zgegs.f(3)

NAME
zgegs.f -

SYNOPSIS

  Functions/Subroutines

subroutine zgegs (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO)
ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine zgegs (characterJOBVSL, characterJOBVSR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvsl, * )VSL, integerLDVSL, complex*16, dimension( ldvsr, * )VSR, integerLDVSR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

     This routine is deprecated and has been replaced by routine ZGGES.

     ZGEGS computes the eigenvalues, Schur form, and, optionally, the
     left and or/right Schur vectors of a complex matrix pair (A,B).
     Given two square matrices A and B, the generalized Schur
     factorization has the form

        A = Q*S*Z**H,  B = Q*T*Z**H

     where Q and Z are unitary matrices and S and T are upper triangular.
     The columns of Q are the left Schur vectors
     and the columns of Z are the right Schur vectors.

     If only the eigenvalues of (A,B) are needed, the driver routine
     ZGEGV should be used instead.  See ZGEGV for a description of the
     eigenvalues of the generalized nonsymmetric eigenvalue problem
     (GNEP).

Parameters:
    JOBVSL

              JOBVSL is CHARACTER*1
              = 'N':  do not compute the left Schur vectors;
              = 'V':  compute the left Schur vectors (returned in VSL).

    JOBVSR

              JOBVSR is CHARACTER*1
              = 'N':  do not compute the right Schur vectors;
              = 'V':  compute the right Schur vectors (returned in VSR).

    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 matrix A.
              On exit, the upper triangular matrix S from the generalized
              Schur factorization.

    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 matrix B.
              On exit, the upper triangular matrix T from the generalized
              Schur factorization.

    LDB

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

    ALPHA

              ALPHA is COMPLEX*16 array, dimension (N)
              The complex scalars alpha that define the eigenvalues of
              GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
              form of A.

    BETA

              BETA is COMPLEX*16 array, dimension (N)
              The non-negative real scalars beta that define the
              eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
              of the triangular factor T.

              Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
              represent the j-th eigenvalue of the matrix pair (A,B), in
              one of the forms lambda = alpha/beta or mu = beta/alpha.
              Since either lambda or mu may overflow, they should not,
              in general, be computed.

    VSL

              VSL is COMPLEX*16 array, dimension (LDVSL,N)
              If JOBVSL = 'V', the matrix of left Schur vectors Q.
              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', the matrix of right Schur vectors Z.
              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.
              To compute the optimal value of LWORK, call ILAENV to get
              blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:
              NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
              the optimal LWORK is N*(NB+1).

              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 (3*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:  errors that usually indicate LAPACK problems:
                    =N+1: error return from ZGGBAL
                    =N+2: error return from ZGEQRF
                    =N+3: error return from ZUNMQR
                    =N+4: error return from ZUNGQR
                    =N+5: error return from ZGGHRD
                    =N+6: error return from ZHGEQZ (other than failed
                                                   iteration)
                    =N+7: error return from ZGGBAK (computing VSL)
                    =N+8: error return from ZGGBAK (computing VSR)
                    =N+9: error return from ZLASCL (various places)

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 224 of file zgegs.f.

Author

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