zggev3()

subroutine zggev3	(	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 )

ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

Download ZGGEV3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZGGEV3 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.