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):

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).

ARGUMENTS¶

SIDE (input) CHARACTER*1

= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.

HOWMNY (input) 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 (input) 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 (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 = '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 (input) INTEGER

The leading dimension of array VL. LDVL >= 1, and if SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.

VR (input/output) 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 (input) INTEGER

The leading dimension of the array VR. LDVR >= 1, and if SIDE = 'R' or 'B', 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 = 'A' or 'B', 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.