SRC/cggev.f(3)

NAME
SRC/cggev.f

SYNOPSIS

  Functions/Subroutines
subroutine cggev (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
CGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine cggev (character jobvl, character jobvr, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) alpha, complex, dimension( * ) beta, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

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

Purpose:

     CGGEV 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 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 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 array, dimension (N)

    BETA

              BETA is COMPLEX 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 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 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 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)

    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 CHGEQZ,
                    =N+2: error return from CTGEVC.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 215 of file cggev.f.

Author

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