zhsein (3)  Linux Manuals
NAME
zhsein.f 
SYNOPSIS
Functions/Subroutines
subroutine zhsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
ZHSEIN
Function/Subroutine Documentation
subroutine zhsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( * )SELECT, integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16, dimension( * )W, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)
ZHSEIN
Purpose:

ZHSEIN 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
SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors.
EIGSRCEIGSRC is CHARACTER*1 Specifies the source of eigenvalues supplied in W: = 'Q': the eigenvalues were found using ZHSEQR; thus, if H has zero subdiagonal elements, and so is blocktriangular, then the jth eigenvalue can be assumed to be an eigenvalue of the block containing the jth row/column. This property allows ZHSEIN 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, ZHSEIN must always perform inverse iteration using the whole matrix H.
INITVINITV is CHARACTER*1 = 'N': no initial vectors are supplied; = 'U': usersupplied initial vectors are stored in the arrays VL and/or VR.
SELECTSELECT 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..
NN is INTEGER The order of the matrix H. N >= 0.
HH is COMPLEX*16 array, dimension (LDH,N) The upper Hessenberg matrix H. If a NaN is detected in H, the routine will return with INFO=6.
LDHLDH is INTEGER The leading dimension of the array H. LDH >= max(1,N).
WW is COMPLEX*16 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.
VLVL is COMPLEX*16 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.
LDVLLDVL is INTEGER The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
VRVR is COMPLEX*16 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.
LDVRLDVR is INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
MMMM is INTEGER The number of columns in the arrays VL and/or VR. MM >= M.
MM 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).
WORKWORK is COMPLEX*16 array, dimension (N*N)
RWORKRWORK is DOUBLE PRECISION array, dimension (N)
IFAILLIFAILL is INTEGER array, dimension (MM) If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvector in the ith 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.
IFAILRIFAILR is INTEGER array, dimension (MM) If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigenvector in the ith 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2013
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 244 of file zhsein.f.
Author
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