SRC/cggev3.f(3)            Library Functions Manual            SRC/cggev3.f(3)

NAME
       SRC/cggev3.f

SYNOPSIS
   Functions/Subroutines
       subroutine cggev3 (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl,
           ldvl, vr, ldvr, work, lwork, rwork, info)
            CGGEV3 computes the eigenvalues and, optionally, the left and/or
           right eigenvectors for GE matrices (blocked algorithm)

Function/Subroutine Documentation
   subroutine cggev3 (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)
        CGGEV3 computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for GE matrices (blocked algorithm)

       Purpose:


            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).

       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.

                     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 214 of file cggev3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/cggev3.f(3)