 |
LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
|
|
LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
|
Go to the source code of this file.
Functions/Subroutines | |
| subroutine | CHSEIN (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO) |
| CHSEIN | |
| subroutine CHSEIN | ( | CHARACTER | SIDE, |
| CHARACTER | EIGSRC, | ||
| CHARACTER | INITV, | ||
| LOGICAL, dimension( * ) | SELECT, | ||
| INTEGER | N, | ||
| COMPLEX, dimension( ldh, * ) | H, | ||
| INTEGER | LDH, | ||
| COMPLEX, dimension( * ) | W, | ||
| COMPLEX, dimension( ldvl, * ) | VL, | ||
| INTEGER | LDVL, | ||
| COMPLEX, dimension( ldvr, * ) | VR, | ||
| INTEGER | LDVR, | ||
| INTEGER | MM, | ||
| INTEGER | M, | ||
| COMPLEX, dimension( * ) | WORK, | ||
| REAL, dimension( * ) | RWORK, | ||
| INTEGER, dimension( * ) | IFAILL, | ||
| INTEGER, dimension( * ) | IFAILR, | ||
| INTEGER | INFO | ||
| ) |
CHSEIN
Download CHSEIN + dependencies [TGZ] [ZIP] [TXT]
CHSEIN 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
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.
| [in] | SIDE |
SIDE is CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
|
| [in] | EIGSRC |
EIGSRC is CHARACTER*1
Specifies the source of eigenvalues supplied in W:
= 'Q': the eigenvalues were found using CHSEQR; 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 CHSEIN 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, CHSEIN must always perform inverse iteration
using the whole matrix H.
|
| [in] | INITV |
INITV is CHARACTER*1
= 'N': no initial vectors are supplied;
= 'U': user-supplied initial vectors are stored in the arrays
VL and/or VR.
|
| [in] | SELECT |
SELECT is LOGICAL array, dimension (N)
Specifies the eigenvectors to be computed. To select the
eigenvector corresponding to the eigenvalue W(j),
SELECT(j) must be set to .TRUE..
|
| [in] | N |
N is INTEGER
The order of the matrix H. N >= 0.
|
| [in] | H |
H is COMPLEX array, dimension (LDH,N)
The upper Hessenberg matrix H.
|
| [in] | LDH |
LDH is INTEGER
The leading dimension of the array H. LDH >= max(1,N).
|
| [in,out] | W |
W is COMPLEX array, dimension (N)
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.
|
| [in,out] | VL |
VL is COMPLEX array, dimension (LDVL,MM)
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 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.
If SIDE = 'R', VL is not referenced.
|
| [in] | LDVL |
LDVL is INTEGER
The leading dimension of the array VL.
LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
|
| [in,out] | VR |
VR is COMPLEX array, dimension (LDVR,MM)
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 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.
If SIDE = 'L', VR is not referenced.
|
| [in] | LDVR |
LDVR is INTEGER
The leading dimension of the array VR.
LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
|
| [in] | MM |
MM is INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
|
| [out] | M |
M is INTEGER
The number of columns in the arrays VL and/or VR required to
store the eigenvectors (= the number of .TRUE. elements in
SELECT).
|
| [out] | WORK |
WORK is COMPLEX array, dimension (N*N)
|
| [out] | RWORK |
RWORK is REAL array, dimension (N)
|
| [out] | IFAILL |
IFAILL is INTEGER array, dimension (MM)
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 SIDE = 'R', IFAILL is not referenced.
|
| [out] | IFAILR |
IFAILR is INTEGER array, dimension (MM)
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 SIDE = 'L', IFAILR is not referenced.
|
| [out] | INFO |
INFO is INTEGER
= 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|.
Definition at line 243 of file chsein.f.
1.7.6.1