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zgeev.f(3) LAPACK zgeev.f(3)

NAME

zgeev.f -

SYNOPSIS

Functions/Subroutines


subroutine zgeev (JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

subroutine zgeev (characterJOBVL, characterJOBVR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )W, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

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

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.

Parameters:

JOBVL


JOBVL is CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.

JOBVR


JOBVR is CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.

N


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

A


A is COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.

LDA


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

W


W is COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.

VL


VL is 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


LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.

VR


VR is 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


LDVR is INTEGER
The leading dimension of the array VR. LDVR >= 1; 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 (2*N)

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 and i+1:N of W contain eigenvalues which have
converged.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 177 of file zgeev.f.

Author

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Tue Sep 25 2012 Version 3.4.2