.TH CTGEVC 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CTGEVC - 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 .SH SYNOPSIS .TP 19 SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER HOWMNY, SIDE .TP 19 .ti +4 INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N .TP 19 .ti +4 LOGICAL SELECT( * ) .TP 19 .ti +4 REAL RWORK( * ) .TP 19 .ti +4 COMPLEX P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * ) .SH 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): .br .br A = Q*S*Z**H, B = Q*P*Z**H .br .br as computed by CGGHRD + CHGEQZ. .br .br The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by: .br .br S*x = w*P*x, (y**H)*S = w*(y**H)*P, .br .br where y**H denotes the conjugate tranpose of y. .br The eigenvalues are not input to this routine, but are computed directly from the diagonal elements of S and P. .br .br 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, .br where Z and Q are input matrices. .br 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 .br are the matrices of right and left eigenvectors of (A,B). .SH ARGUMENTS .TP 8 SIDE (input) CHARACTER*1 = \(aqR\(aq: compute right eigenvectors only; .br = \(aqL\(aq: compute left eigenvectors only; .br = \(aqB\(aq: compute both right and left eigenvectors. .TP 8 HOWMNY (input) CHARACTER*1 .br = \(aqA\(aq: compute all right and/or left eigenvectors; .br = \(aqB\(aq: compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = \(aqS\(aq: compute selected right and/or left eigenvectors, specified by the logical array SELECT. .TP 8 SELECT (input) LOGICAL array, dimension (N) If HOWMNY=\(aqS\(aq, 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 = \(aqA\(aq or \(aqB\(aq. .TP 8 N (input) INTEGER The order of the matrices S and P. N >= 0. .TP 8 S (input) COMPLEX array, dimension (LDS,N) The upper triangular matrix S from a generalized Schur factorization, as computed by CHGEQZ. .TP 8 LDS (input) INTEGER The leading dimension of array S. LDS >= max(1,N). .TP 8 P (input) 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. .TP 8 LDP (input) INTEGER The leading dimension of array P. LDP >= max(1,N). .TP 8 VL (input/output) COMPLEX array, dimension (LDVL,MM) On entry, if SIDE = \(aqL\(aq or \(aqB\(aq and HOWMNY = \(aqB\(aq, 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 = \(aqL\(aq or \(aqB\(aq, VL contains: if HOWMNY = \(aqA\(aq, the matrix Y of left eigenvectors of (S,P); if HOWMNY = \(aqB\(aq, the matrix Q*Y; if HOWMNY = \(aqS\(aq, 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 = \(aqR\(aq. .TP 8 LDVL (input) INTEGER The leading dimension of array VL. LDVL >= 1, and if SIDE = \(aqL\(aq or \(aql\(aq or \(aqB\(aq or \(aqb\(aq, LDVL >= N. .TP 8 VR (input/output) COMPLEX array, dimension (LDVR,MM) On entry, if SIDE = \(aqR\(aq or \(aqB\(aq and HOWMNY = \(aqB\(aq, 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 = \(aqR\(aq or \(aqB\(aq, VR contains: if HOWMNY = \(aqA\(aq, the matrix X of right eigenvectors of (S,P); if HOWMNY = \(aqB\(aq, the matrix Z*X; if HOWMNY = \(aqS\(aq, 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 = \(aqL\(aq. .TP 8 LDVR (input) INTEGER The leading dimension of the array VR. LDVR >= 1, and if SIDE = \(aqR\(aq or \(aqB\(aq, LDVR >= N. .TP 8 MM (input) INTEGER The number of columns in the arrays VL and/or VR. MM >= M. .TP 8 M (output) INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = \(aqA\(aq or \(aqB\(aq, M is set to N. Each selected eigenvector occupies one column. .TP 8 WORK (workspace) COMPLEX array, dimension (2*N) .TP 8 RWORK (workspace) REAL array, dimension (2*N) .TP 8 INFO (output) INTEGER = 0: successful exit. .br < 0: if INFO = -i, the i-th argument had an illegal value.