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chsein-f(3)

chsein.f –

Synopsis

Functions/Subroutines

subroutine chsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHSEIN

Function/Subroutine Documentation

subroutine chsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( * )SELECT, integerN, complex, dimension( ldh, * )H, integerLDH, complex, dimension( * )W, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)

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

 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.

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

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.

Author

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