subroutine chsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHSEIN
CHSEIN
Purpose:
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.
Parameters:
SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors.
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.
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.
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..
N
N is INTEGER The order of the matrix H. N >= 0.
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.
LDH
LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N).
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.
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.
LDVL
LDVL is INTEGER The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
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.
LDVR
LDVR is INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
MM
MM is INTEGER The number of columns in the arrays VL and/or VR. MM >= M.
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).
WORK
WORK is COMPLEX array, dimension (N*N)
RWORK
RWORK is REAL array, dimension (N)
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.
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.
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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
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