ctgevc (l)  Linux Man Pages
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
NAME
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 triangularSYNOPSIS
 SUBROUTINE CTGEVC(
 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( * )
 REAL RWORK( * )
 COMPLEX P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )
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):A
as computed by CGGHRD + CHGEQZ.
The right eigenvector x and the left eigenvector y of (S,P) corresponding to an eigenvalue w are defined by:
S*x
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 jth 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 array, dimension (LDS,N)
 The upper triangular matrix S from a generalized Schur factorization, as computed by CHGEQZ.
 LDS (input) INTEGER
 The leading dimension of array S. LDS >= max(1,N).
 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.
 LDP (input) INTEGER
 The leading dimension of array P. LDP >= max(1,N).
 VL (input/output) COMPLEX array, dimension (LDVL,MM)
 On entry, if SIDE = aqLaq or aqBaq and HOWMNY = aqBaq, VL must contain an NbyN matrix Q (usually the unitary matrix Q of left Schur vectors returned by CHGEQZ). 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 array, dimension (LDVR,MM)
 On entry, if SIDE = aqRaq or aqBaq and HOWMNY = aqBaq, VR must contain an NbyN matrix Q (usually the unitary matrix Z of right Schur vectors returned by CHGEQZ). 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 array, dimension (2*N)
 RWORK (workspace) REAL array, dimension (2*N)
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.