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-- LAPACK driver routine (version 3.0) --

Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

Courant Institute, Argonne National Lab, and Rice University

June 30, 1999

Purpose

=======

ZGEEV 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.

Arguments

=========

JOBVL (input) CHARACTER*1

= 'N': left eigenvectors of A are not computed;

= 'V': left eigenvectors of are computed.

JOBVR (input) CHARACTER*1

= 'N': right eigenvectors of A are not computed;

= 'V': right eigenvectors of A are computed.

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input/output) COMPLEX*16 array, dimension (LDA,N)

On entry, the N-by-N matrix A.

On exit, A has been overwritten.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

W (output) COMPLEX*16 array, dimension (N)

W contains the computed eigenvalues.

VL (output) COMPLEX*16 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.

LDVL (input) INTEGER

The leading dimension of the array VL. LDVL >= 1; if

JOBVL = 'V', LDVL >= N.

VR (output) COMPLEX*16 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.

LDVR (input) INTEGER

The leading dimension of the array VR. LDVR >= 1; if

JOBVR = 'V', LDVR >= N.

WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK (input) 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 (workspace) DOUBLE PRECISION array, dimension (2*N)

INFO (output) 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 and i+1:N of W contain eigenvalues which have

converged.