cggev3.f3

!>
!> CGGEV3 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).
!> 

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.
!> 

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