dgeev(3P) Sun Performance Library dgeev(3P)NAMEdgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues and, optionally, the left and/or right eigenvectors
SYNOPSIS
SUBROUTINE DGEEV(JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR,
WORK, LDWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
INTEGER N, LDA, LDVL, LDVR, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
SUBROUTINE DGEEV_64(JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
LDVR, WORK, LDWORK, INFO)
CHARACTER * 1 JOBVL, JOBVR
INTEGER*8 N, LDA, LDVL, LDVR, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
F95 INTERFACE
SUBROUTINE GEEV(JOBVL, JOBVR, [N], A, [LDA], WR, WI, VL, [LDVL], VR,
[LDVR], [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
INTEGER :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, VL, VR
SUBROUTINE GEEV_64(JOBVL, JOBVR, [N], A, [LDA], WR, WI, VL, [LDVL],
VR, [LDVR], [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
INTEGER(8) :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: A, VL, VR
C INTERFACE
#include <sunperf.h>
void dgeev(char jobvl, char jobvr, int n, double *a, int lda, double
*wr, double *wi, double *vl, int ldvl, double *vr, int ldvr,
int *info);
void dgeev_64(char jobvl, char jobvr, long n, double *a, long lda, dou‐
ble *wr, double *wi, double *vl, long ldvl, double *vr, long
ldvr, long *info);
PURPOSEdgeev computes for an N-by-N real nonsymmetric matrix A, the eigenval‐
ues 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 A 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).
WR (output)
WR and WI contain the real and imaginary parts, respectively,
of the computed eigenvalues. Complex conjugate pairs of ei‐
genvalues appear consecutively with the eigenvalue having the
positive imaginary part first.
WI (output)
See the description for WR.
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. If
the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th
column of VL. If the j-th and (j+1)-st eigenvalues form a
complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
u(j+1) = VL(:,j) - i*VL(:,j+1).
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. If
the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th
column of VR. If the j-th and (j+1)-st eigenvalues form a
complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
v(j+1) = VR(:,j) - i*VR(:,j+1).
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(1,3*N), and
if JOBVL = 'V' or JOBVR = 'V', LDWORK >= 4*N. For good per‐
formance, 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.
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
i+1:N of WR and WI contain eigenvalues which have converged.
6 Mar 2009 dgeev(3P)
