*> \brief DGGES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGGES + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, * SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, * LDVSR, WORK, LWORK, BWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBVSL, JOBVSR, SORT * INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM * .. * .. Array Arguments .. * LOGICAL BWORK( * ) * DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), * \$ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), * \$ VSR( LDVSR, * ), WORK( * ) * .. * .. Function Arguments .. * LOGICAL SELCTG * EXTERNAL SELCTG * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B), *> the generalized eigenvalues, the generalized real Schur form (S,T), *> optionally, the left and/or right matrices of Schur vectors (VSL and *> VSR). This gives the generalized Schur factorization *> *> (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) *> *> Optionally, it also orders the eigenvalues so that a selected cluster *> of eigenvalues appears in the leading diagonal blocks of the upper *> quasi-triangular matrix S and the upper triangular matrix T.The *> leading columns of VSL and VSR then form an orthonormal basis for the *> corresponding left and right eigenspaces (deflating subspaces). *> *> (If only the generalized eigenvalues are needed, use the driver *> DGGEV instead, which is faster.) *> *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w *> or a ratio alpha/beta = w, such that A - w*B is singular. It is *> usually represented as the pair (alpha,beta), as there is a *> reasonable interpretation for beta=0 or both being zero. *> *> A pair of matrices (S,T) is in generalized real Schur form if T is *> upper triangular with non-negative diagonal and S is block upper *> triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond *> to real generalized eigenvalues, while 2-by-2 blocks of S will be *> "standardized" by making the corresponding elements of T have the *> form: *> [ a 0 ] *> [ 0 b ] *> *> and the pair of corresponding 2-by-2 blocks in S and T will have a *> complex conjugate pair of generalized eigenvalues. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBVSL *> \verbatim *> JOBVSL is CHARACTER*1 *> = 'N': do not compute the left Schur vectors; *> = 'V': compute the left Schur vectors. *> \endverbatim *> *> \param[in] JOBVSR *> \verbatim *> JOBVSR is CHARACTER*1 *> = 'N': do not compute the right Schur vectors; *> = 'V': compute the right Schur vectors. *> \endverbatim *> *> \param[in] SORT *> \verbatim *> SORT is CHARACTER*1 *> Specifies whether or not to order the eigenvalues on the *> diagonal of the generalized Schur form. *> = 'N': Eigenvalues are not ordered; *> = 'S': Eigenvalues are ordered (see SELCTG); *> \endverbatim *> *> \param[in] SELCTG *> \verbatim *> SELCTG is a LOGICAL FUNCTION of three DOUBLE PRECISION arguments *> SELCTG must be declared EXTERNAL in the calling subroutine. *> If SORT = 'N', SELCTG is not referenced. *> If SORT = 'S', SELCTG is used to select eigenvalues to sort *> to the top left of the Schur form. *> An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if *> SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either *> one of a complex conjugate pair of eigenvalues is selected, *> then both complex eigenvalues are selected. *> *> Note that in the ill-conditioned case, a selected complex *> eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), *> BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 *> in this case. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A, B, VSL, and VSR. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> On entry, the first of the pair of matrices. *> On exit, A has been overwritten by its generalized Schur *> form S. *> \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 DOUBLE PRECISION array, dimension (LDB, N) *> On entry, the second of the pair of matrices. *> On exit, B has been overwritten by its generalized Schur *> form T. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] SDIM *> \verbatim *> SDIM is INTEGER *> If SORT = 'N', SDIM = 0. *> If SORT = 'S', SDIM = number of eigenvalues (after sorting) *> for which SELCTG is true. (Complex conjugate pairs for which *> SELCTG is true for either eigenvalue count as 2.) *> \endverbatim *> *> \param[out] ALPHAR *> \verbatim *> ALPHAR is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] ALPHAI *> \verbatim *> ALPHAI is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) *> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will *> be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i, *> and BETA(j),j=1,...,N are the diagonals of the complex Schur *> form (S,T) that would result if the 2-by-2 diagonal blocks of *> the real Schur form of (A,B) were further reduced to *> triangular form using 2-by-2 complex unitary transformations. *> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if *> positive, then the j-th and (j+1)-st eigenvalues are a *> complex conjugate pair, with ALPHAI(j+1) negative. *> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio. *> However, ALPHAR and ALPHAI 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] VSL *> \verbatim *> VSL is DOUBLE PRECISION array, dimension (LDVSL,N) *> If JOBVSL = 'V', VSL will contain the left Schur vectors. *> Not referenced if JOBVSL = 'N'. *> \endverbatim *> *> \param[in] LDVSL *> \verbatim *> LDVSL is INTEGER *> The leading dimension of the matrix VSL. LDVSL >=1, and *> if JOBVSL = 'V', LDVSL >= N. *> \endverbatim *> *> \param[out] VSR *> \verbatim *> VSR is DOUBLE PRECISION array, dimension (LDVSR,N) *> If JOBVSR = 'V', VSR will contain the right Schur vectors. *> Not referenced if JOBVSR = 'N'. *> \endverbatim *> *> \param[in] LDVSR *> \verbatim *> LDVSR is INTEGER *> The leading dimension of the matrix VSR. LDVSR >= 1, and *> if JOBVSR = 'V', LDVSR >= N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION 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. *> If N = 0, LWORK >= 1, else LWORK >= 8*N+16. *> For good performance , LWORK must generally be larger. *> *> 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] BWORK *> \verbatim *> BWORK is LOGICAL array, dimension (N) *> Not referenced if SORT = 'N'. *> \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. (A,B) are not in Schur *> form, but ALPHAR(j), ALPHAI(j), and BETA(j) should *> be correct for j=INFO+1,...,N. *> > N: =N+1: other than QZ iteration failed in DHGEQZ. *> =N+2: after reordering, roundoff changed values of *> some complex eigenvalues so that leading *> eigenvalues in the Generalized Schur form no *> longer satisfy SELCTG=.TRUE. This could also *> be caused due to scaling. *> =N+3: reordering failed in DTGSEN. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEeigen * * ===================================================================== SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, \$ SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, \$ LDVSR, WORK, LWORK, 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..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBVSL, JOBVSR, SORT INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM * .. * .. Array Arguments .. LOGICAL BWORK( * ) DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), \$ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), \$ VSR( LDVSR, * ), WORK( * ) * .. * .. Function Arguments .. LOGICAL SELCTG EXTERNAL SELCTG * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL, \$ LQUERY, LST2SL, WANTST INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, \$ ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK, \$ MINWRK DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL, \$ PVSR, SAFMAX, SAFMIN, SMLNUM * .. * .. Local Arrays .. INTEGER IDUM( 1 ) DOUBLE PRECISION DIF( 2 ) * .. * .. External Subroutines .. EXTERNAL DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD, \$ DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN, \$ XERBLA * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * * Decode the input arguments * IF( LSAME( JOBVSL, 'N' ) ) THEN IJOBVL = 1 ILVSL = .FALSE. ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN IJOBVL = 2 ILVSL = .TRUE. ELSE IJOBVL = -1 ILVSL = .FALSE. END IF * IF( LSAME( JOBVSR, 'N' ) ) THEN IJOBVR = 1 ILVSR = .FALSE. ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN IJOBVR = 2 ILVSR = .TRUE. ELSE IJOBVR = -1 ILVSR = .FALSE. END IF * WANTST = LSAME( SORT, 'S' ) * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( IJOBVL.LE.0 ) THEN INFO = -1 ELSE IF( IJOBVR.LE.0 ) THEN INFO = -2 ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN INFO = -3 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( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN INFO = -15 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN INFO = -17 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.) * IF( INFO.EQ.0 ) THEN IF( N.GT.0 )THEN MINWRK = MAX( 8*N, 6*N + 16 ) MAXWRK = MINWRK - N + \$ N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) MAXWRK = MAX( MAXWRK, MINWRK - N + \$ N*ILAENV( 1, 'DORMQR', ' ', N, 1, N, -1 ) ) IF( ILVSL ) THEN MAXWRK = MAX( MAXWRK, MINWRK - N + \$ N*ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) ) END IF ELSE MINWRK = 1 MAXWRK = 1 END IF WORK( 1 ) = MAXWRK * IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) \$ INFO = -19 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGGES ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN SDIM = 0 RETURN END IF * * Get machine constants * EPS = DLAMCH( 'P' ) SAFMIN = DLAMCH( 'S' ) SAFMAX = ONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) SMLNUM = SQRT( SAFMIN ) / EPS BIGNUM = ONE / SMLNUM * * Scale A if max element outside range [SMLNUM,BIGNUM] * ANRM = DLANGE( 'M', N, N, A, LDA, WORK ) 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 DLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR ) * * Scale B if max element outside range [SMLNUM,BIGNUM] * BNRM = DLANGE( 'M', N, N, B, LDB, WORK ) 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 DLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR ) * * Permute the matrix to make it more nearly triangular * (Workspace: need 6*N + 2*N space for storing balancing factors) * ILEFT = 1 IRIGHT = N + 1 IWRK = IRIGHT + N CALL DGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ), \$ WORK( IRIGHT ), WORK( IWRK ), IERR ) * * Reduce B to triangular form (QR decomposition of B) * (Workspace: need N, prefer N*NB) * IROWS = IHI + 1 - ILO ICOLS = N + 1 - ILO ITAU = IWRK IWRK = ITAU + IROWS CALL DGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ), \$ WORK( IWRK ), LWORK+1-IWRK, IERR ) * * Apply the orthogonal transformation to matrix A * (Workspace: need N, prefer N*NB) * CALL DORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB, \$ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ), \$ LWORK+1-IWRK, IERR ) * * Initialize VSL * (Workspace: need N, prefer N*NB) * IF( ILVSL ) THEN CALL DLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL ) IF( IROWS.GT.1 ) THEN CALL DLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB, \$ VSL( ILO+1, ILO ), LDVSL ) END IF CALL DORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL, \$ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR ) END IF * * Initialize VSR * IF( ILVSR ) \$ CALL DLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR ) * * Reduce to generalized Hessenberg form * (Workspace: none needed) * CALL DGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL, \$ LDVSL, VSR, LDVSR, IERR ) * * Perform QZ algorithm, computing Schur vectors if desired * (Workspace: need N) * IWRK = ITAU CALL DHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, \$ ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, \$ WORK( IWRK ), LWORK+1-IWRK, 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 50 END IF * * Sort eigenvalues ALPHA/BETA if desired * (Workspace: need 4*N+16 ) * SDIM = 0 IF( WANTST ) THEN * * Undo scaling on eigenvalues before SELCTGing * IF( ILASCL ) THEN CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, \$ IERR ) CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, \$ IERR ) END IF IF( ILBSCL ) \$ CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) * * Select eigenvalues * DO 10 I = 1, N BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) ) 10 CONTINUE * CALL DTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHAR, \$ ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, \$ PVSR, DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, \$ IERR ) IF( IERR.EQ.1 ) \$ INFO = N + 3 * END IF * * Apply back-permutation to VSL and VSR * (Workspace: none needed) * IF( ILVSL ) \$ CALL DGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ), \$ WORK( IRIGHT ), N, VSL, LDVSL, IERR ) * IF( ILVSR ) \$ CALL DGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ), \$ WORK( IRIGHT ), N, VSR, LDVSR, IERR ) * * Check if unscaling would cause over/underflow, if so, rescale * (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of * B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) * IF( ILASCL ) THEN DO 20 I = 1, N IF( ALPHAI( I ).NE.ZERO ) THEN IF( ( ALPHAR( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) .OR. \$ ( SAFMIN / ALPHAR( I ) ).GT.( ANRM / ANRMTO ) ) THEN WORK( 1 ) = ABS( A( I, I ) / ALPHAR( I ) ) BETA( I ) = BETA( I )*WORK( 1 ) ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) ELSE IF( ( ALPHAI( I ) / SAFMAX ).GT. \$ ( ANRMTO / ANRM ) .OR. \$ ( SAFMIN / ALPHAI( I ) ).GT.( ANRM / ANRMTO ) ) \$ THEN WORK( 1 ) = ABS( A( I, I+1 ) / ALPHAI( I ) ) BETA( I ) = BETA( I )*WORK( 1 ) ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) END IF END IF 20 CONTINUE END IF * IF( ILBSCL ) THEN DO 30 I = 1, N IF( ALPHAI( I ).NE.ZERO ) THEN IF( ( BETA( I ) / SAFMAX ).GT.( BNRMTO / BNRM ) .OR. \$ ( SAFMIN / BETA( I ) ).GT.( BNRM / BNRMTO ) ) THEN WORK( 1 ) = ABS( B( I, I ) / BETA( I ) ) BETA( I ) = BETA( I )*WORK( 1 ) ALPHAR( I ) = ALPHAR( I )*WORK( 1 ) ALPHAI( I ) = ALPHAI( I )*WORK( 1 ) END IF END IF 30 CONTINUE END IF * * Undo scaling * IF( ILASCL ) THEN CALL DLASCL( 'H', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR ) CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR ) CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR ) END IF * IF( ILBSCL ) THEN CALL DLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR ) CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) END IF * IF( WANTST ) THEN * * Check if reordering is correct * LASTSL = .TRUE. LST2SL = .TRUE. SDIM = 0 IP = 0 DO 40 I = 1, N CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) ) IF( ALPHAI( I ).EQ.ZERO ) THEN IF( CURSL ) \$ SDIM = SDIM + 1 IP = 0 IF( CURSL .AND. .NOT.LASTSL ) \$ INFO = N + 2 ELSE IF( IP.EQ.1 ) THEN * * Last eigenvalue of conjugate pair * CURSL = CURSL .OR. LASTSL LASTSL = CURSL IF( CURSL ) \$ SDIM = SDIM + 2 IP = -1 IF( CURSL .AND. .NOT.LST2SL ) \$ INFO = N + 2 ELSE * * First eigenvalue of conjugate pair * IP = 1 END IF END IF LST2SL = LASTSL LASTSL = CURSL 40 CONTINUE * END IF * 50 CONTINUE * WORK( 1 ) = MAXWRK * RETURN * * End of DGGES * END