CGEEV (3) Linux Manual Page

cgeev.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

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

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:

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 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 array, dimension (N)

 W contains the computed eigenvalues.

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.

LDVL

 LDVL is INTEGER

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

 JOBVL = ‘V’, LDVL >= N.

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.

LDVR

 LDVR is INTEGER

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

 JOBVR = ‘V’, LDVR >= N.

WORK

 WORK is COMPLEX 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 REAL 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 cgeev.f.

Author

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