zggev.f(3)							      LAPACK								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
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013							zggev.f(3)