Man page - trevc(3)

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Manual

trevc

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctrevc (character side, character howmny, logical, dimension( *) select, integer n, complex, dimension( ldt, * ) t, integer ldt,complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension(ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension(* ) work, real, dimension( * ) rwork, integer info)
subroutine dtrevc (character side, character howmny, logical, dimension( *) select, integer n, double precision, dimension( ldt, * ) t, integerldt, double precision, dimension( ldvl, * ) vl, integer ldvl, doubleprecision, dimension( ldvr, * ) vr, integer ldvr, integer mm, integerm, double precision, dimension( * ) work, integer info)
subroutine strevc (character side, character howmny, logical, dimension( *) select, integer n, real, dimension( ldt, * ) t, integer ldt, real,dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr,integer ldvr, integer mm, integer m, real, dimension( * ) work, integerinfo)
subroutine ztrevc (character side, character howmny, logical, dimension( *) select, integer n, complex*16, dimension( ldt, * ) t, integer ldt,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 info)
Author

NAME

trevc - trevc: eigenvectors of triangular Schur form, old

SYNOPSIS

Functions

subroutine ctrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
CTREVC
subroutine dtrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)
DTREVC
subroutine strevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, info)
STREVC
subroutine ztrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
ZTREVC

Detailed Description

Function Documentation

subroutine ctrevc (character side, character howmny, logical, dimension( *) select, integer n, complex, dimension( ldt, * ) t, integer ldt,complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension(ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension(* ) work, real, dimension( * ) rwork, integer info)

CTREVC

Purpose:

CTREVC computes some or all of the right and/or left eigenvectors of
a complex upper triangular matrix T.
Matrices of this type are produced by the Schur factorization of
a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:

T*x = w*x, (y**H)*T = w*(y**H)

where y**H denotes the conjugate transpose of the vector y.
The eigenvalues are not input to this routine, but are read directly
from the diagonal of T.

This routine returns the matrices X and/or Y of right and left
eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
input matrix. If Q is the unitary factor that reduces a matrix A to
Schur form T, then Q*X and Q*Y are the matrices of right and left
eigenvectors of A.

Parameters

SIDE

SIDE is CHARACTER*1
= ’R’: compute right eigenvectors only;
= ’L’: compute left eigenvectors only;
= ’B’: compute both right and left eigenvectors.

HOWMNY

HOWMNY is CHARACTER*1
= ’A’: compute all right and/or left eigenvectors;
= ’B’: compute all right and/or left eigenvectors,
backtransformed using the matrices supplied in
VR and/or VL;
= ’S’: compute selected right and/or left eigenvectors,
as indicated by the logical array SELECT.

SELECT

SELECT is LOGICAL array, dimension (N)
If HOWMNY = ’S’, SELECT specifies the eigenvectors to be
computed.
The eigenvector corresponding to the j-th eigenvalue is
computed if SELECT(j) = .TRUE..
Not referenced if HOWMNY = ’A’ or ’B’.

N

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

T

T is COMPLEX array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored
on exit.

LDT

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

VL

VL is COMPLEX array, dimension (LDVL,MM)
On entry, if SIDE = ’L’ or ’B’ and HOWMNY = ’B’, VL must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by CHSEQR).
On exit, if SIDE = ’L’ or ’B’, VL contains:
if HOWMNY = ’A’, the matrix Y of left eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*Y;
if HOWMNY = ’S’, the left eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VL, in the same order as their
eigenvalues.
Not referenced if SIDE = ’R’.

LDVL

LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1, and if
SIDE = ’L’ or ’B’, LDVL >= N.

VR

VR is COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = ’R’ or ’B’ and HOWMNY = ’B’, VR must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by CHSEQR).
On exit, if SIDE = ’R’ or ’B’, VR contains:
if HOWMNY = ’A’, the matrix X of right eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*X;
if HOWMNY = ’S’, the right eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VR, in the same order as their
eigenvalues.
Not referenced if SIDE = ’L’.

LDVR

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

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 actually
used to store the eigenvectors. If HOWMNY = ’A’ or ’B’, M
is set to N. Each selected eigenvector occupies one
column.

WORK

WORK is COMPLEX array, dimension (2*N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.

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 dtrevc (character side, character howmny, logical, dimension( *) select, integer n, double precision, dimension( ldt, * ) t, integerldt, double precision, dimension( ldvl, * ) vl, integer ldvl, doubleprecision, dimension( ldvr, * ) vr, integer ldvr, integer mm, integerm, double precision, dimension( * ) work, integer info)

DTREVC

Purpose:

DTREVC computes some or all of the right and/or left eigenvectors of
a real upper quasi-triangular matrix T.
Matrices of this type are produced by the Schur factorization of
a real general matrix: A = Q*T*Q**T, as computed by DHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:

T*x = w*x, (y**H)*T = w*(y**H)

where y**H denotes the conjugate transpose of y.
The eigenvalues are not input to this routine, but are read directly
from the diagonal blocks of T.

This routine returns the matrices X and/or Y of right and left
eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
input matrix. If Q is the orthogonal factor that reduces a matrix
A to Schur form T, then Q*X and Q*Y are the matrices of right and
left eigenvectors of A.

Parameters

SIDE

SIDE is CHARACTER*1
= ’R’: compute right eigenvectors only;
= ’L’: compute left eigenvectors only;
= ’B’: compute both right and left eigenvectors.

HOWMNY

HOWMNY is CHARACTER*1
= ’A’: compute all right and/or left eigenvectors;
= ’B’: compute all right and/or left eigenvectors,
backtransformed by the matrices in VR and/or VL;
= ’S’: compute selected right and/or left eigenvectors,
as indicated by the logical array SELECT.

SELECT

SELECT is LOGICAL array, dimension (N)
If HOWMNY = ’S’, SELECT specifies the eigenvectors to be
computed.
If w(j) is a real eigenvalue, the corresponding real
eigenvector is computed if SELECT(j) is .TRUE..
If w(j) and w(j+1) are the real and imaginary parts of a
complex eigenvalue, the corresponding complex eigenvector is
computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
.FALSE..
Not referenced if HOWMNY = ’A’ or ’B’.

N

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

T

T is DOUBLE PRECISION array, dimension (LDT,N)
The upper quasi-triangular matrix T in Schur canonical form.

LDT

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

VL

VL is DOUBLE PRECISION array, dimension (LDVL,MM)
On entry, if SIDE = ’L’ or ’B’ and HOWMNY = ’B’, VL must
contain an N-by-N matrix Q (usually the orthogonal matrix Q
of Schur vectors returned by DHSEQR).
On exit, if SIDE = ’L’ or ’B’, VL contains:
if HOWMNY = ’A’, the matrix Y of left eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*Y;
if HOWMNY = ’S’, the left eigenvectors of T specified by
SELECT, 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.
Not referenced if SIDE = ’R’.

LDVL

LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1, and if
SIDE = ’L’ or ’B’, LDVL >= N.

VR

VR is DOUBLE PRECISION array, dimension (LDVR,MM)
On entry, if SIDE = ’R’ or ’B’ and HOWMNY = ’B’, VR must
contain an N-by-N matrix Q (usually the orthogonal matrix Q
of Schur vectors returned by DHSEQR).
On exit, if SIDE = ’R’ or ’B’, VR contains:
if HOWMNY = ’A’, the matrix X of right eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*X;
if HOWMNY = ’S’, the right eigenvectors of T specified by
SELECT, 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.
Not referenced if SIDE = ’L’.

LDVR

LDVR is INTEGER
The leading dimension of the array VR. LDVR >= 1, and if
SIDE = ’R’ or ’B’, LDVR >= N.

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 actually
used to store the eigenvectors.
If HOWMNY = ’A’ or ’B’, M is set to N.
Each selected real eigenvector occupies one column and each
selected complex eigenvector occupies two columns.

WORK

WORK is DOUBLE PRECISION array, dimension (3*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.

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 strevc (character side, character howmny, logical, dimension( *) select, integer n, real, dimension( ldt, * ) t, integer ldt, real,dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr,integer ldvr, integer mm, integer m, real, dimension( * ) work, integerinfo)

STREVC

Purpose:

STREVC computes some or all of the right and/or left eigenvectors of
a real upper quasi-triangular matrix T.
Matrices of this type are produced by the Schur factorization of
a real general matrix: A = Q*T*Q**T, as computed by SHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:

T*x = w*x, (y**H)*T = w*(y**H)

where y**H denotes the conjugate transpose of y.
The eigenvalues are not input to this routine, but are read directly
from the diagonal blocks of T.

This routine returns the matrices X and/or Y of right and left
eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
input matrix. If Q is the orthogonal factor that reduces a matrix
A to Schur form T, then Q*X and Q*Y are the matrices of right and
left eigenvectors of A.

Parameters

SIDE

SIDE is CHARACTER*1
= ’R’: compute right eigenvectors only;
= ’L’: compute left eigenvectors only;
= ’B’: compute both right and left eigenvectors.

HOWMNY

HOWMNY is CHARACTER*1
= ’A’: compute all right and/or left eigenvectors;
= ’B’: compute all right and/or left eigenvectors,
backtransformed by the matrices in VR and/or VL;
= ’S’: compute selected right and/or left eigenvectors,
as indicated by the logical array SELECT.

SELECT

SELECT is LOGICAL array, dimension (N)
If HOWMNY = ’S’, SELECT specifies the eigenvectors to be
computed.
If w(j) is a real eigenvalue, the corresponding real
eigenvector is computed if SELECT(j) is .TRUE..
If w(j) and w(j+1) are the real and imaginary parts of a
complex eigenvalue, the corresponding complex eigenvector is
computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
.FALSE..
Not referenced if HOWMNY = ’A’ or ’B’.

N

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

T

T is REAL array, dimension (LDT,N)
The upper quasi-triangular matrix T in Schur canonical form.

LDT

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

VL

VL is REAL array, dimension (LDVL,MM)
On entry, if SIDE = ’L’ or ’B’ and HOWMNY = ’B’, VL must
contain an N-by-N matrix Q (usually the orthogonal matrix Q
of Schur vectors returned by SHSEQR).
On exit, if SIDE = ’L’ or ’B’, VL contains:
if HOWMNY = ’A’, the matrix Y of left eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*Y;
if HOWMNY = ’S’, the left eigenvectors of T specified by
SELECT, 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.
Not referenced if SIDE = ’R’.

LDVL

LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1, and if
SIDE = ’L’ or ’B’, LDVL >= N.

VR

VR is REAL array, dimension (LDVR,MM)
On entry, if SIDE = ’R’ or ’B’ and HOWMNY = ’B’, VR must
contain an N-by-N matrix Q (usually the orthogonal matrix Q
of Schur vectors returned by SHSEQR).
On exit, if SIDE = ’R’ or ’B’, VR contains:
if HOWMNY = ’A’, the matrix X of right eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*X;
if HOWMNY = ’S’, the right eigenvectors of T specified by
SELECT, 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.
Not referenced if SIDE = ’L’.

LDVR

LDVR is INTEGER
The leading dimension of the array VR. LDVR >= 1, and if
SIDE = ’R’ or ’B’, LDVR >= N.

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 actually
used to store the eigenvectors.
If HOWMNY = ’A’ or ’B’, M is set to N.
Each selected real eigenvector occupies one column and each
selected complex eigenvector occupies two columns.

WORK

WORK is REAL array, dimension (3*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.

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 ztrevc (character side, character howmny, logical, dimension( *) select, integer n, complex*16, dimension( ldt, * ) t, integer ldt,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 info)

ZTREVC

Purpose:

ZTREVC computes some or all of the right and/or left eigenvectors of
a complex upper triangular matrix T.
Matrices of this type are produced by the Schur factorization of
a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding
to an eigenvalue w are defined by:

T*x = w*x, (y**H)*T = w*(y**H)

where y**H denotes the conjugate transpose of the vector y.
The eigenvalues are not input to this routine, but are read directly
from the diagonal of T.

This routine returns the matrices X and/or Y of right and left
eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
input matrix. If Q is the unitary factor that reduces a matrix A to
Schur form T, then Q*X and Q*Y are the matrices of right and left
eigenvectors of A.

Parameters

SIDE

SIDE is CHARACTER*1
= ’R’: compute right eigenvectors only;
= ’L’: compute left eigenvectors only;
= ’B’: compute both right and left eigenvectors.

HOWMNY

HOWMNY is CHARACTER*1
= ’A’: compute all right and/or left eigenvectors;
= ’B’: compute all right and/or left eigenvectors,
backtransformed using the matrices supplied in
VR and/or VL;
= ’S’: compute selected right and/or left eigenvectors,
as indicated by the logical array SELECT.

SELECT

SELECT is LOGICAL array, dimension (N)
If HOWMNY = ’S’, SELECT specifies the eigenvectors to be
computed.
The eigenvector corresponding to the j-th eigenvalue is
computed if SELECT(j) = .TRUE..
Not referenced if HOWMNY = ’A’ or ’B’.

N

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

T

T is COMPLEX*16 array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored
on exit.

LDT

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

VL

VL is COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = ’L’ or ’B’ and HOWMNY = ’B’, VL must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by ZHSEQR).
On exit, if SIDE = ’L’ or ’B’, VL contains:
if HOWMNY = ’A’, the matrix Y of left eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*Y;
if HOWMNY = ’S’, the left eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VL, in the same order as their
eigenvalues.
Not referenced if SIDE = ’R’.

LDVL

LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1, and if
SIDE = ’L’ or ’B’, LDVL >= N.

VR

VR is COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = ’R’ or ’B’ and HOWMNY = ’B’, VR must
contain an N-by-N matrix Q (usually the unitary matrix Q of
Schur vectors returned by ZHSEQR).
On exit, if SIDE = ’R’ or ’B’, VR contains:
if HOWMNY = ’A’, the matrix X of right eigenvectors of T;
if HOWMNY = ’B’, the matrix Q*X;
if HOWMNY = ’S’, the right eigenvectors of T specified by
SELECT, stored consecutively in the columns
of VR, in the same order as their
eigenvalues.
Not referenced if SIDE = ’L’.

LDVR

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

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 actually
used to store the eigenvectors. If HOWMNY = ’A’ or ’B’, M
is set to N. Each selected eigenvector occupies one
column.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The algorithm used in this program is basically backward (forward)
substitution, with scaling to make the the code robust against
possible overflow.

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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