cgeev()

subroutine cgeev	(	character	jobvl,
		character	jobvr,
		integer	n,
		complex, dimension( lda, * )	a,
		integer	lda,
		complex, dimension( * )	w,
		complex, dimension( ldvl, * )	vl,
		integer	ldvl,
		complex, dimension( ldvr, * )	vr,
		integer	ldvr,
		complex, dimension( * )	work,
		integer	lwork,
		real, dimension( * )	rwork,
		integer	info )

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

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Purpose:

!>
!> CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
!> eigenvalues and, optionally, the left and/or right eigenvectors.
!>
!> The right eigenvector v(j) of A satisfies
!>                  A * v(j) = lambda(j) * v(j)
!> where lambda(j) is its eigenvalue.
!> The left eigenvector u(j) of A satisfies
!>               u(j)**H * A = lambda(j) * u(j)**H
!> where u(j)**H denotes the conjugate transpose of u(j).
!>
!> The computed eigenvectors are normalized to have Euclidean norm
!> equal to 1 and largest component real.
!> 

Parameters

[in]	JOBVL	!> JOBVL is CHARACTER*1 !> = 'N': left eigenvectors of A are not computed; !> = 'V': left eigenvectors of are computed. !>
[in]	JOBVR	!> JOBVR is CHARACTER*1 !> = 'N': right eigenvectors of A are not computed; !> = 'V': right eigenvectors of A are computed. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in,out]	A	!> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> On exit, A has been overwritten. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	W	!> W is COMPLEX array, dimension (N) !> W contains the computed eigenvalues. !>
[out]	VL	!> VL is COMPLEX array, dimension (LDVL,N) !> If JOBVL = 'V', the left eigenvectors u(j) are stored one !> after another in the columns of VL, in the same order !> as their eigenvalues. !> If JOBVL = 'N', VL is not referenced. !> u(j) = VL(:,j), the j-th column of VL. !>
[in]	LDVL	!> LDVL is INTEGER !> The leading dimension of the array VL. LDVL >= 1; if !> JOBVL = 'V', LDVL >= N. !>
[out]	VR	!> VR is COMPLEX array, dimension (LDVR,N) !> If JOBVR = 'V', the right eigenvectors v(j) are stored one !> after another in the columns of VR, in the same order !> as their eigenvalues. !> If JOBVR = 'N', VR is not referenced. !> v(j) = VR(:,j), the j-th column of VR. !>
[in]	LDVR	!> LDVR is INTEGER !> The leading dimension of the array VR. LDVR >= 1; if !> JOBVR = 'V', LDVR >= N. !>
[out]	WORK	!> WORK is COMPLEX 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 REAL array, dimension (2*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if INFO = i, the QR algorithm failed to compute all the !> eigenvalues, and no eigenvectors have been computed; !> elements i+1:N of W contain eigenvalues which have !> converged. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.