ztgevc(3)

NAME

ZTGEVC - compute some or all of the right and/or left gen

eralized eigenvectors of a pair of complex upper triangular ma

trices (A,B)

SYNOPSIS

SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT,  N,  A,  LDA,  B,
LDB, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
    CHARACTER      HOWMNY, SIDE
    INTEGER        INFO, LDA, LDB, LDVL, LDVR, M, MM, N
    LOGICAL        SELECT( * )
    DOUBLE         PRECISION RWORK( * )
    COMPLEX*16      A(  LDA, * ), B( LDB, * ), VL( LDVL, *
), VR( LDVR, * ), WORK( * )

PURPOSE

ZTGEVC computes some or all of the right and/or left gen

eralized eigenvectors of a pair of complex upper triangular ma

trices (A,B). The right generalized eigenvector x and the left

generalized eigenvector y of (A,B) corresponding to a generalized

eigenvalue w are defined by:

(A - wB) * x = 0 and y**H * (A - wB) = 0

where y**H denotes the conjugate tranpose of y.

If an eigenvalue w is determined by zero diagonal elements

of both A and B, a unit vector is returned as the corresponding

eigenvector.

If all eigenvectors are requested, the routine may either

return the matrices X and/or Y of right or left eigenvectors of

(A,B), or the products Z*X and/or Q*Y, where Z and Q are input

unitary matrices. If (A,B) was obtained from the generalized

Schur factorization of an original pair of matrices

(A0,B0) = (Q*A*Z**H,Q*B*Z**H),

then Z*X and Q*Y are the matrices of right or left eigen

vectors of A.

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,

and backtransform them using the input matrices supplied in VR

and/or VL; = 'S': compute selected right and/or left eigenvec

tors, specified by the logical array SELECT.

SELECT (input) LOGICAL array, dimension (N)

If HOWMNY='S', SELECT specifies the eigenvectors

to be computed. If HOWMNY='A' or 'B', SELECT is not referenced.

To select the eigenvector corresponding to the j-th eigenvalue,

SELECT(j) must be set to .TRUE..

N (input) INTEGER

The order of the matrices A and B. N >= 0.

A (input) COMPLEX*16 array, dimension (LDA,N)

The upper triangular matrix A.

LDA (input) INTEGER

The leading dimension of array A. LDA >=

max(1,N).

B (input) COMPLEX*16 array, dimension (LDB,N)

The upper triangular matrix B. B must have real

diagonal elements.

LDB (input) INTEGER

The leading dimension of array B. LDB >=

max(1,N).

VL (input/output) COMPLEX*16 array, dimension (LD

VL,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 (A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY

= 'S', the left eigenvectors of (A,B) specified by SELECT, stored

consecutively in the columns of VL, in the same order as their

eigenvalues. If SIDE = 'R', VL is not referenced.

LDVL (input) INTEGER

The leading dimension of array VL. LDVL >=

max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

VR (input/output) COMPLEX*16 array, dimension (LD

VR,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 (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY

= 'S', the right eigenvectors of (A,B) specified by SELECT,

stored consecutively in the columns of VR, in the same order as

their eigenvalues. If SIDE = 'L', VR is not referenced.

LDVR (input) INTEGER

The leading dimension of the array VR. LDVR >=

max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.

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 ille

gal value.

LAPACK version 3.0 15 June 2000

ZTGEVC(3)