shsein
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.
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* SIDE (input)
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* EIGSRC (input)
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Specifies the source of eigenvalues supplied in (WR,WI):
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* INITV (input)
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* SELECT (input/output)
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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
.TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is
.FALSE..
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* N (input)
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The order of the matrix H. N >= 0.
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* H (input)
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The upper Hessenberg matrix H.
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* LDH (input)
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The leading dimension of the array H. LDH >= max(1,N).
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* WR (input/output)
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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.
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* WI (input)
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See the description of WR.
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* VL (input/output)
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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 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.
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* LDVL (input)
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The leading dimension of the array VL.
LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
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* VR (input/output)
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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 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.
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* LDVR (input)
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The leading dimension of the array VR.
LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
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* MM (input)
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The number of columns in the arrays VL and/or VR. MM >= M.
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* M (output)
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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.
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* WORK (workspace)
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dimension((N+2)*N)
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* IFAILL (output)
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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 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.
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* IFAILR (output)
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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 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.
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* INFO (output)
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