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zggesx.f(3) LAPACK zggesx.f(3)

zggesx.f -


subroutine zggesx (JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA, B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, RWORK, IWORK, LIWORK, BWORK, INFO)
 
ZGGESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

ZGGESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices
Purpose:
 ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices
 (A,B), the generalized eigenvalues, the complex 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)**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; 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 complex Schur form if T is upper triangular with non-negative diagonal and S is upper triangular.
Parameters:
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 procedure) 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.
          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+3 see INFO below).
SENSE
          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'.
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) and BETA(j),j=1,...,N  are
          the diagonals of the complex Schur form (S,T).  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.
RCONDE
          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'.
RCONDV
          RCONDV is DOUBLE PRECISION array, dimension ( 2 )
          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
          reciprocal condition number for the selected deflating
          subspaces.
          Not referenced if SENSE = 'N' or 'E'.
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.
          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B',
          LWORK >= MAX(1,2*N,2*SDIM*(N-SDIM)), else
          LWORK >= MAX(1,2*N).  Note that 2*SDIM*(N-SDIM) <= N*N/2.
          Note also that an error is only returned if
          LWORK < MAX(1,2*N), 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.
RWORK
          RWORK is DOUBLE PRECISION array, dimension ( 8*N )
          Real workspace.
IWORK
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
LIWORK
          LIWORK is INTEGER
          The dimension of the array IWORK.
          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise
          LIWORK >= N+2.
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
          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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 328 of file zggesx.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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