*> \brief ZGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZGGEVX + dependencies
*>
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*>
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*>
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
* ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
* LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV,
* WORK, LWORK, RWORK, IWORK, BWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER BALANC, JOBVL, JOBVR, SENSE
* INTEGER IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
* DOUBLE PRECISION ABNRM, BBNRM
* ..
* .. Array Arguments ..
* LOGICAL BWORK( * )
* INTEGER IWORK( * )
* DOUBLE PRECISION LSCALE( * ), RCONDE( * ), RCONDV( * ),
* $ RSCALE( * ), RWORK( * )
* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
* $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
* $ WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
*> (A,B) the generalized eigenvalues, and optionally, the left and/or
*> right generalized eigenvectors.
*>
*> Optionally, it also computes a balancing transformation to improve
*> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
*> LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
*> the eigenvalues (RCONDE), and reciprocal condition numbers for the
*> right eigenvectors (RCONDV).
*>
*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar
*> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
*> singular. It is usually represented as the pair (alpha,beta), as
*> there is a reasonable interpretation for beta=0, and even for both
*> being zero.
*>
*> The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
*> of (A,B) satisfies
*> A * v(j) = lambda(j) * B * v(j) .
*> The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
*> of (A,B) satisfies
*> u(j)**H * A = lambda(j) * u(j)**H * B.
*> where u(j)**H is the conjugate-transpose of u(j).
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] BALANC
*> \verbatim
*> BALANC is CHARACTER*1
*> Specifies the balance option to be performed:
*> = 'N': do not diagonally scale or permute;
*> = 'P': permute only;
*> = 'S': scale only;
*> = 'B': both permute and scale.
*> Computed reciprocal condition numbers will be for the
*> matrices after permuting and/or balancing. Permuting does
*> not change condition numbers (in exact arithmetic), but
*> balancing does.
*> \endverbatim
*>
*> \param[in] JOBVL
*> \verbatim
*> JOBVL is CHARACTER*1
*> = 'N': do not compute the left generalized eigenvectors;
*> = 'V': compute the left generalized eigenvectors.
*> \endverbatim
*>
*> \param[in] JOBVR
*> \verbatim
*> JOBVR is CHARACTER*1
*> = 'N': do not compute the right generalized eigenvectors;
*> = 'V': compute the right generalized eigenvectors.
*> \endverbatim
*>
*> \param[in] SENSE
*> \verbatim
*> SENSE is CHARACTER*1
*> Determines which reciprocal condition numbers are computed.
*> = 'N': none are computed;
*> = 'E': computed for eigenvalues only;
*> = 'V': computed for eigenvectors only;
*> = 'B': computed for eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrices A, B, VL, and VR. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA, N)
*> On entry, the matrix A in the pair (A,B).
*> On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'
*> or both, then A contains the first part of the complex Schur
*> form of the "balanced" versions of the input A and B.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB, N)
*> On entry, the matrix B in the pair (A,B).
*> On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'
*> or both, then B contains the second part of the complex
*> Schur form of the "balanced" versions of the input A and B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] ALPHA
*> \verbatim
*> ALPHA is COMPLEX*16 array, dimension (N)
*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> BETA is COMPLEX*16 array, dimension (N)
*> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized
*> eigenvalues.
*>
*> Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or
*> underflow, and BETA(j) may even be zero. Thus, the user
*> should avoid naively computing the ratio ALPHA/BETA.
*> However, ALPHA will be always less than and usually
*> comparable with norm(A) in magnitude, and BETA always less
*> than and usually comparable with norm(B).
*> \endverbatim
*>
*> \param[out] VL
*> \verbatim
*> VL is COMPLEX*16 array, dimension (LDVL,N)
*> If JOBVL = 'V', the left generalized eigenvectors u(j) are
*> stored one after another in the columns of VL, in the same
*> order as their eigenvalues.
*> Each eigenvector will be scaled so the largest component
*> will have abs(real part) + abs(imag. part) = 1.
*> Not referenced if JOBVL = 'N'.
*> \endverbatim
*>
*> \param[in] LDVL
*> \verbatim
*> LDVL is INTEGER
*> The leading dimension of the matrix VL. LDVL >= 1, and
*> if JOBVL = 'V', LDVL >= N.
*> \endverbatim
*>
*> \param[out] VR
*> \verbatim
*> VR is COMPLEX*16 array, dimension (LDVR,N)
*> If JOBVR = 'V', the right generalized eigenvectors v(j) are
*> stored one after another in the columns of VR, in the same
*> order as their eigenvalues.
*> Each eigenvector will be scaled so the largest component
*> will have abs(real part) + abs(imag. part) = 1.
*> Not referenced if JOBVR = 'N'.
*> \endverbatim
*>
*> \param[in] LDVR
*> \verbatim
*> LDVR is INTEGER
*> The leading dimension of the matrix VR. LDVR >= 1, and
*> if JOBVR = 'V', LDVR >= N.
*> \endverbatim
*>
*> \param[out] ILO
*> \verbatim
*> ILO is INTEGER
*> \endverbatim
*>
*> \param[out] IHI
*> \verbatim
*> IHI is INTEGER
*> ILO and IHI are integer values such that on exit
*> A(i,j) = 0 and B(i,j) = 0 if i > j and
*> j = 1,...,ILO-1 or i = IHI+1,...,N.
*> If BALANC = 'N' or 'S', ILO = 1 and IHI = N.
*> \endverbatim
*>
*> \param[out] LSCALE
*> \verbatim
*> LSCALE is DOUBLE PRECISION array, dimension (N)
*> Details of the permutations and scaling factors applied
*> to the left side of A and B. If PL(j) is the index of the
*> row interchanged with row j, and DL(j) is the scaling
*> factor applied to row j, then
*> LSCALE(j) = PL(j) for j = 1,...,ILO-1
*> = DL(j) for j = ILO,...,IHI
*> = PL(j) for j = IHI+1,...,N.
*> The order in which the interchanges are made is N to IHI+1,
*> then 1 to ILO-1.
*> \endverbatim
*>
*> \param[out] RSCALE
*> \verbatim
*> RSCALE is DOUBLE PRECISION array, dimension (N)
*> Details of the permutations and scaling factors applied
*> to the right side of A and B. If PR(j) is the index of the
*> column interchanged with column j, and DR(j) is the scaling
*> factor applied to column j, then
*> RSCALE(j) = PR(j) for j = 1,...,ILO-1
*> = DR(j) for j = ILO,...,IHI
*> = PR(j) for j = IHI+1,...,N
*> The order in which the interchanges are made is N to IHI+1,
*> then 1 to ILO-1.
*> \endverbatim
*>
*> \param[out] ABNRM
*> \verbatim
*> ABNRM is DOUBLE PRECISION
*> The one-norm of the balanced matrix A.
*> \endverbatim
*>
*> \param[out] BBNRM
*> \verbatim
*> BBNRM is DOUBLE PRECISION
*> The one-norm of the balanced matrix B.
*> \endverbatim
*>
*> \param[out] RCONDE
*> \verbatim
*> RCONDE is DOUBLE PRECISION array, dimension (N)
*> If SENSE = 'E' or 'B', the reciprocal condition numbers of
*> the eigenvalues, stored in consecutive elements of the array.
*> If SENSE = 'N' or 'V', RCONDE is not referenced.
*> \endverbatim
*>
*> \param[out] RCONDV
*> \verbatim
*> RCONDV is DOUBLE PRECISION array, dimension (N)
*> If JOB = 'V' or 'B', the estimated reciprocal condition
*> numbers of the eigenvectors, stored in consecutive elements
*> of the array. If the eigenvalues cannot be reordered to
*> compute RCONDV(j), RCONDV(j) is set to 0; this can only occur
*> when the true value would be very small anyway.
*> If SENSE = 'N' or 'E', RCONDV is not referenced.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= max(1,2*N).
*> If SENSE = 'E', LWORK >= max(1,4*N).
*> If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N).
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (lrwork)
*> lrwork must be at least max(1,6*N) if BALANC = 'S' or 'B',
*> and at least max(1,2*N) otherwise.
*> Real workspace.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N+2)
*> If SENSE = 'E', IWORK is not referenced.
*> \endverbatim
*>
*> \param[out] BWORK
*> \verbatim
*> BWORK is LOGICAL array, dimension (N)
*> If SENSE = 'N', BWORK is not referenced.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> = 1,...,N:
*> The QZ iteration failed. No eigenvectors have been
*> calculated, but ALPHA(j) and BETA(j) should be correct
*> for j=INFO+1,...,N.
*> > N: =N+1: other than QZ iteration failed in ZHGEQZ.
*> =N+2: error return from ZTGEVC.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date April 2012
*
*> \ingroup complex16GEeigen
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Balancing a matrix pair (A,B) includes, first, permuting rows and
*> columns to isolate eigenvalues, second, applying diagonal similarity
*> transformation to the rows and columns to make the rows and columns
*> as close in norm as possible. The computed reciprocal condition
*> numbers correspond to the balanced matrix. Permuting rows and columns
*> will not change the condition numbers (in exact arithmetic) but
*> diagonal scaling will. For further explanation of balancing, see
*> section 4.11.1.2 of LAPACK Users' Guide.
*>
*> An approximate error bound on the chordal distance between the i-th
*> computed generalized eigenvalue w and the corresponding exact
*> eigenvalue lambda is
*>
*> chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)
*>
*> An approximate error bound for the angle between the i-th computed
*> eigenvector VL(i) or VR(i) is given by
*>
*> EPS * norm(ABNRM, BBNRM) / DIF(i).
*>
*> For further explanation of the reciprocal condition numbers RCONDE
*> and RCONDV, see section 4.11 of LAPACK User's Guide.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
$ ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
$ LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV,
$ WORK, LWORK, RWORK, IWORK, BWORK, INFO )
*
* -- LAPACK driver routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* April 2012
*
* .. Scalar Arguments ..
CHARACTER BALANC, JOBVL, JOBVR, SENSE
INTEGER IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
DOUBLE PRECISION ABNRM, BBNRM
* ..
* .. Array Arguments ..
LOGICAL BWORK( * )
INTEGER IWORK( * )
DOUBLE PRECISION LSCALE( * ), RCONDE( * ), RCONDV( * ),
$ RSCALE( * ), RWORK( * )
COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
$ BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
$ WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, NOSCL,
$ WANTSB, WANTSE, WANTSN, WANTSV
CHARACTER CHTEMP
INTEGER I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
$ ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK, MINWRK
DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
$ SMLNUM, TEMP
COMPLEX*16 X
* ..
* .. Local Arrays ..
LOGICAL LDUMMA( 1 )
* ..
* .. External Subroutines ..
EXTERNAL DLABAD, DLASCL, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL,
$ ZGGHRD, ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGEVC,
$ ZTGSNA, ZUNGQR, ZUNMQR
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
* ..
* .. Statement Functions ..
DOUBLE PRECISION ABS1
* ..
* .. Statement Function definitions ..
ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
* ..
* .. Executable Statements ..
*
* Decode the input arguments
*
IF( LSAME( JOBVL, 'N' ) ) THEN
IJOBVL = 1
ILVL = .FALSE.
ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
IJOBVL = 2
ILVL = .TRUE.
ELSE
IJOBVL = -1
ILVL = .FALSE.
END IF
*
IF( LSAME( JOBVR, 'N' ) ) THEN
IJOBVR = 1
ILVR = .FALSE.
ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
IJOBVR = 2
ILVR = .TRUE.
ELSE
IJOBVR = -1
ILVR = .FALSE.
END IF
ILV = ILVL .OR. ILVR
*
NOSCL = LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'P' )
WANTSN = LSAME( SENSE, 'N' )
WANTSE = LSAME( SENSE, 'E' )
WANTSV = LSAME( SENSE, 'V' )
WANTSB = LSAME( SENSE, 'B' )
*
* Test the input arguments
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
IF( .NOT.( NOSCL .OR. LSAME( BALANC,'S' ) .OR.
$ LSAME( BALANC, 'B' ) ) ) THEN
INFO = -1
ELSE IF( IJOBVL.LE.0 ) THEN
INFO = -2
ELSE IF( IJOBVR.LE.0 ) THEN
INFO = -3
ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSB .OR. WANTSV ) )
$ THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -9
ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
INFO = -13
ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
INFO = -15
END IF
*
* Compute workspace
* (Note: Comments in the code beginning "Workspace:" describe the
* minimal amount of workspace needed at that point in the code,
* as well as the preferred amount for good performance.
* NB refers to the optimal block size for the immediately
* following subroutine, as returned by ILAENV. The workspace is
* computed assuming ILO = 1 and IHI = N, the worst case.)
*
IF( INFO.EQ.0 ) THEN
IF( N.EQ.0 ) THEN
MINWRK = 1
MAXWRK = 1
ELSE
MINWRK = 2*N
IF( WANTSE ) THEN
MINWRK = 4*N
ELSE IF( WANTSV .OR. WANTSB ) THEN
MINWRK = 2*N*( N + 1)
END IF
MAXWRK = MINWRK
MAXWRK = MAX( MAXWRK,
$ N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
MAXWRK = MAX( MAXWRK,
$ N + N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, 0 ) )
IF( ILVL ) THEN
MAXWRK = MAX( MAXWRK, N +
$ N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, 0 ) )
END IF
END IF
WORK( 1 ) = MAXWRK
*
IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
INFO = -25
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZGGEVX', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Get machine constants
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' )
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
SMLNUM = SQRT( SMLNUM ) / EPS
BIGNUM = ONE / SMLNUM
*
* Scale A if max element outside range [SMLNUM,BIGNUM]
*
ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
ILASCL = .FALSE.
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
ANRMTO = SMLNUM
ILASCL = .TRUE.
ELSE IF( ANRM.GT.BIGNUM ) THEN
ANRMTO = BIGNUM
ILASCL = .TRUE.
END IF
IF( ILASCL )
$ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
*
* Scale B if max element outside range [SMLNUM,BIGNUM]
*
BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
ILBSCL = .FALSE.
IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
BNRMTO = SMLNUM
ILBSCL = .TRUE.
ELSE IF( BNRM.GT.BIGNUM ) THEN
BNRMTO = BIGNUM
ILBSCL = .TRUE.
END IF
IF( ILBSCL )
$ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
*
* Permute and/or balance the matrix pair (A,B)
* (Real Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise)
*
CALL ZGGBAL( BALANC, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
$ RWORK, IERR )
*
* Compute ABNRM and BBNRM
*
ABNRM = ZLANGE( '1', N, N, A, LDA, RWORK( 1 ) )
IF( ILASCL ) THEN
RWORK( 1 ) = ABNRM
CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, 1, 1, RWORK( 1 ), 1,
$ IERR )
ABNRM = RWORK( 1 )
END IF
*
BBNRM = ZLANGE( '1', N, N, B, LDB, RWORK( 1 ) )
IF( ILBSCL ) THEN
RWORK( 1 ) = BBNRM
CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, 1, 1, RWORK( 1 ), 1,
$ IERR )
BBNRM = RWORK( 1 )
END IF
*
* Reduce B to triangular form (QR decomposition of B)
* (Complex Workspace: need N, prefer N*NB )
*
IROWS = IHI + 1 - ILO
IF( ILV .OR. .NOT.WANTSN ) THEN
ICOLS = N + 1 - ILO
ELSE
ICOLS = IROWS
END IF
ITAU = 1
IWRK = ITAU + IROWS
CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
$ WORK( IWRK ), LWORK+1-IWRK, IERR )
*
* Apply the unitary transformation to A
* (Complex Workspace: need N, prefer N*NB)
*
CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
$ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
$ LWORK+1-IWRK, IERR )
*
* Initialize VL and/or VR
* (Workspace: need N, prefer N*NB)
*
IF( ILVL ) THEN
CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
IF( IROWS.GT.1 ) THEN
CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
$ VL( ILO+1, ILO ), LDVL )
END IF
CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
$ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
END IF
*
IF( ILVR )
$ CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
*
* Reduce to generalized Hessenberg form
* (Workspace: none needed)
*
IF( ILV .OR. .NOT.WANTSN ) THEN
*
* Eigenvectors requested -- work on whole matrix.
*
CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
$ LDVL, VR, LDVR, IERR )
ELSE
CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
$ B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR )
END IF
*
* Perform QZ algorithm (Compute eigenvalues, and optionally, the
* Schur forms and Schur vectors)
* (Complex Workspace: need N)
* (Real Workspace: need N)
*
IWRK = ITAU
IF( ILV .OR. .NOT.WANTSN ) THEN
CHTEMP = 'S'
ELSE
CHTEMP = 'E'
END IF
*
CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
$ ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWRK ),
$ LWORK+1-IWRK, RWORK, IERR )
IF( IERR.NE.0 ) THEN
IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
INFO = IERR
ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
INFO = IERR - N
ELSE
INFO = N + 1
END IF
GO TO 90
END IF
*
* Compute Eigenvectors and estimate condition numbers if desired
* ZTGEVC: (Complex Workspace: need 2*N )
* (Real Workspace: need 2*N )
* ZTGSNA: (Complex Workspace: need 2*N*N if SENSE='V' or 'B')
* (Integer Workspace: need N+2 )
*
IF( ILV .OR. .NOT.WANTSN ) THEN
IF( ILV ) THEN
IF( ILVL ) THEN
IF( ILVR ) THEN
CHTEMP = 'B'
ELSE
CHTEMP = 'L'
END IF
ELSE
CHTEMP = 'R'
END IF
*
CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL,
$ LDVL, VR, LDVR, N, IN, WORK( IWRK ), RWORK,
$ IERR )
IF( IERR.NE.0 ) THEN
INFO = N + 2
GO TO 90
END IF
END IF
*
IF( .NOT.WANTSN ) THEN
*
* compute eigenvectors (DTGEVC) and estimate condition
* numbers (DTGSNA). Note that the definition of the condition
* number is not invariant under transformation (u,v) to
* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized
* Schur form (S,T), Q and Z are orthogonal matrices. In order
* to avoid using extra 2*N*N workspace, we have to
* re-calculate eigenvectors and estimate the condition numbers
* one at a time.
*
DO 20 I = 1, N
*
DO 10 J = 1, N
BWORK( J ) = .FALSE.
10 CONTINUE
BWORK( I ) = .TRUE.
*
IWRK = N + 1
IWRK1 = IWRK + N
*
IF( WANTSE .OR. WANTSB ) THEN
CALL ZTGEVC( 'B', 'S', BWORK, N, A, LDA, B, LDB,
$ WORK( 1 ), N, WORK( IWRK ), N, 1, M,
$ WORK( IWRK1 ), RWORK, IERR )
IF( IERR.NE.0 ) THEN
INFO = N + 2
GO TO 90
END IF
END IF
*
CALL ZTGSNA( SENSE, 'S', BWORK, N, A, LDA, B, LDB,
$ WORK( 1 ), N, WORK( IWRK ), N, RCONDE( I ),
$ RCONDV( I ), 1, M, WORK( IWRK1 ),
$ LWORK-IWRK1+1, IWORK, IERR )
*
20 CONTINUE
END IF
END IF
*
* Undo balancing on VL and VR and normalization
* (Workspace: none needed)
*
IF( ILVL ) THEN
CALL ZGGBAK( BALANC, 'L', N, ILO, IHI, LSCALE, RSCALE, N, VL,
$ LDVL, IERR )
*
DO 50 JC = 1, N
TEMP = ZERO
DO 30 JR = 1, N
TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
30 CONTINUE
IF( TEMP.LT.SMLNUM )
$ GO TO 50
TEMP = ONE / TEMP
DO 40 JR = 1, N
VL( JR, JC ) = VL( JR, JC )*TEMP
40 CONTINUE
50 CONTINUE
END IF
*
IF( ILVR ) THEN
CALL ZGGBAK( BALANC, 'R', N, ILO, IHI, LSCALE, RSCALE, N, VR,
$ LDVR, IERR )
DO 80 JC = 1, N
TEMP = ZERO
DO 60 JR = 1, N
TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
60 CONTINUE
IF( TEMP.LT.SMLNUM )
$ GO TO 80
TEMP = ONE / TEMP
DO 70 JR = 1, N
VR( JR, JC ) = VR( JR, JC )*TEMP
70 CONTINUE
80 CONTINUE
END IF
*
* Undo scaling if necessary
*
90 CONTINUE
*
IF( ILASCL )
$ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
*
IF( ILBSCL )
$ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
*
WORK( 1 ) = MAXWRK
RETURN
*
* End of ZGGEVX
*
END