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(*)
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
#include <sunperf.h>
void shsein(char side, char eigsrc, char initv, logical *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, logical *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.
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
= '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 containing 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 diagonal blocks. In this case, SHSEIN must always perform inverse iteration using the whole matrix H.
= 'N': no initial vectors are supplied;
= 'U': user-supplied initial vectors are stored in the arrays VL and/or VR.
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
.TRUE.; then on exit SELECT(j)
is .TRUE. and SELECT(j+1)
is
.FALSE..
column(s)
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
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.
max(1,N)
if SIDE = 'L' or 'B'; LDVL > = 1 otherwise.
column(s)
in which the eigenvector will
be stored.
On exit, if SIDE = 'R' or 'B', the right eigenvectors
specified by SELECT will be stored consecutively 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.
max(1,N)
if SIDE = 'R' or 'B'; LDVR > = 1 otherwise.
dimension((N+2)*N)
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 converged 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(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 converged 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.
= 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.
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|.