Contents
sgeev - compute for an N-by-N real nonsymmetric matrix A,
the eigenvalues and, optionally, the left and/or right
eigenvectors
SUBROUTINE SGEEV(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
REAL A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE SGEEV_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
REAL 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, DIMENSION(:) :: WR, WI, WORK
REAL, 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, DIMENSION(:) :: WR, WI, WORK
REAL, DIMENSION(:,:) :: A, VL, VR
C INTERFACE
#include <sunperf.h>
void sgeev(char jobvl, char jobvr, int n, float *a, int lda,
float *wr, float *wi, float *vl, int ldvl, float
*vr, int ldvr, int *info);
void sgeev_64(char jobvl, char jobvr, long n, float *a, long
lda, float *wr, float *wi, float *vl, long ldvl,
float *vr, long ldvr, long *info);
sgeev computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvec-
tors.
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.
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 overwritten.
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. Com-
plex conjugate pairs of eigenvalues appear con-
secutively 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 (input)
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 performance, LDWORK must
generally be larger.
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.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: if INFO = i, the QR algorithm failed to com-
pute all the eigenvalues, and no eigenvectors have
been computed; elements i+1:N of WR and WI contain
eigenvalues which have converged.