( IINFO )
            GO TO 300
         END IF
*
*        Compare condition number for average of selected eigenvalues
*        taking its condition number into account
*
         ANORM = DLANGE( '1', N, N, A, LDA, WORK )
         V = MAX( DBLE( N )*EPS*ANORM, SMLNUM )
         IF( ANORM.EQ.ZERO )
     $      V = ONE
         IF( V.GT.RCONDV ) THEN
            TOL = ONE
         ELSE
            TOL = V / RCONDV
         END IF
         IF( V.GT.RCDVIN ) THEN
            TOLIN = ONE
         ELSE
            TOLIN = V / RCDVIN
         END IF
         TOL = MAX( TOL, SMLNUM / EPS )
         TOLIN = MAX( TOLIN, SMLNUM / EPS )
         IF( EPS*( RCDEIN-TOLIN ).GT.RCONDE+TOL ) THEN
            RESULT( 16 ) = ULPINV
         ELSE IF( RCDEIN-TOLIN.GT.RCONDE+TOL ) THEN
            RESULT( 16 ) = ( RCDEIN-TOLIN ) / ( RCONDE+TOL )
         ELSE IF( RCDEIN+TOLIN.LT.EPS*( RCONDE-TOL ) ) THEN
            RESULT( 16 ) = ULPINV
         ELSE IF( RCDEIN+TOLIN.LT.RCONDE-TOL ) THEN
            RESULT( 16 ) = ( RCONDE-TOL ) / ( RCDEIN+TOLIN )
         ELSE
            RESULT( 16 ) = ONE
         END IF
*
*        Compare condition numbers for right invariant subspace
*        taking its condition number into account
*
         IF( V.GT.RCONDV*RCONDE ) THEN
            TOL = RCONDV
         ELSE
            TOL = V / RCONDE
         END IF
         IF( V.GT.RCDVIN*RCDEIN ) THEN
            TOLIN = RCDVIN
         ELSE
            TOLIN = V / RCDEIN
         END IF
         TOL = MAX( TOL, SMLNUM / EPS )
         TOLIN = MAX( TOLIN, SMLNUM / EPS )
         IF( EPS*( RCDVIN-TOLIN ).GT.RCONDV+TOL ) THEN
            RESULT( 17 ) = ULPINV
         ELSE IF( RCDVIN-TOLIN.GT.RCONDV+TOL ) THEN
            RESULT( 17 ) = ( RCDVIN-TOLIN ) / ( RCONDV+TOL )
         ELSE IF( RCDVIN+TOLIN.LT.EPS*( RCONDV-TOL ) ) THEN
            RESULT( 17 ) = ULPINV
         ELSE IF( RCDVIN+TOLIN.LT.RCONDV-TOL ) THEN
            RESULT( 17 ) = ( RCONDV-TOL ) / ( RCDVIN+TOLIN )
         ELSE
            RESULT( 17 ) = ONE
         END IF
*
  300    CONTINUE
*
      END IF
*
 9999 FORMAT( ' DGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
     $      I6, ', INPUT EXAMPLE NUMBER = ', I4 )
 9998 FORMAT( ' DGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
     $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
      RETURN
*
*     End of DGET24
*
      END