!>
!> CGGES computes for a pair of N-by-N complex nonsymmetric matrices
!> (A,B), the generalized eigenvalues, the generalized complex Schur
!> form (S, T), and optionally left and/or right Schur vectors (VSL
!> and VSR). This gives the generalized Schur factorization
!>
!>         (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
!>
!> where (VSR)**H is the conjugate-transpose of VSR.
!>
!> Optionally, it also orders the eigenvalues so that a selected cluster
!> of eigenvalues appears in the leading diagonal blocks of the upper
!> triangular matrix S and the upper triangular matrix T. The leading
!> columns of VSL and VSR then form an unitary basis for the
!> corresponding left and right eigenspaces (deflating subspaces).
!>
!> (If only the generalized eigenvalues are needed, use the driver
!> CGGEV 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, and even for both being zero.
!>
!> A pair of matrices (S,T) is in generalized complex Schur form if S
!> and T are upper triangular and, in addition, the diagonal elements
!> of T are non-negative real numbers.
!> 

JOBVSL

!>          JOBVSL is CHARACTER*1
!>          = 'N':  do not compute the left Schur vectors;
!>          = 'V':  compute the left Schur vectors.
!> 

JOBVSR

!>          JOBVSR is CHARACTER*1
!>          = 'N':  do not compute the right Schur vectors;
!>          = 'V':  compute the right Schur vectors.
!> 

SORT

!>          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).
!> 

SELCTG

!>          SELCTG is a LOGICAL FUNCTION of two COMPLEX 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 ALPHA(j)/BETA(j) is selected if
!>          SELCTG(ALPHA(j),BETA(j)) is true.
!>
!>          Note that a selected complex eigenvalue may no longer satisfy
!>          SELCTG(ALPHA(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+2 (See INFO below).
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
!> 

A

!>          A is COMPLEX 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

!>          LDA is INTEGER
!>          The leading dimension of A.  LDA >= max(1,N).
!> 

B

!>          B is COMPLEX 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

!>          LDB is INTEGER
!>          The leading dimension of B.  LDB >= max(1,N).
!> 

SDIM

!>          SDIM is INTEGER
!>          If SORT = 'N', SDIM = 0.
!>          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
!>          for which SELCTG is true.
!> 

ALPHA

!>          ALPHA is COMPLEX array, dimension (N)
!> 

BETA

!>          BETA is COMPLEX array, dimension (N)
!>          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
!>          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
!>          j=1,...,N  are the diagonals of the complex Schur form (A,B)
!>          output by CGGES. The  BETA(j) will be non-negative real.
!>
!>          Note: the quotients 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).
!> 

VSL

!>          VSL is COMPLEX array, dimension (LDVSL,N)
!>          If JOBVSL = 'V', VSL will contain the left Schur vectors.
!>          Not referenced if JOBVSL = 'N'.
!> 

LDVSL

!>          LDVSL is INTEGER
!>          The leading dimension of the matrix VSL. LDVSL >= 1, and
!>          if JOBVSL = 'V', LDVSL >= N.
!> 

VSR

!>          VSR is COMPLEX array, dimension (LDVSR,N)
!>          If JOBVSR = 'V', VSR will contain the right Schur vectors.
!>          Not referenced if JOBVSR = 'N'.
!> 

LDVSR

!>          LDVSR is INTEGER
!>          The leading dimension of the matrix VSR. LDVSR >= 1, and
!>          if JOBVSR = 'V', LDVSR >= N.
!> 

WORK

!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= max(1,2*N).
!>          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.
!> 

RWORK

!>          RWORK is REAL array, dimension (8*N)
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (N)
!>          Not referenced if SORT = 'N'.
!> 

INFO

!>          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 ALPHA(j) and BETA(j) should be correct for
!>                j=INFO+1,...,N.
!>          > N:  =N+1: other than QZ iteration failed in CHGEQZ
!>                =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 CTGSEN.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> 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
!>  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.
!>
!> 

JOBVSL

!>          JOBVSL is CHARACTER*1
!>          = 'N':  do not compute the left Schur vectors;
!>          = 'V':  compute the left Schur vectors.
!> 

JOBVSR

!>          JOBVSR is CHARACTER*1
!>          = 'N':  do not compute the right Schur vectors;
!>          = 'V':  compute the right Schur vectors.
!> 

SORT

!>          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);
!> 

SELCTG

!>          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.
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
!> 

A

!>          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.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of A.  LDA >= max(1,N).
!> 

B

!>          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.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of B.  LDB >= max(1,N).
!> 

SDIM

!>          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.)
!> 

ALPHAR

!>          ALPHAR is DOUBLE PRECISION array, dimension (N)
!> 

ALPHAI

!>          ALPHAI is DOUBLE PRECISION array, dimension (N)
!> 

BETA

!>          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).
!> 

VSL

!>          VSL is DOUBLE PRECISION array, dimension (LDVSL,N)
!>          If JOBVSL = 'V', VSL will contain the left Schur vectors.
!>          Not referenced if JOBVSL = 'N'.
!> 

LDVSL

!>          LDVSL is INTEGER
!>          The leading dimension of the matrix VSL. LDVSL >=1, and
!>          if JOBVSL = 'V', LDVSL >= N.
!> 

VSR

!>          VSR is DOUBLE PRECISION array, dimension (LDVSR,N)
!>          If JOBVSR = 'V', VSR will contain the right Schur vectors.
!>          Not referenced if JOBVSR = 'N'.
!> 

LDVSR

!>          LDVSR is INTEGER
!>          The leading dimension of the matrix VSR. LDVSR >= 1, and
!>          if JOBVSR = 'V', LDVSR >= N.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          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.
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (N)
!>          Not referenced if SORT = 'N'.
!> 

INFO

!>          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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> SGGES 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
!> SGGEV 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
!>  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.
!>
!> 

JOBVSL

!>          JOBVSL is CHARACTER*1
!>          = 'N':  do not compute the left Schur vectors;
!>          = 'V':  compute the left Schur vectors.
!> 

JOBVSR

!>          JOBVSR is CHARACTER*1
!>          = 'N':  do not compute the right Schur vectors;
!>          = 'V':  compute the right Schur vectors.
!> 

SORT

!>          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);
!> 

SELCTG

!>          SELCTG is a LOGICAL FUNCTION of three REAL 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.
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
!> 

A

!>          A is REAL 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

!>          LDA is INTEGER
!>          The leading dimension of A.  LDA >= max(1,N).
!> 

B

!>          B is REAL 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

!>          LDB is INTEGER
!>          The leading dimension of B.  LDB >= max(1,N).
!> 

SDIM

!>          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.)
!> 

ALPHAR

!>          ALPHAR is REAL array, dimension (N)
!> 

ALPHAI

!>          ALPHAI is REAL array, dimension (N)
!> 

BETA

!>          BETA is REAL 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

!>          VSL is REAL array, dimension (LDVSL,N)
!>          If JOBVSL = 'V', VSL will contain the left Schur vectors.
!>          Not referenced if JOBVSL = 'N'.
!> 

LDVSL

!>          LDVSL is INTEGER
!>          The leading dimension of the matrix VSL. LDVSL >=1, and
!>          if JOBVSL = 'V', LDVSL >= N.
!> 

VSR

!>          VSR is REAL array, dimension (LDVSR,N)
!>          If JOBVSR = 'V', VSR will contain the right Schur vectors.
!>          Not referenced if JOBVSR = 'N'.
!> 

LDVSR

!>          LDVSR is INTEGER
!>          The leading dimension of the matrix VSR. LDVSR >= 1, and
!>          if JOBVSR = 'V', LDVSR >= N.
!> 

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If N = 0, LWORK >= 1, else LWORK >= max(8*N,6*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.
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (N)
!>          Not referenced if SORT = 'N'.
!> 

INFO

!>          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 SHGEQZ.
!>                =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 STGSEN.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
!> (A,B), the generalized eigenvalues, the generalized complex Schur
!> form (S, T), and optionally left and/or right Schur vectors (VSL
!> and VSR). This gives the generalized Schur factorization
!>
!>         (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
!>
!> where (VSR)**H is the conjugate-transpose of VSR.
!>
!> Optionally, it also orders the eigenvalues so that a selected cluster
!> of eigenvalues appears in the leading diagonal blocks of the upper
!> triangular matrix S and the upper triangular matrix T. The leading
!> columns of VSL and VSR then form an unitary basis for the
!> corresponding left and right eigenspaces (deflating subspaces).
!>
!> (If only the generalized eigenvalues are needed, use the driver
!> ZGGEV 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, and even for both being zero.
!>
!> A pair of matrices (S,T) is in generalized complex Schur form if S
!> and T are upper triangular and, in addition, the diagonal elements
!> of T are non-negative real numbers.
!> 

JOBVSL

!>          JOBVSL is CHARACTER*1
!>          = 'N':  do not compute the left Schur vectors;
!>          = 'V':  compute the left Schur vectors.
!> 

JOBVSR

!>          JOBVSR is CHARACTER*1
!>          = 'N':  do not compute the right Schur vectors;
!>          = 'V':  compute the right Schur vectors.
!> 

SORT

!>          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).
!> 

SELCTG

!>          SELCTG is a LOGICAL FUNCTION of two COMPLEX*16 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 ALPHA(j)/BETA(j) is selected if
!>          SELCTG(ALPHA(j),BETA(j)) is true.
!>
!>          Note that a selected complex eigenvalue may no longer satisfy
!>          SELCTG(ALPHA(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+2 (See INFO below).
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
!> 

A

!>          A is COMPLEX*16 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

!>          LDA is INTEGER
!>          The leading dimension of A.  LDA >= max(1,N).
!> 

B

!>          B is COMPLEX*16 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

!>          LDB is INTEGER
!>          The leading dimension of B.  LDB >= max(1,N).
!> 

SDIM

!>          SDIM is INTEGER
!>          If SORT = 'N', SDIM = 0.
!>          If SORT = 'S', SDIM = number of eigenvalues (after sorting)
!>          for which SELCTG is true.
!> 

ALPHA

!>          ALPHA is COMPLEX*16 array, dimension (N)
!> 

BETA

!>          BETA is COMPLEX*16 array, dimension (N)
!>          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
!>          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
!>          j=1,...,N  are the diagonals of the complex Schur form (A,B)
!>          output by ZGGES. The  BETA(j) will be non-negative real.
!>
!>          Note: the quotients 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).
!> 

VSL

!>          VSL is COMPLEX*16 array, dimension (LDVSL,N)
!>          If JOBVSL = 'V', VSL will contain the left Schur vectors.
!>          Not referenced if JOBVSL = 'N'.
!> 

LDVSL

!>          LDVSL is INTEGER
!>          The leading dimension of the matrix VSL. LDVSL >= 1, and
!>          if JOBVSL = 'V', LDVSL >= N.
!> 

VSR

!>          VSR is COMPLEX*16 array, dimension (LDVSR,N)
!>          If JOBVSR = 'V', VSR will contain the right Schur vectors.
!>          Not referenced if JOBVSR = 'N'.
!> 

LDVSR

!>          LDVSR is INTEGER
!>          The leading dimension of the matrix VSR. LDVSR >= 1, and
!>          if JOBVSR = 'V', LDVSR >= N.
!> 

WORK

!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= max(1,2*N).
!>          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.
!> 

RWORK

!>          RWORK is DOUBLE PRECISION array, dimension (8*N)
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (N)
!>          Not referenced if SORT = 'N'.
!> 

INFO

!>          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 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: 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 ZTGSEN.
!> 

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