zhsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
SUBROUTINE ZHSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) CHARACTER*1 SIDE, EIGSRC, INITV DOUBLE COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*) INTEGER N, LDH, LDVL, LDVR, MM, M, INFO INTEGER IFAILL(*), IFAILR(*) LOGICAL SELECT(*) DOUBLE PRECISION RWORK(*) SUBROUTINE ZHSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) CHARACTER*1 SIDE, EIGSRC, INITV DOUBLE COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*) INTEGER*8 N, LDH, LDVL, LDVR, MM, M, INFO INTEGER*8 IFAILL(*), IFAILR(*) LOGICAL*8 SELECT(*) DOUBLE PRECISION RWORK(*) F95 INTERFACE SUBROUTINE HSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV COMPLEX(8), DIMENSION(:) :: W, WORK COMPLEX(8), DIMENSION(:,:) :: H, VL, VR INTEGER :: N, LDH, LDVL, LDVR, MM, M, INFO INTEGER, DIMENSION(:) :: IFAILL, IFAILR LOGICAL, DIMENSION(:) :: SELECT REAL(8), DIMENSION(:) :: RWORK SUBROUTINE HSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV COMPLEX(8), DIMENSION(:) :: W, WORK COMPLEX(8), DIMENSION(:,:) :: H, VL, VR INTEGER(8) :: N, LDH, LDVL, LDVR, MM, M, INFO INTEGER(8), DIMENSION(:) :: IFAILL, IFAILR LOGICAL(8), DIMENSION(:) :: SELECT REAL(8), DIMENSION(:) :: RWORK C INTERFACE #include <sunperf.h> void zhsein(char side, char eigsrc, char initv, int *select, int n, doublecomplex *h, int ldh, doublecomplex *w, doublecomplex *vl, int ldvl, doublecomplex *vr, int ldvr, int mm, int *m, int *ifaill, int *ifailr, int *info); void zhsein_64(char side, char eigsrc, char initv, long *select, long n, doublecomplex *h, long ldh, doublecomplex *w, doublecom- plex *vl, long ldvl, doublecomplex *vr, long ldvr, long mm, long *m, long *ifaill, long *ifailr, long *info);
Oracle Solaris Studio Performance Library zhsein(3P)
NAME
zhsein - use inverse iteration to find specified right and/or left
eigenvectors of a complex upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE ZHSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHARACTER*1 SIDE, EIGSRC, INITV
DOUBLE COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER IFAILL(*), IFAILR(*)
LOGICAL SELECT(*)
DOUBLE PRECISION RWORK(*)
SUBROUTINE ZHSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHARACTER*1 SIDE, EIGSRC, INITV
DOUBLE COMPLEX H(LDH,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER*8 IFAILL(*), IFAILR(*)
LOGICAL*8 SELECT(*)
DOUBLE PRECISION RWORK(*)
F95 INTERFACE
SUBROUTINE HSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
COMPLEX(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: H, VL, VR
INTEGER :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER, DIMENSION(:) :: IFAILL, IFAILR
LOGICAL, DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: RWORK
SUBROUTINE HSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W,
VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR,
INFO)
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
COMPLEX(8), DIMENSION(:) :: W, WORK
COMPLEX(8), DIMENSION(:,:) :: H, VL, VR
INTEGER(8) :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER(8), DIMENSION(:) :: IFAILL, IFAILR
LOGICAL(8), DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void zhsein(char side, char eigsrc, char initv, int *select, int n,
doublecomplex *h, int ldh, doublecomplex *w, doublecomplex
*vl, int ldvl, doublecomplex *vr, int ldvr, int mm, int *m,
int *ifaill, int *ifailr, int *info);
void zhsein_64(char side, char eigsrc, char initv, long *select, long
n, doublecomplex *h, long ldh, doublecomplex *w, doublecom-
plex *vl, long ldvl, doublecomplex *vr, long ldvr, long mm,
long *m, long *ifaill, long *ifailr, long *info);
PURPOSE
zhsein uses inverse iteration to find specified right and/or left
eigenvectors of a complex upper Hessenberg matrix H.
The right eigenvector x and the left eigenvector y of the matrix H cor-
responding 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.
ARGUMENTS
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 W:
= 'Q': the eigenvalues were found using ZHSEQR; 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 containing the j-th row/column. This property
allows ZHSEIN to perform inverse iteration on just one diago-
nal block. = 'N': no assumptions are made on the correspon-
dence between eigenvalues and diagonal blocks. In this case,
ZHSEIN must always perform 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)
Specifies the eigenvectors to be computed. To select the
eigenvector corresponding to the eigenvalue W(j), SELECT(j)
must be set to .TRUE..
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).
W (input/output)
On entry, the eigenvalues of H. On exit, the real parts of W
may have been altered since close eigenvalues are perturbed
slightly in searching for independent eigenvectors.
VL (input/output)
On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must con-
tain starting vectors for the inverse iteration for the left
eigenvectors; the starting vector for each eigenvector must
be in the same column in which the eigenvector will be
stored. On exit, if SIDE = 'L' or 'B', the left eigenvectors
specified by SELECT will be stored consecutively in the col-
umns of VL, in the same order as their eigenvalues. 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 otherwise.
VR (input/output)
On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must con-
tain starting vectors for the inverse iteration for the right
eigenvectors; the starting vector for each eigenvector must
be in the same column in which the eigenvector will be
stored. On exit, if SIDE = 'R' or 'B', the right eigenvec-
tors specified by SELECT will be stored consecutively in the
columns of VR, in the same order as their eigenvalues. 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 otherwise.
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 (= the number of .TRUE. elements in
SELECT).
WORK (workspace)
dimension(N*N)
RWORK (workspace)
dimension(N)
IFAILL (output) INTEGER array, dimension (MM)
If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvec-
tor in the i-th column of VL (corresponding to the eigenvalue
w(j)) failed to converge; IFAILL(i) = 0 if the eigenvector
converged satisfactorily. If SIDE = 'R', IFAILL is not ref-
erenced.
IFAILR (output) INTEGER array, dimension (MM)
If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigen-
vector in the i-th column of VR (corresponding to the eigen-
value w(j)) failed to converge; IFAILR(i) = 0 if the eigen-
vector converged satisfactorily. If SIDE = 'L', IFAILR is
not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, i is the number of eigenvectors which
failed to converge; see IFAILL and IFAILR for further
details.
FURTHER DETAILS
Each eigenvector is normalized so that the element of largest magnitude
has magnitude 1; here the magnitude of a complex number (x,y) is taken
to be |x|+|y|.
7 Nov 2015 zhsein(3P)