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## zggev()

subroutine zggev | ( | character | jobvl,
|  | character | jobvr,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex*16, dimension( * ) | alpha,
|  | complex*16, dimension( * ) | beta,
|  | complex*16, dimension( ldvl, * ) | vl,
|  | integer | ldvl,
|  | complex*16, dimension( ldvr, * ) | vr,
|  | integer | ldvr,
|  | complex*16, dimension( * ) | work,
|  | integer | lwork,
|  | double precision, dimension( * ) | rwork,
|  | integer | info )

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

Download ZGGEV + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  JOBVL

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

  [in]

  JOBVR

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

  [in]

  N

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

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [in,out]

  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.
      !>

  [in]

  LDB

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

  [out]

  ALPHA

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

  [out]

  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).
      !>

  [out]

  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'.
      !>

  [in]

  LDVL

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

  [out]

  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'.
      !>

  [in]

  LDVR

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

  [out]

  WORK

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

  [in]

  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.
      !>

  [out]

  RWORK

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

  [out]

  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 ZHGEQZ,
      !>                =N+2: error return from ZTGEVC.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.