chsein.f (3) Linux Manual Page

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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