ztgevc.f man page

ztgevc.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine ztgevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex*16, dimension( lds, * )S, integerLDS, complex*16, dimension( ldp, * )P, integerLDP, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZTGEVC

Purpose:

ZTGEVC 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 ZGGHRD + ZHGEQZ.

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*16 array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur
factorization, as computed by ZHGEQZ.

LDS

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

P

P is COMPLEX*16 array, dimension (LDP,N)
The upper triangular matrix P from a generalized Schur
factorization, as computed by ZHGEQZ.  P must have real
diagonal elements.

LDP

LDP is INTEGER
The leading dimension of array P.  LDP >= 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 left Schur vectors returned by ZHGEQZ).
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*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 Z
of right Schur vectors returned by ZHGEQZ).
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*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION 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 ztgevc.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK