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*> \brief \b DGET23
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
* A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR,
* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
* WORK, LWORK, IWORK, INFO )
*
* .. Scalar Arguments ..
* LOGICAL COMP
* CHARACTER BALANC
* INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N,
* $ NOUNIT
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 ), IWORK( * )
* DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
* $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
* $ RESULT( 11 ), SCALE( * ), SCALE1( * ),
* $ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
* $ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX.
*> If COMP = .FALSE., the first 8 of the following tests will be
*> performed on the input matrix A, and also test 9 if LWORK is
*> sufficiently large.
*> if COMP is .TRUE. all 11 tests will be performed.
*>
*> (1) | A * VR - VR * W | / ( n |A| ulp )
*>
*> Here VR is the matrix of unit right eigenvectors.
*> W is a block diagonal matrix, with a 1x1 block for each
*> real eigenvalue and a 2x2 block for each complex conjugate
*> pair. If eigenvalues j and j+1 are a complex conjugate pair,
*> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
*> 2 x 2 block corresponding to the pair will be:
*>
*> ( wr wi )
*> ( -wi wr )
*>
*> Such a block multiplying an n x 2 matrix ( ur ui ) on the
*> right will be the same as multiplying ur + i*ui by wr + i*wi.
*>
*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
*>
*> Here VL is the matrix of unit left eigenvectors, A**H is the
*> conjugate transpose of A, and W is as above.
*>
*> (3) | |VR(i)| - 1 | / ulp and largest component real
*>
*> VR(i) denotes the i-th column of VR.
*>
*> (4) | |VL(i)| - 1 | / ulp and largest component real
*>
*> VL(i) denotes the i-th column of VL.
*>
*> (5) 0 if W(full) = W(partial), 1/ulp otherwise
*>
*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
*> and RCONDE are also computed, and W(partial) denotes the
*> eigenvalues computed when only some of VR, VL, RCONDV, and
*> RCONDE are computed.
*>
*> (6) 0 if VR(full) = VR(partial), 1/ulp otherwise
*>
*> VR(full) denotes the right eigenvectors computed when VL, RCONDV
*> and RCONDE are computed, and VR(partial) denotes the result
*> when only some of VL and RCONDV are computed.
*>
*> (7) 0 if VL(full) = VL(partial), 1/ulp otherwise
*>
*> VL(full) denotes the left eigenvectors computed when VR, RCONDV
*> and RCONDE are computed, and VL(partial) denotes the result
*> when only some of VR and RCONDV are computed.
*>
*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
*> SCALE, ILO, IHI, ABNRM (partial)
*> 1/ulp otherwise
*>
*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
*> (partial) is when some are not computed.
*>
*> (9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise
*>
*> RCONDV(full) denotes the reciprocal condition numbers of the
*> right eigenvectors computed when VR, VL and RCONDE are also
*> computed. RCONDV(partial) denotes the reciprocal condition
*> numbers when only some of VR, VL and RCONDE are computed.
*>
*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
*>
*> RCONDV is the reciprocal right eigenvector condition number
*> computed by DGEEVX 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.
*>
*> (11) |RCONDE - RCDEIN| / cond(RCONDE)
*>
*> RCONDE is the reciprocal eigenvalue condition number
*> computed by DGEEVX 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.
*> \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] BALANC
*> \verbatim
*> BALANC is CHARACTER
*> Describes the balancing option to be tested.
*> = 'N' for no permuting or diagonal scaling
*> = 'P' for permuting but no diagonal scaling
*> = 'S' for no permuting but diagonal scaling
*> = 'B' for permuting and diagonal scaling
*> \endverbatim
*>
*> \param[in] JTYPE
*> \verbatim
*> JTYPE is INTEGER
*> Type of input matrix. 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] 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] 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 DGEEVX.
*> \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] WR1
*> \verbatim
*> WR1 is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] WI1
*> \verbatim
*> WI1 is DOUBLE PRECISION array, dimension (N)
*>
*> Like WR, WI, these arrays contain the eigenvalues of A,
*> but those computed when DGEEVX only computes a partial
*> eigendecomposition, i.e. not the eigenvalues and left
*> and right eigenvectors.
*> \endverbatim
*>
*> \param[out] VL
*> \verbatim
*> VL is DOUBLE PRECISION array, dimension (LDVL,N)
*> VL holds the computed left eigenvectors.
*> \endverbatim
*>
*> \param[in] LDVL
*> \verbatim
*> LDVL is INTEGER
*> Leading dimension of VL. Must be at least max(1,N).
*> \endverbatim
*>
*> \param[out] VR
*> \verbatim
*> VR is DOUBLE PRECISION array, dimension (LDVR,N)
*> VR holds the computed right eigenvectors.
*> \endverbatim
*>
*> \param[in] LDVR
*> \verbatim
*> LDVR is INTEGER
*> Leading dimension of VR. Must be at least max(1,N).
*> \endverbatim
*>
*> \param[out] LRE
*> \verbatim
*> LRE is DOUBLE PRECISION array, dimension (LDLRE,N)
*> LRE holds the computed right or left eigenvectors.
*> \endverbatim
*>
*> \param[in] LDLRE
*> \verbatim
*> LDLRE is INTEGER
*> Leading dimension of LRE. Must be at least max(1,N).
*> \endverbatim
*>
*> \param[out] RCONDV
*> \verbatim
*> RCONDV is DOUBLE PRECISION array, dimension (N)
*> RCONDV holds the computed reciprocal condition numbers
*> for eigenvectors.
*> \endverbatim
*>
*> \param[out] RCNDV1
*> \verbatim
*> RCNDV1 is DOUBLE PRECISION array, dimension (N)
*> RCNDV1 holds more computed reciprocal condition numbers
*> for eigenvectors.
*> \endverbatim
*>
*> \param[in] RCDVIN
*> \verbatim
*> RCDVIN is DOUBLE PRECISION array, dimension (N)
*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
*> condition numbers for eigenvectors to be compared with
*> RCONDV.
*> \endverbatim
*>
*> \param[out] RCONDE
*> \verbatim
*> RCONDE is DOUBLE PRECISION array, dimension (N)
*> RCONDE holds the computed reciprocal condition numbers
*> for eigenvalues.
*> \endverbatim
*>
*> \param[out] RCNDE1
*> \verbatim
*> RCNDE1 is DOUBLE PRECISION array, dimension (N)
*> RCNDE1 holds more computed reciprocal condition numbers
*> for eigenvalues.
*> \endverbatim
*>
*> \param[in] RCDEIN
*> \verbatim
*> RCDEIN is DOUBLE PRECISION array, dimension (N)
*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
*> condition numbers for eigenvalues to be compared with
*> RCONDE.
*> \endverbatim
*>
*> \param[out] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION array, dimension (N)
*> Holds information describing balancing of matrix.
*> \endverbatim
*>
*> \param[out] SCALE1
*> \verbatim
*> SCALE1 is DOUBLE PRECISION array, dimension (N)
*> Holds information describing balancing of matrix.
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (11)
*> The values computed by the 11 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. This must be at least
*> 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> If 0, successful exit.
*> If <0, input parameter -INFO had an incorrect value.
*> If >0, DGEEVX 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 DGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N,
$ A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR,
$ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
$ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
$ WORK, LWORK, IWORK, 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
CHARACTER BALANC
INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N,
$ NOUNIT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 ), IWORK( * )
DOUBLE PRECISION A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
$ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
$ RESULT( 11 ), SCALE( * ), SCALE1( * ),
$ VL( LDVL, * ), VR( LDVR, * ), WI( * ),
$ WI1( * ), WORK( * ), WR( * ), WR1( * )
* ..
*
* =====================================================================
*
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
DOUBLE PRECISION EPSIN
PARAMETER ( EPSIN = 5.9605D-8 )
* ..
* .. Local Scalars ..
LOGICAL BALOK, NOBAL
CHARACTER SENSE
INTEGER I, IHI, IHI1, IINFO, ILO, ILO1, ISENS, ISENSM,
$ J, JJ, KMIN
DOUBLE PRECISION ABNRM, ABNRM1, EPS, SMLNUM, TNRM, TOL, TOLIN,
$ ULP, ULPINV, V, VIMIN, VMAX, VMX, VRMIN, VRMX,
$ VTST
* ..
* .. Local Arrays ..
CHARACTER SENS( 2 )
DOUBLE PRECISION DUM( 1 ), RES( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
EXTERNAL LSAME, DLAMCH, DLAPY2, DNRM2
* ..
* .. External Subroutines ..
EXTERNAL DGEEVX, DGET22, DLACPY, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN
* ..
* .. Data statements ..
DATA SENS / 'N', 'V' /
* ..
* .. Executable Statements ..
*
* Check for errors
*
NOBAL = LSAME( BALANC, 'N' )
BALOK = NOBAL .OR. LSAME( BALANC, 'P' ) .OR.
$ LSAME( BALANC, 'S' ) .OR. LSAME( BALANC, 'B' )
INFO = 0
IF( .NOT.BALOK ) THEN
INFO = -2
ELSE IF( THRESH.LT.ZERO ) THEN
INFO = -4
ELSE IF( NOUNIT.LE.0 ) THEN
INFO = -6
ELSE IF( N.LT.0 ) THEN
INFO = -7
ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN
INFO = -9
ELSE IF( LDVL.LT.1 .OR. LDVL.LT.N ) THEN
INFO = -16
ELSE IF( LDVR.LT.1 .OR. LDVR.LT.N ) THEN
INFO = -18
ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.N ) THEN
INFO = -20
ELSE IF( LWORK.LT.3*N .OR. ( COMP .AND. LWORK.LT.6*N+N*N ) ) THEN
INFO = -31
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGET23', -INFO )
RETURN
END IF
*
* Quick return if nothing to do
*
DO 10 I = 1, 11
RESULT( I ) = -ONE
10 CONTINUE
*
IF( N.EQ.0 )
$ RETURN
*
* More Important constants
*
ULP = DLAMCH( 'Precision' )
SMLNUM = DLAMCH( 'S' )
ULPINV = ONE / ULP
*
* Compute eigenvalues and eigenvectors, and test them
*
IF( LWORK.GE.6*N+N*N ) THEN
SENSE = 'B'
ISENSM = 2
ELSE
SENSE = 'E'
ISENSM = 1
END IF
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
CALL DGEEVX( BALANC, 'V', 'V', SENSE, N, H, LDA, WR, WI, VL, LDVL,
$ VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV,
$ WORK, LWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
IF( JTYPE.NE.22 ) THEN
WRITE( NOUNIT, FMT = 9998 )'DGEEVX1', IINFO, N, JTYPE,
$ BALANC, ISEED
ELSE
WRITE( NOUNIT, FMT = 9999 )'DGEEVX1', IINFO, N, ISEED( 1 )
END IF
INFO = ABS( IINFO )
RETURN
END IF
*
* Do Test (1)
*
CALL DGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, WR, WI, WORK,
$ RES )
RESULT( 1 ) = RES( 1 )
*
* Do Test (2)
*
CALL DGET22( 'T', 'N', 'T', N, A, LDA, VL, LDVL, WR, WI, WORK,
$ RES )
RESULT( 2 ) = RES( 1 )
*
* Do Test (3)
*
DO 30 J = 1, N
TNRM = ONE
IF( WI( J ).EQ.ZERO ) THEN
TNRM = DNRM2( N, VR( 1, J ), 1 )
ELSE IF( WI( J ).GT.ZERO ) THEN
TNRM = DLAPY2( DNRM2( N, VR( 1, J ), 1 ),
$ DNRM2( N, VR( 1, J+1 ), 1 ) )
END IF
RESULT( 3 ) = MAX( RESULT( 3 ),
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
IF( WI( J ).GT.ZERO ) THEN
VMX = ZERO
VRMX = ZERO
DO 20 JJ = 1, N
VTST = DLAPY2( VR( JJ, J ), VR( JJ, J+1 ) )
IF( VTST.GT.VMX )
$ VMX = VTST
IF( VR( JJ, J+1 ).EQ.ZERO .AND. ABS( VR( JJ, J ) ).GT.
$ VRMX )VRMX = ABS( VR( JJ, J ) )
20 CONTINUE
IF( VRMX / VMX.LT.ONE-TWO*ULP )
$ RESULT( 3 ) = ULPINV
END IF
30 CONTINUE
*
* Do Test (4)
*
DO 50 J = 1, N
TNRM = ONE
IF( WI( J ).EQ.ZERO ) THEN
TNRM = DNRM2( N, VL( 1, J ), 1 )
ELSE IF( WI( J ).GT.ZERO ) THEN
TNRM = DLAPY2( DNRM2( N, VL( 1, J ), 1 ),
$ DNRM2( N, VL( 1, J+1 ), 1 ) )
END IF
RESULT( 4 ) = MAX( RESULT( 4 ),
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
IF( WI( J ).GT.ZERO ) THEN
VMX = ZERO
VRMX = ZERO
DO 40 JJ = 1, N
VTST = DLAPY2( VL( JJ, J ), VL( JJ, J+1 ) )
IF( VTST.GT.VMX )
$ VMX = VTST
IF( VL( JJ, J+1 ).EQ.ZERO .AND. ABS( VL( JJ, J ) ).GT.
$ VRMX )VRMX = ABS( VL( JJ, J ) )
40 CONTINUE
IF( VRMX / VMX.LT.ONE-TWO*ULP )
$ RESULT( 4 ) = ULPINV
END IF
50 CONTINUE
*
* Test for all options of computing condition numbers
*
DO 200 ISENS = 1, ISENSM
*
SENSE = SENS( ISENS )
*
* Compute eigenvalues only, and test them
*
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
CALL DGEEVX( BALANC, 'N', 'N', SENSE, N, H, LDA, WR1, WI1, DUM,
$ 1, DUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1,
$ RCNDV1, WORK, LWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
IF( JTYPE.NE.22 ) THEN
WRITE( NOUNIT, FMT = 9998 )'DGEEVX2', IINFO, N, JTYPE,
$ BALANC, ISEED
ELSE
WRITE( NOUNIT, FMT = 9999 )'DGEEVX2', IINFO, N,
$ ISEED( 1 )
END IF
INFO = ABS( IINFO )
GO TO 190
END IF
*
* Do Test (5)
*
DO 60 J = 1, N
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
$ RESULT( 5 ) = ULPINV
60 CONTINUE
*
* Do Test (8)
*
IF( .NOT.NOBAL ) THEN
DO 70 J = 1, N
IF( SCALE( J ).NE.SCALE1( J ) )
$ RESULT( 8 ) = ULPINV
70 CONTINUE
IF( ILO.NE.ILO1 )
$ RESULT( 8 ) = ULPINV
IF( IHI.NE.IHI1 )
$ RESULT( 8 ) = ULPINV
IF( ABNRM.NE.ABNRM1 )
$ RESULT( 8 ) = ULPINV
END IF
*
* Do Test (9)
*
IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN
DO 80 J = 1, N
IF( RCONDV( J ).NE.RCNDV1( J ) )
$ RESULT( 9 ) = ULPINV
80 CONTINUE
END IF
*
* Compute eigenvalues and right eigenvectors, and test them
*
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
CALL DGEEVX( BALANC, 'N', 'V', SENSE, N, H, LDA, WR1, WI1, DUM,
$ 1, LRE, LDLRE, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1,
$ RCNDV1, WORK, LWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
IF( JTYPE.NE.22 ) THEN
WRITE( NOUNIT, FMT = 9998 )'DGEEVX3', IINFO, N, JTYPE,
$ BALANC, ISEED
ELSE
WRITE( NOUNIT, FMT = 9999 )'DGEEVX3', IINFO, N,
$ ISEED( 1 )
END IF
INFO = ABS( IINFO )
GO TO 190
END IF
*
* Do Test (5) again
*
DO 90 J = 1, N
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
$ RESULT( 5 ) = ULPINV
90 CONTINUE
*
* Do Test (6)
*
DO 110 J = 1, N
DO 100 JJ = 1, N
IF( VR( J, JJ ).NE.LRE( J, JJ ) )
$ RESULT( 6 ) = ULPINV
100 CONTINUE
110 CONTINUE
*
* Do Test (8) again
*
IF( .NOT.NOBAL ) THEN
DO 120 J = 1, N
IF( SCALE( J ).NE.SCALE1( J ) )
$ RESULT( 8 ) = ULPINV
120 CONTINUE
IF( ILO.NE.ILO1 )
$ RESULT( 8 ) = ULPINV
IF( IHI.NE.IHI1 )
$ RESULT( 8 ) = ULPINV
IF( ABNRM.NE.ABNRM1 )
$ RESULT( 8 ) = ULPINV
END IF
*
* Do Test (9) again
*
IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN
DO 130 J = 1, N
IF( RCONDV( J ).NE.RCNDV1( J ) )
$ RESULT( 9 ) = ULPINV
130 CONTINUE
END IF
*
* Compute eigenvalues and left eigenvectors, and test them
*
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
CALL DGEEVX( BALANC, 'V', 'N', SENSE, N, H, LDA, WR1, WI1, LRE,
$ LDLRE, DUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1,
$ RCNDV1, WORK, LWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
IF( JTYPE.NE.22 ) THEN
WRITE( NOUNIT, FMT = 9998 )'DGEEVX4', IINFO, N, JTYPE,
$ BALANC, ISEED
ELSE
WRITE( NOUNIT, FMT = 9999 )'DGEEVX4', IINFO, N,
$ ISEED( 1 )
END IF
INFO = ABS( IINFO )
GO TO 190
END IF
*
* Do Test (5) again
*
DO 140 J = 1, N
IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
$ RESULT( 5 ) = ULPINV
140 CONTINUE
*
* Do Test (7)
*
DO 160 J = 1, N
DO 150 JJ = 1, N
IF( VL( J, JJ ).NE.LRE( J, JJ ) )
$ RESULT( 7 ) = ULPINV
150 CONTINUE
160 CONTINUE
*
* Do Test (8) again
*
IF( .NOT.NOBAL ) THEN
DO 170 J = 1, N
IF( SCALE( J ).NE.SCALE1( J ) )
$ RESULT( 8 ) = ULPINV
170 CONTINUE
IF( ILO.NE.ILO1 )
$ RESULT( 8 ) = ULPINV
IF( IHI.NE.IHI1 )
$ RESULT( 8 ) = ULPINV
IF( ABNRM.NE.ABNRM1 )
$ RESULT( 8 ) = ULPINV
END IF
*
* Do Test (9) again
*
IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN
DO 180 J = 1, N
IF( RCONDV( J ).NE.RCNDV1( J ) )
$ RESULT( 9 ) = ULPINV
180 CONTINUE
END IF
*
190 CONTINUE
*
200 CONTINUE
*
* If COMP, compare condition numbers to precomputed ones
*
IF( COMP ) THEN
CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
CALL DGEEVX( 'N', 'V', 'V', 'B', N, H, LDA, WR, WI, VL, LDVL,
$ VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV,
$ WORK, LWORK, IWORK, IINFO )
IF( IINFO.NE.0 ) THEN
RESULT( 1 ) = ULPINV
WRITE( NOUNIT, FMT = 9999 )'DGEEVX5', IINFO, N, ISEED( 1 )
INFO = ABS( IINFO )
GO TO 250
END IF
*
* Sort eigenvalues and condition numbers lexicographically
* to compare with inputs
*
DO 220 I = 1, N - 1
KMIN = I
VRMIN = WR( I )
VIMIN = WI( I )
DO 210 J = I + 1, N
IF( WR( J ).LT.VRMIN ) THEN
KMIN = J
VRMIN = WR( J )
VIMIN = WI( J )
END IF
210 CONTINUE
WR( KMIN ) = WR( I )
WI( KMIN ) = WI( I )
WR( I ) = VRMIN
WI( I ) = VIMIN
VRMIN = RCONDE( KMIN )
RCONDE( KMIN ) = RCONDE( I )
RCONDE( I ) = VRMIN
VRMIN = RCONDV( KMIN )
RCONDV( KMIN ) = RCONDV( I )
RCONDV( I ) = VRMIN
220 CONTINUE
*
* Compare condition numbers for eigenvectors
* taking their condition numbers into account
*
RESULT( 10 ) = ZERO
EPS = MAX( EPSIN, ULP )
V = MAX( DBLE( N )*EPS*ABNRM, SMLNUM )
IF( ABNRM.EQ.ZERO )
$ V = ONE
DO 230 I = 1, N
IF( V.GT.RCONDV( I )*RCONDE( I ) ) THEN
TOL = RCONDV( I )
ELSE
TOL = V / RCONDE( I )
END IF
IF( V.GT.RCDVIN( I )*RCDEIN( I ) ) THEN
TOLIN = RCDVIN( I )
ELSE
TOLIN = V / RCDEIN( I )
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( RCDVIN( I )-TOLIN ).GT.RCONDV( I )+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( RCDVIN( I )-TOLIN.GT.RCONDV( I )+TOL ) THEN
VMAX = ( RCDVIN( I )-TOLIN ) / ( RCONDV( I )+TOL )
ELSE IF( RCDVIN( I )+TOLIN.LT.EPS*( RCONDV( I )-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( RCDVIN( I )+TOLIN.LT.RCONDV( I )-TOL ) THEN
VMAX = ( RCONDV( I )-TOL ) / ( RCDVIN( I )+TOLIN )
ELSE
VMAX = ONE
END IF
RESULT( 10 ) = MAX( RESULT( 10 ), VMAX )
230 CONTINUE
*
* Compare condition numbers for eigenvalues
* taking their condition numbers into account
*
RESULT( 11 ) = ZERO
DO 240 I = 1, N
IF( V.GT.RCONDV( I ) ) THEN
TOL = ONE
ELSE
TOL = V / RCONDV( I )
END IF
IF( V.GT.RCDVIN( I ) ) THEN
TOLIN = ONE
ELSE
TOLIN = V / RCDVIN( I )
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( RCDEIN( I )-TOLIN ).GT.RCONDE( I )+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( RCDEIN( I )-TOLIN.GT.RCONDE( I )+TOL ) THEN
VMAX = ( RCDEIN( I )-TOLIN ) / ( RCONDE( I )+TOL )
ELSE IF( RCDEIN( I )+TOLIN.LT.EPS*( RCONDE( I )-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( RCDEIN( I )+TOLIN.LT.RCONDE( I )-TOL ) THEN
VMAX = ( RCONDE( I )-TOL ) / ( RCDEIN( I )+TOLIN )
ELSE
VMAX = ONE
END IF
RESULT( 11 ) = MAX( RESULT( 11 ), VMAX )
240 CONTINUE
250 CONTINUE
*
END IF
*
9999 FORMAT( ' DGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', INPUT EXAMPLE NUMBER = ', I4 )
9998 FORMAT( ' DGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', BALANC = ', A, ', ISEED=(',
$ 3( I5, ',' ), I5, ')' )
*
RETURN
*
* End of DGET23
*
END
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