Contents
shsein - use inverse iteration to find specified right
and/or left eigenvectors of a real upper Hessenberg matrix H
SUBROUTINE SHSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL,
LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
CHARACTER * 1 SIDE, EIGSRC, INITV
INTEGER N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER IFAILL(*), IFAILR(*)
LOGICAL SELECT(*)
REAL H(LDH,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
SUBROUTINE SHSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI,
VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
CHARACTER * 1 SIDE, EIGSRC, INITV
INTEGER*8 N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER*8 IFAILL(*), IFAILR(*)
LOGICAL*8 SELECT(*)
REAL H(LDH,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
F95 INTERFACE
SUBROUTINE HSEIN(SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], WR, WI,
VL, [LDVL], VR, [LDVR], MM, M, [WORK], IFAILL, IFAILR, [INFO])
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
INTEGER :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER, DIMENSION(:) :: IFAILL, IFAILR
LOGICAL, DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: WR, WI, WORK
REAL, DIMENSION(:,:) :: H, VL, VR
SUBROUTINE HSEIN_64(SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], WR,
WI, VL, [LDVL], VR, [LDVR], MM, M, [WORK], IFAILL, IFAILR, [INFO])
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
INTEGER(8) :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER(8), DIMENSION(:) :: IFAILL, IFAILR
LOGICAL(8), DIMENSION(:) :: SELECT
REAL, DIMENSION(:) :: WR, WI, WORK
REAL, DIMENSION(:,:) :: H, VL, VR
C INTERFACE
#include <sunperf.h>
void shsein(char side, char eigsrc, char initv, int *select,
int n, float *h, int ldh, float *wr, float *wi,
float *vl, int ldvl, float *vr, int ldvr, int mm,
int *m, int *ifaill, int *ifailr, int *info);
void shsein_64(char side, char eigsrc, char initv, long
*select, long n, float *h, long ldh, float *wr,
float *wi, float *vl, long ldvl, float *vr, long
ldvr, long mm, long *m, long *ifaill, long
*ifailr, long *info);
shsein uses inverse iteration to find specified right and/or
left eigenvectors of a real upper Hessenberg matrix H.
The right eigenvector x and the left eigenvector y of the
matrix H corresponding to an eigenvalue w are defined by:
H * x = w * x, y**h * H = w * y**h
where y**h denotes the conjugate transpose of the vector y.
SIDE (input)
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
EIGSRC (input)
Specifies the source of eigenvalues supplied in
(WR,WI):
= 'Q': the eigenvalues were found using SHSEQR;
thus, if H has zero subdiagonal elements, and so
is block-triangular, then the j-th eigenvalue can
be assumed to be an eigenvalue of the block con-
taining the j-th row/column. This property allows
SHSEIN to perform inverse iteration on just one
diagonal block. = 'N': no assumptions are made on
the correspondence between eigenvalues and diago-
nal blocks. In this case, SHSEIN must always per-
form inverse iteration using the whole matrix H.
INITV (input)
= 'N': no initial vectors are supplied;
= 'U': user-supplied initial vectors are stored in
the arrays VL and/or VR.
SELECT (input/output)
Specifies the eigenvectors to be computed. To
select the real eigenvector corresponding to a
real eigenvalue WR(j), SELECT(j) must be set to
.TRUE.. To select the complex eigenvector
corresponding to a complex eigenvalue
(WR(j),WI(j)), with complex conjugate
(WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1)
or both must be set to
N (input) The order of the matrix H. N >= 0.
H (input) The upper Hessenberg matrix H.
LDH (input)
The leading dimension of the array H. LDH >=
max(1,N).
WR (input/output)
On entry, the real and imaginary parts of the
eigenvalues of H; a complex conjugate pair of
eigenvalues must be stored in consecutive elements
of WR and WI. On exit, WR may have been altered
since close eigenvalues are perturbed slightly in
searching for independent eigenvectors.
WI (input)
See the description of WR.
VL (input/output)
On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL
must contain starting vectors for the inverse
iteration for the left eigenvectors; the starting
vector for each eigenvector must be in the same
column(s) in which the eigenvector will be stored.
On exit, if SIDE = 'L' or 'B', the left eigenvec-
tors specified by SELECT will be stored consecu-
tively in the columns of VL, in the same order as
their eigenvalues. A complex eigenvector
corresponding to a complex eigenvalue is stored in
two consecutive columns, the first holding the
real part and the second the imaginary part. If
SIDE = 'R', VL is not referenced.
LDVL (input)
The leading dimension of the array VL. LDVL >=
max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 other-
wise.
VR (input/output)
On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR
must contain starting vectors for the inverse
iteration for the right eigenvectors; the starting
vector for each eigenvector must be in the same
column(s) in which the eigenvector will be stored.
On exit, if SIDE = 'R' or 'B', the right eigenvec-
tors specified by SELECT will be stored consecu-
tively in the columns of VR, in the same order as
their eigenvalues. A complex eigenvector
corresponding to a complex eigenvalue is stored in
two consecutive columns, the first holding the
real part and the second the imaginary part. If
SIDE = 'L', VR is not referenced.
LDVR (input)
The leading dimension of the array VR. LDVR >=
max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 other-
wise.
MM (input)
The number of columns in the arrays VL and/or VR.
MM >= M.
M (output)
The number of columns in the arrays VL and/or VR
required to store the eigenvectors; each selected
real eigenvector occupies one column and each
selected complex eigenvector occupies two columns.
WORK (workspace)
dimension((N+2)*N)
IFAILL (output)
If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the
left eigenvector in the i-th column of VL
(corresponding to the eigenvalue w(j)) failed to
converge; IFAILL(i) = 0 if the eigenvector con-
verged satisfactorily. If the i-th and (i+1)th
columns of VL hold a complex eigenvector, then
IFAILL(i) and IFAILL(i+1) are set to the same
value. If SIDE = 'R', IFAILL is not referenced.
IFAILR (output)
If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the
right eigenvector in the i-th column of VR
(corresponding to the eigenvalue w(j)) failed to
converge; IFAILR(i) = 0 if the eigenvector con-
verged satisfactorily. If the i-th and (i+1)th
columns of VR hold a complex eigenvector, then
IFAILR(i) and IFAILR(i+1) are set to the same
value. If SIDE = 'L', IFAILR is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: if INFO = i, i is the number of eigenvectors
which failed to converge; see IFAILL and IFAILR
for further details.
Each eigenvector is normalized so that the element of larg-
est magnitude has magnitude 1; here the magnitude of a com-
plex number (x,y) is taken to be |x|+|y|.