zgeev(3P) Sun Performance Library zgeev(3P)NAMEzgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
SYNOPSIS
SUBROUTINE ZGEEV(JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVL, JOBVR
DOUBLE COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDA, LDVL, LDVR, LDWORK, INFO
DOUBLE PRECISION WORK2(*)
SUBROUTINE ZGEEV_64(JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVL, JOBVR
DOUBLE COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDA, LDVL, LDVR, LDWORK, INFO
DOUBLE PRECISION WORK2(*)
F95 INTERFACE
SUBROUTINE GEEV(JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR, [LDVR],
[WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: A, VL, VR
INTEGER :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL(8), DIMENSION(:) :: WORK2
SUBROUTINE GEEV_64(JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR,
[LDVR], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: A, VL, VR
INTEGER(8) :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL(8), DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void zgeev(char jobvl, char jobvr, int n, doublecomplex *a, int lda,
doublecomplex *w, doublecomplex *vl, int ldvl, doublecomplex
*vr, int ldvr, int *info);
void zgeev_64(char jobvl, char jobvr, long n, doublecomplex *a, long
lda, doublecomplex *w, doublecomplex *vl, long ldvl, double‐
complex *vr, long ldvr, long *info);
PURPOSEzgeev computes for an N-by-N complex nonsymmetric matrix A, the eigen‐
values 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)
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input)
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the N-by-N matrix A. On exit, A has been overwrit‐
ten.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
W (output)
W contains the computed eigenvalues.
VL (output)
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)
The leading dimension of the array VL. LDVL >= 1; if JOBVL =
'V', LDVL >= N.
VR (output)
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)
The leading dimension of the array VR. LDVR >= 1; if JOBVR =
'V', LDVR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,2*N). For
good performance, LDWORK must generally be larger.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(2*N)
INFO (output)
= 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.
6 Mar 2009 zgeev(3P)
