dgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
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(*)
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
#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, double *wr, double *wi, double *vl, long ldvl, double *vr, long ldvr, long *info);
dgeev computes for an N-by-N real 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.
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of A are computed.
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
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).
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).
WORK(1)
returns the optimal LDWORK.
If LDWORK = -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 LDWORK is issued by XERBLA.
= 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.