zggev.f(3)

NAME
zggev.f -

SYNOPSIS

  Functions/Subroutines

subroutine zggev (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine zggev (characterJOBVL, characterJOBVR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

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

Purpose:

     ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices
     (A,B), the generalized eigenvalues, and optionally, the left and/or
     right generalized eigenvectors.

     A generalized eigenvalue for a pair of matrices (A,B) is a scalar
     lambda or a ratio alpha/beta = lambda, such that A - lambda*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.

     The right generalized eigenvector v(j) corresponding to the
     generalized eigenvalue lambda(j) of (A,B) satisfies

                  A * v(j) = lambda(j) * B * v(j).

     The left generalized eigenvector u(j) corresponding to the
     generalized eigenvalues lambda(j) of (A,B) satisfies

                  u(j)**H * A = lambda(j) * u(j)**H * B

     where u(j)**H is the conjugate-transpose of u(j).

Parameters:
    JOBVL

              JOBVL is CHARACTER*1
              = 'N':  do not compute the left generalized eigenvectors;
              = 'V':  compute the left generalized eigenvectors.

    JOBVR

              JOBVR is CHARACTER*1
              = 'N':  do not compute the right generalized eigenvectors;
              = 'V':  compute the right generalized eigenvectors.

    N

              N is INTEGER
              The order of the matrices A, B, VL, and VR.  N >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA, N)
              On entry, the matrix A in the pair (A,B).
              On exit, A has been overwritten.

    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 in the pair (A,B).
              On exit, B has been overwritten.

    LDB

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

    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.

              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).

    VL

              VL is COMPLEX*16 array, dimension (LDVL,N)
              If JOBVL = 'V', the left generalized eigenvectors u(j) are
              stored one after another in the columns of VL, in the same
              order as their eigenvalues.
              Each eigenvector is scaled so the largest component has
              abs(real part) + abs(imag. part) = 1.
              Not referenced if JOBVL = 'N'.

    LDVL

              LDVL is INTEGER
              The leading dimension of the matrix VL. LDVL >= 1, and
              if JOBVL = 'V', LDVL >= N.

    VR

              VR is COMPLEX*16 array, dimension (LDVR,N)
              If JOBVR = 'V', the right generalized eigenvectors v(j) are
              stored one after another in the columns of VR, in the same
              order as their eigenvalues.
              Each eigenvector is scaled so the largest component has
              abs(real part) + abs(imag. part) = 1.
              Not referenced if JOBVR = 'N'.

    LDVR

              LDVR is INTEGER
              The leading dimension of the matrix VR. LDVR >= 1, and
              if JOBVR = 'V', LDVR >= 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)

    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.  No eigenvectors have been
                    calculated, but ALPHA(j) and BETA(j) should be
                    correct for j=INFO+1,...,N.
              > N:  =N+1: other then QZ iteration failed in DHGEQZ,
                    =N+2: error return from DTGEVC.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    April 2012

Definition at line 217 of file zggev.f.

Author

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