ctgevc.f man page

ctgevc.f —

Synopsis

Functions/Subroutines

subroutine ctgevc (SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTGEVC

Function/Subroutine Documentation

subroutine ctgevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex, dimension( lds, * )S, integerLDS, complex, dimension( ldp, * )P, integerLDP, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CTGEVC

Purpose:

CTGEVC computes some or all of the right and/or left eigenvectors of
a pair of complex matrices (S,P), where S and P are upper triangular.
Matrix pairs of this type are produced by the generalized Schur
factorization of a complex matrix pair (A,B):

   A = Q*S*Z**H,  B = Q*P*Z**H

as computed by CGGHRD + CHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P)
corresponding to an eigenvalue w are defined by:

   S*x = w*P*x,  (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate tranpose of y.
The eigenvalues are not input to this routine, but are computed
directly from the diagonal elements of S and P.

This routine returns the matrices X and/or Y of right and left
eigenvectors of (S,P), or the products Z*X and/or Q*Y,
where Z and Q are input matrices.
If Q and Z are the unitary factors from the generalized Schur
factorization of a matrix pair (A,B), then Z*X and Q*Y
are the matrices of right and left eigenvectors of (A,B).

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,
       specified 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 matrices S and P.  N >= 0.

S

S is COMPLEX array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur
factorization, as computed by CHGEQZ.

LDS

LDS is INTEGER
The leading dimension of array S.  LDS >= max(1,N).

P

P is COMPLEX array, dimension (LDP,N)
The upper triangular matrix P from a generalized Schur
factorization, as computed by CHGEQZ.  P must have real
diagonal elements.

LDP

LDP is INTEGER
The leading dimension of array P.  LDP >= 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 left Schur vectors returned by CHGEQZ).
On exit, if SIDE = 'L' or 'B', VL contains:
if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
if HOWMNY = 'B', the matrix Q*Y;
if HOWMNY = 'S', the left eigenvectors of (S,P) 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 array VL.  LDVL >= 1, and if
SIDE = 'L' or 'l' or 'B' 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 Z
of right Schur vectors returned by CHGEQZ).
On exit, if SIDE = 'R' or 'B', VR contains:
if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
if HOWMNY = 'B', the matrix Z*X;
if HOWMNY = 'S', the right eigenvectors of (S,P) 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 (2*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.

Date:

November 2011

Definition at line 219 of file ctgevc.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

ctgevc(3) is an alias of ctgevc.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK