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   *> \brief <b> DGGESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGGESX + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggesx.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggesx.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggesx.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
   *                          B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
   *                          VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, IWORK,
   *                          LIWORK, BWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT
   *       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK, N,
   *      $                   SDIM
   *       ..
   *       .. Array Arguments ..
   *       LOGICAL            BWORK( * )
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
   *      $                   B( LDB, * ), BETA( * ), RCONDE( 2 ),
   *      $                   RCONDV( 2 ), VSL( LDVSL, * ), VSR( LDVSR, * ),
   *      $                   WORK( * )
   *       ..
   *       .. Function Arguments ..
   *       LOGICAL            SELCTG
   *       EXTERNAL           SELCTG
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGGESX computes for a pair of N-by-N real nonsymmetric matrices
   *> (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
   *> 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; computes
   *> a reciprocal condition number for the average of the selected
   *> eigenvalues (RCONDE); and computes a reciprocal condition number for
   *> the right and left deflating subspaces corresponding to the selected
   *> eigenvalues (RCONDV). The leading columns of VSL and VSR then form
   *> an orthonormal basis for the corresponding left and right eigenspaces
   *> (deflating subspaces).
   *>
   *> 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 for 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 procedure) 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 a selected complex eigenvalue may no longer satisfy
   *>          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering,
   *>          since ordering may change the value of complex eigenvalues
   *>          (especially if the eigenvalue is ill-conditioned), in this
   *>          case INFO is set to N+3.
   *> \endverbatim
   *>
   *> \param[in] SENSE
   *> \verbatim
   *>          SENSE is CHARACTER*1
   *>          Determines which reciprocal condition numbers are computed.
   *>          = 'N' : None are computed;
   *>          = 'E' : Computed for average of selected eigenvalues only;
   *>          = 'V' : Computed for selected deflating subspaces only;
   *>          = 'B' : Computed for both.
   *>          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
   *> \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] RCONDE
   *> \verbatim
   *>          RCONDE is DOUBLE PRECISION array, dimension ( 2 )
   *>          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
   *>          reciprocal condition numbers for the average of the selected
   *>          eigenvalues.
   *>          Not referenced if SENSE = 'N' or 'V'.
   *> \endverbatim
   *>
   *> \param[out] RCONDV
   *> \verbatim
   *>          RCONDV is DOUBLE PRECISION array, dimension ( 2 )
   *>          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
   *>          reciprocal condition numbers for the selected deflating
   *>          subspaces.
   *>          Not referenced if SENSE = 'N' or 'E'.
   *> \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 if SENSE = 'E', 'V', or 'B',
   *>          LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else
   *>          LWORK >= max( 8*N, 6*N+16 ).
   *>          Note that 2*SDIM*(N-SDIM) <= N*N/2.
   *>          Note also that an error is only returned if
   *>          LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B'
   *>          this may not be large enough.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the bound on the optimal size of the WORK
   *>          array and the minimum size of the IWORK array, returns these
   *>          values as the first entries of the WORK and IWORK arrays, and
   *>          no error message related to LWORK or LIWORK is issued by
   *>          XERBLA.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
   *>          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of the array IWORK.
   *>          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise
   *>          LIWORK >= N+6.
   *>
   *>          If LIWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the bound on the optimal size of the
   *>          WORK array and the minimum size of the IWORK array, returns
   *>          these values as the first entries of the WORK and IWORK
   *>          arrays, and no error message related to LWORK or LIWORK 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 November 2011
   *
   *> \ingroup doubleGEeigen
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  An approximate (asymptotic) bound on the average absolute error of
   *>  the selected eigenvalues is
   *>
   *>       EPS * norm((A, B)) / RCONDE( 1 ).
   *>
   *>  An approximate (asymptotic) bound on the maximum angular error in
   *>  the computed deflating subspaces is
   *>
   *>       EPS * norm((A, B)) / RCONDV( 2 ).
   *>
   *>  See LAPACK User's Guide, section 4.11 for more information.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,        SUBROUTINE DGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
      $                   B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,       $                   B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL,
      $                   VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, IWORK,       $                   VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, IWORK,
      $                   LIWORK, BWORK, INFO )       $                   LIWORK, BWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2.1)                           --  *  -- LAPACK driver routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2009                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT        CHARACTER          JOBVSL, JOBVSR, SENSE, SORT
Line 26 Line 388
       EXTERNAL           SELCTG        EXTERNAL           SELCTG
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGGESX computes for a pair of N-by-N real nonsymmetric matrices  
 *  (A,B), the generalized eigenvalues, the real Schur form (S,T), and,  
 *  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; computes  
 *  a reciprocal condition number for the average of the selected  
 *  eigenvalues (RCONDE); and computes a reciprocal condition number for  
 *  the right and left deflating subspaces corresponding to the selected  
 *  eigenvalues (RCONDV). The leading columns of VSL and VSR then form  
 *  an orthonormal basis for the corresponding left and right eigenspaces  
 *  (deflating subspaces).  
 *  
 *  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 for 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.  
 *  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBVSL  (input) CHARACTER*1  
 *          = 'N':  do not compute the left Schur vectors;  
 *          = 'V':  compute the left Schur vectors.  
 *  
 *  JOBVSR  (input) CHARACTER*1  
 *          = 'N':  do not compute the right Schur vectors;  
 *          = 'V':  compute the right Schur vectors.  
 *  
 *  SORT    (input) 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).  
 *  
 *  SELCTG  (external procedure) 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 a selected complex eigenvalue may no longer satisfy  
 *          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering,  
 *          since ordering may change the value of complex eigenvalues  
 *          (especially if the eigenvalue is ill-conditioned), in this  
 *          case INFO is set to N+3.  
 *  
 *  SENSE   (input) CHARACTER*1  
 *          Determines which reciprocal condition numbers are computed.  
 *          = 'N' : None are computed;  
 *          = 'E' : Computed for average of selected eigenvalues only;  
 *          = 'V' : Computed for selected deflating subspaces only;  
 *          = 'B' : Computed for both.  
 *          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A, B, VSL, and VSR.  N >= 0.  
 *  
 *  A       (input/output) 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.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of A.  LDA >= max(1,N).  
 *  
 *  B       (input/output) 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.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of B.  LDB >= max(1,N).  
 *  
 *  SDIM    (output) 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.)  
 *  
 *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)  
 *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)  
 *  BETA    (output) 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).  
 *  
 *  VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N)  
 *          If JOBVSL = 'V', VSL will contain the left Schur vectors.  
 *          Not referenced if JOBVSL = 'N'.  
 *  
 *  LDVSL   (input) INTEGER  
 *          The leading dimension of the matrix VSL. LDVSL >=1, and  
 *          if JOBVSL = 'V', LDVSL >= N.  
 *  
 *  VSR     (output) DOUBLE PRECISION array, dimension (LDVSR,N)  
 *          If JOBVSR = 'V', VSR will contain the right Schur vectors.  
 *          Not referenced if JOBVSR = 'N'.  
 *  
 *  LDVSR   (input) INTEGER  
 *          The leading dimension of the matrix VSR. LDVSR >= 1, and  
 *          if JOBVSR = 'V', LDVSR >= N.  
 *  
 *  RCONDE  (output) DOUBLE PRECISION array, dimension ( 2 )  
 *          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the  
 *          reciprocal condition numbers for the average of the selected  
 *          eigenvalues.  
 *          Not referenced if SENSE = 'N' or 'V'.  
 *  
 *  RCONDV  (output) DOUBLE PRECISION array, dimension ( 2 )  
 *          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the  
 *          reciprocal condition numbers for the selected deflating  
 *          subspaces.  
 *          Not referenced if SENSE = 'N' or 'E'.  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B',  
 *          LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else  
 *          LWORK >= max( 8*N, 6*N+16 ).  
 *          Note that 2*SDIM*(N-SDIM) <= N*N/2.  
 *          Note also that an error is only returned if  
 *          LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B'  
 *          this may not be large enough.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the bound on the optimal size of the WORK  
 *          array and the minimum size of the IWORK array, returns these  
 *          values as the first entries of the WORK and IWORK arrays, and  
 *          no error message related to LWORK or LIWORK is issued by  
 *          XERBLA.  
 *  
 *  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK))  
 *          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.  
 *  
 *  LIWORK  (input) INTEGER  
 *          The dimension of the array IWORK.  
 *          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise  
 *          LIWORK >= N+6.  
 *  
 *          If LIWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the bound on the optimal size of the  
 *          WORK array and the minimum size of the IWORK array, returns  
 *          these values as the first entries of the WORK and IWORK  
 *          arrays, and no error message related to LWORK or LIWORK is  
 *          issued by XERBLA.  
 *  
 *  BWORK   (workspace) LOGICAL array, dimension (N)  
 *          Not referenced if SORT = 'N'.  
 *  
 *  INFO    (output) 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.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  An approximate (asymptotic) bound on the average absolute error of  
 *  the selected eigenvalues is  
 *  
 *       EPS * norm((A, B)) / RCONDE( 1 ).  
 *  
 *  An approximate (asymptotic) bound on the maximum angular error in  
 *  the computed deflating subspaces is  
 *  
 *       EPS * norm((A, B)) / RCONDV( 2 ).  
 *  
 *  See LAPACK User's Guide, section 4.11 for more information.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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