862 lines
27 KiB
Fortran
862 lines
27 KiB
Fortran
*> \brief \b ZGET23
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
|
|
* NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
|
|
* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
|
|
* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
|
|
* WORK, LWORK, RWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* LOGICAL COMP
|
|
* CHARACTER BALANC
|
|
* INTEGER INFO, ISRT, JTYPE, LDA, LDLRE, LDVL, LDVR,
|
|
* $ LWORK, N, NOUNIT
|
|
* DOUBLE PRECISION THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER ISEED( 4 )
|
|
* DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
|
|
* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
|
|
* $ RESULT( 11 ), RWORK( * ), SCALE( * ),
|
|
* $ SCALE1( * )
|
|
* COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
|
|
* $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
|
|
* $ WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX.
|
|
*> 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 diagonal matrix with diagonal entries W(j).
|
|
*>
|
|
*> (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 ZGEEVX 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 ZGEEVX 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] ISRT
|
|
*> \verbatim
|
|
*> ISRT is INTEGER
|
|
*> If COMP = .TRUE., ISRT indicates in how the eigenvalues
|
|
*> corresponding to values in RCDVIN and RCDEIN are ordered:
|
|
*> = 0 means the eigenvalues are sorted by
|
|
*> increasing real part
|
|
*> = 1 means the eigenvalues are sorted by
|
|
*> increasing imaginary part
|
|
*> If COMP = .FALSE., ISRT is not referenced.
|
|
*> \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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDA,N)
|
|
*> Another copy of the test matrix A, modified by ZGEEVX.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] W
|
|
*> \verbatim
|
|
*> W is COMPLEX*16 array, dimension (N)
|
|
*> Contains the eigenvalues of A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] W1
|
|
*> \verbatim
|
|
*> W1 is COMPLEX*16 array, dimension (N)
|
|
*> Like W, this array contains the eigenvalues of A,
|
|
*> but those computed when ZGEEVX only computes a partial
|
|
*> eigendecomposition, i.e. not the eigenvalues and left
|
|
*> and right eigenvectors.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] VL
|
|
*> \verbatim
|
|
*> VL is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LWORK)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The number of entries in WORK. This must be at least
|
|
*> 2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RWORK
|
|
*> \verbatim
|
|
*> RWORK is DOUBLE PRECISION 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, ZGEEVX 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.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup complex16_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
|
|
$ NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
|
|
$ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
|
|
$ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
|
|
$ WORK, LWORK, RWORK, INFO )
|
|
*
|
|
* -- LAPACK test routine (version 3.4.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* November 2011
|
|
*
|
|
* .. Scalar Arguments ..
|
|
LOGICAL COMP
|
|
CHARACTER BALANC
|
|
INTEGER INFO, ISRT, JTYPE, LDA, LDLRE, LDVL, LDVR,
|
|
$ LWORK, N, NOUNIT
|
|
DOUBLE PRECISION THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER ISEED( 4 )
|
|
DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
|
|
$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
|
|
$ RESULT( 11 ), RWORK( * ), SCALE( * ),
|
|
$ SCALE1( * )
|
|
COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
|
|
$ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
|
|
$ WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. 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, VMAX, VMX, VRICMP, VRIMIN,
|
|
$ VRMX, VTST
|
|
COMPLEX*16 CTMP
|
|
* ..
|
|
* .. Local Arrays ..
|
|
CHARACTER SENS( 2 )
|
|
DOUBLE PRECISION RES( 2 )
|
|
COMPLEX*16 CDUM( 1 )
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
DOUBLE PRECISION DLAMCH, DZNRM2
|
|
EXTERNAL LSAME, DLAMCH, DZNRM2
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA, ZGEEVX, ZGET22, ZLACPY
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DBLE, DIMAG, 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( ISRT.NE.0 .AND. ISRT.NE.1 ) THEN
|
|
INFO = -2
|
|
ELSE IF( .NOT.BALOK ) THEN
|
|
INFO = -3
|
|
ELSE IF( THRESH.LT.ZERO ) THEN
|
|
INFO = -5
|
|
ELSE IF( NOUNIT.LE.0 ) THEN
|
|
INFO = -7
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -8
|
|
ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN
|
|
INFO = -10
|
|
ELSE IF( LDVL.LT.1 .OR. LDVL.LT.N ) THEN
|
|
INFO = -15
|
|
ELSE IF( LDVR.LT.1 .OR. LDVR.LT.N ) THEN
|
|
INFO = -17
|
|
ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.N ) THEN
|
|
INFO = -19
|
|
ELSE IF( LWORK.LT.2*N .OR. ( COMP .AND. LWORK.LT.2*N+N*N ) ) THEN
|
|
INFO = -30
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'ZGET23', -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.2*N+N*N ) THEN
|
|
SENSE = 'B'
|
|
ISENSM = 2
|
|
ELSE
|
|
SENSE = 'E'
|
|
ISENSM = 1
|
|
END IF
|
|
CALL ZLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL ZGEEVX( BALANC, 'V', 'V', SENSE, N, H, LDA, W, VL, LDVL, VR,
|
|
$ LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK,
|
|
$ LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEEVX1', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEEVX1', IINFO, N, ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do Test (1)
|
|
*
|
|
CALL ZGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, W, WORK, RWORK,
|
|
$ RES )
|
|
RESULT( 1 ) = RES( 1 )
|
|
*
|
|
* Do Test (2)
|
|
*
|
|
CALL ZGET22( 'C', 'N', 'C', N, A, LDA, VL, LDVL, W, WORK, RWORK,
|
|
$ RES )
|
|
RESULT( 2 ) = RES( 1 )
|
|
*
|
|
* Do Test (3)
|
|
*
|
|
DO 30 J = 1, N
|
|
TNRM = DZNRM2( N, VR( 1, J ), 1 )
|
|
RESULT( 3 ) = MAX( RESULT( 3 ),
|
|
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
|
|
VMX = ZERO
|
|
VRMX = ZERO
|
|
DO 20 JJ = 1, N
|
|
VTST = ABS( VR( JJ, J ) )
|
|
IF( VTST.GT.VMX )
|
|
$ VMX = VTST
|
|
IF( DIMAG( VR( JJ, J ) ).EQ.ZERO .AND.
|
|
$ ABS( DBLE( VR( JJ, J ) ) ).GT.VRMX )
|
|
$ VRMX = ABS( DBLE( VR( JJ, J ) ) )
|
|
20 CONTINUE
|
|
IF( VRMX / VMX.LT.ONE-TWO*ULP )
|
|
$ RESULT( 3 ) = ULPINV
|
|
30 CONTINUE
|
|
*
|
|
* Do Test (4)
|
|
*
|
|
DO 50 J = 1, N
|
|
TNRM = DZNRM2( N, VL( 1, J ), 1 )
|
|
RESULT( 4 ) = MAX( RESULT( 4 ),
|
|
$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
|
|
VMX = ZERO
|
|
VRMX = ZERO
|
|
DO 40 JJ = 1, N
|
|
VTST = ABS( VL( JJ, J ) )
|
|
IF( VTST.GT.VMX )
|
|
$ VMX = VTST
|
|
IF( DIMAG( VL( JJ, J ) ).EQ.ZERO .AND.
|
|
$ ABS( DBLE( VL( JJ, J ) ) ).GT.VRMX )
|
|
$ VRMX = ABS( DBLE( VL( JJ, J ) ) )
|
|
40 CONTINUE
|
|
IF( VRMX / VMX.LT.ONE-TWO*ULP )
|
|
$ RESULT( 4 ) = ULPINV
|
|
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 ZLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL ZGEEVX( BALANC, 'N', 'N', SENSE, N, H, LDA, W1, CDUM, 1,
|
|
$ CDUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1,
|
|
$ RCNDV1, WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEEVX2', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEEVX2', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 190
|
|
END IF
|
|
*
|
|
* Do Test (5)
|
|
*
|
|
DO 60 J = 1, N
|
|
IF( W( J ).NE.W1( 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 ZLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL ZGEEVX( BALANC, 'N', 'V', SENSE, N, H, LDA, W1, CDUM, 1,
|
|
$ LRE, LDLRE, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1,
|
|
$ RCNDV1, WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEEVX3', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEEVX3', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 190
|
|
END IF
|
|
*
|
|
* Do Test (5) again
|
|
*
|
|
DO 90 J = 1, N
|
|
IF( W( J ).NE.W1( 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 ZLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL ZGEEVX( BALANC, 'V', 'N', SENSE, N, H, LDA, W1, LRE,
|
|
$ LDLRE, CDUM, 1, ILO1, IHI1, SCALE1, ABNRM1,
|
|
$ RCNDE1, RCNDV1, WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEEVX4', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEEVX4', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 190
|
|
END IF
|
|
*
|
|
* Do Test (5) again
|
|
*
|
|
DO 140 J = 1, N
|
|
IF( W( J ).NE.W1( 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 ZLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL ZGEEVX( 'N', 'V', 'V', 'B', N, H, LDA, W, VL, LDVL, VR,
|
|
$ LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV,
|
|
$ WORK, LWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 1 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEEVX5', 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
|
|
IF( ISRT.EQ.0 ) THEN
|
|
VRIMIN = DBLE( W( I ) )
|
|
ELSE
|
|
VRIMIN = DIMAG( W( I ) )
|
|
END IF
|
|
DO 210 J = I + 1, N
|
|
IF( ISRT.EQ.0 ) THEN
|
|
VRICMP = DBLE( W( J ) )
|
|
ELSE
|
|
VRICMP = DIMAG( W( J ) )
|
|
END IF
|
|
IF( VRICMP.LT.VRIMIN ) THEN
|
|
KMIN = J
|
|
VRIMIN = VRICMP
|
|
END IF
|
|
210 CONTINUE
|
|
CTMP = W( KMIN )
|
|
W( KMIN ) = W( I )
|
|
W( I ) = CTMP
|
|
VRIMIN = RCONDE( KMIN )
|
|
RCONDE( KMIN ) = RCONDE( I )
|
|
RCONDE( I ) = VRIMIN
|
|
VRIMIN = RCONDV( KMIN )
|
|
RCONDV( KMIN ) = RCONDV( I )
|
|
RCONDV( I ) = VRIMIN
|
|
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( ' ZGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', INPUT EXAMPLE NUMBER = ', I4 )
|
|
9998 FORMAT( ' ZGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', BALANC = ', A, ', ISEED=(',
|
|
$ 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZGET23
|
|
*
|
|
END
|