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hsein

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
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)
subroutine dhsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, double precision, dimension(ldh, * ) h, integer ldh, double precision, dimension( * ) wr, doubleprecision, dimension( * ) wi, double precision, dimension( ldvl, * )vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integerldvr, integer mm, integer m, double precision, dimension( * ) work,integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integerinfo)
subroutine shsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, real, dimension( ldh, * ) h,integer ldh, real, dimension( * ) wr, real, dimension( * ) wi, real,dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr,integer ldvr, integer mm, integer m, real, dimension( * ) work,integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integerinfo)
subroutine zhsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, complex*16, dimension( ldh,* ) h, integer ldh, complex*16, dimension( * ) w, complex*16,dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * )vr, integer ldvr, integer mm, integer m, complex*16, dimension( * )work, double precision, dimension( * ) rwork, integer, dimension( * )ifaill, integer, dimension( * ) ifailr, integer info)
Author

NAME

hsein - hsein: Hessenberg inverse iteration for eigvec

SYNOPSIS

Functions

subroutine chsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
CHSEIN
subroutine dhsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
DHSEIN
subroutine shsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
SHSEIN
subroutine zhsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
ZHSEIN

Detailed Description

Function Documentation

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

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 is INTEGER
The order of the matrix H. N >= 0.

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 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 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 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 is INTEGER
The number of columns in the arrays VL and/or VR. MM >= 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.

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|.

subroutine dhsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, double precision, dimension(ldh, * ) h, integer ldh, double precision, dimension( * ) wr, doubleprecision, dimension( * ) wi, double precision, dimension( ldvl, * )vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integerldvr, integer mm, integer m, double precision, dimension( * ) work,integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integerinfo)

DHSEIN

Purpose:

DHSEIN uses inverse iteration to find specified right and/or left
eigenvectors of a real 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 (WR,WI):
= ’Q’: the eigenvalues were found using DHSEQR; 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 DHSEIN 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, DHSEIN 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
real eigenvector corresponding to a real eigenvalue WR(j),
SELECT(j) must be set to .TRUE.. To select the complex
eigenvector corresponding to a complex eigenvalue
(WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),
either SELECT(j) or SELECT(j+1) or both must be set to
.TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is
.FALSE..

N is INTEGER
The order of the matrix H. N >= 0.

H is DOUBLE PRECISION 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).

WR is DOUBLE PRECISION array, dimension (N)

WI is DOUBLE PRECISION array, dimension (N)

On entry, the real and imaginary parts of the eigenvalues of
H; a complex conjugate pair of eigenvalues must be stored in
consecutive elements of WR and WI.
On exit, WR may have been altered since close eigenvalues
are perturbed slightly in searching for independent
eigenvectors.

VL is DOUBLE PRECISION 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(s) 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. A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first holding the real
part and the second the imaginary part.
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 is DOUBLE PRECISION 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(s) 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. A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first holding the real
part and the second the imaginary part.
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 is INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.

M is INTEGER
The number of columns in the arrays VL and/or VR required to
store the eigenvectors; each selected real eigenvector
occupies one column and each selected complex eigenvector
occupies two columns.

WORK

WORK is DOUBLE PRECISION array, dimension ((N+2)*N)

IFAILL

IFAILR

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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|.

subroutine shsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, real, dimension( ldh, * ) h,integer ldh, real, dimension( * ) wr, real, dimension( * ) wi, real,dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr,integer ldvr, integer mm, integer m, real, dimension( * ) work,integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integerinfo)

SHSEIN

Purpose:

SHSEIN uses inverse iteration to find specified right and/or left
eigenvectors of a real 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 (WR,WI):
= ’Q’: the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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

N is INTEGER
The order of the matrix H. N >= 0.

H is REAL 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).

WR is REAL array, dimension (N)

WI is REAL array, dimension (N)

VL is REAL 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(s) 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. A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first holding the real
part and the second the imaginary part.
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 is REAL 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(s) 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. A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first holding the real
part and the second the imaginary part.
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 is INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.

WORK

WORK is REAL array, dimension ((N+2)*N)

IFAILL

IFAILR

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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|.

subroutine zhsein (character side, character eigsrc, character initv,logical, dimension( * ) select, integer n, complex16, dimension( ldh, ) h, integer ldh, complex16, dimension( ) w, complex16,dimension( ldvl, ) vl, integer ldvl, complex16, dimension( ldvr, )vr, integer ldvr, integer mm, integer m, complex16, dimension( )work, double precision, dimension( * ) rwork, integer, dimension( * )ifaill, integer, dimension( * ) ifailr, integer info)

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.

EIGSRC

EIGSRC 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
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 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.

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 is INTEGER
The order of the matrix H. N >= 0.

H 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.

LDH

LDH is INTEGER
The leading dimension of the array H. LDH >= max(1,N).

W 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.

VL 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.

LDVL

LDVL is INTEGER
The leading dimension of the array VL.
LDVL >= max(1,N) if SIDE = ’L’ or ’B’; LDVL >= 1 otherwise.

VR 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.

LDVR

LDVR is INTEGER
The leading dimension of the array VR.
LDVR >= max(1,N) if SIDE = ’R’ or ’B’; LDVR >= 1 otherwise.

MM is INTEGER
The number of columns in the arrays VL and/or VR. MM >= 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*16 array, dimension (N*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

IFAILL

IFAILR

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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|.

Author

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