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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| 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
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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.
If a NaN is detected in H, the routine will return with INFO=-6. |
| [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 247 of file chsein.f.
1.8.10