# ztgevc (l) - Linux Manuals

## NAME

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

## SYNOPSIS

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

CHARACTER HOWMNY, SIDE

INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N

LOGICAL SELECT( * )

DOUBLE PRECISION RWORK( * )

COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )

## 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):

Q*S*Z**H,  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).

## ARGUMENTS

SIDE (input) CHARACTER*1
= aqRaq: compute right eigenvectors only;
= aqLaq: compute left eigenvectors only;
= aqBaq: compute both right and left eigenvectors.
HOWMNY (input) CHARACTER*1

= aqAaq: compute all right and/or left eigenvectors;
= aqBaq: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = aqSaq: compute selected right and/or left eigenvectors, specified by the logical array SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY=aqSaq, 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 = aqAaq or aqBaq.
N (input) INTEGER
The order of the matrices S and P. N >= 0.
S (input) COMPLEX*16 array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur factorization, as computed by ZHGEQZ.
LDS (input) INTEGER
The leading dimension of array S. LDS >= max(1,N).
P (input) 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 (input) INTEGER
The leading dimension of array P. LDP >= max(1,N).
VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = aqLaq or aqBaq and HOWMNY = aqBaq, 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 = aqLaq or aqBaq, VL contains: if HOWMNY = aqAaq, the matrix Y of left eigenvectors of (S,P); if HOWMNY = aqBaq, the matrix Q*Y; if HOWMNY = aqSaq, 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 = aqRaq.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= 1, and if SIDE = aqLaq or aqlaq or aqBaq or aqbaq, LDVL >= N.
VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = aqRaq or aqBaq and HOWMNY = aqBaq, 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 = aqRaq or aqBaq, VR contains: if HOWMNY = aqAaq, the matrix X of right eigenvectors of (S,P); if HOWMNY = aqBaq, the matrix Z*X; if HOWMNY = aqSaq, 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 = aqLaq.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1, and if SIDE = aqRaq or aqBaq, LDVR >= N.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = aqAaq or aqBaq, M is set to N. Each selected eigenvector occupies one column.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.