ctgevc man page on Scientific

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CTGEVC(1)		 LAPACK routine (version 3.2)		     CTGEVC(1)

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 triangular

SYNOPSIS
       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 factor‐
       ization of a complex matrix pair (A,B):
	  A = Q*S*Z**H,	 B = Q*P*Z**H
       as computed by CGGHRD + CHGEQZ.
       The right eigenvector x and the left eigenvector y of (S,P) correspond‐
       ing 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 eigen‐
       vectors 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  factor‐
       ization 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, backtrans‐
	       formed 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  com‐
	       puted.  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 array, dimension (LDS,N)
	       The  upper triangular matrix S from a generalized Schur factor‐
	       ization, 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  factor‐
	       ization, as computed by CHGEQZ.	P must have real diagonal ele‐
	       ments.

       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 = 'L' or 'B' and HOWMNY = 'B', VL  must  con‐
	       tain  an	 N-by-N matrix Q (usually the unitary matrix Q of left
	       Schur vectors returned by CHGEQZ).  On exit, if SIDE =  'L'  or
	       'B',  VL contains: if HOWMNY = 'A', the matrix Y of left eigen‐
	       vectors 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 array, dimension (LDVR,MM)
	       On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR  must  con‐
	       tain  an N-by-N matrix Q (usually the unitary matrix Z of right
	       Schur vectors returned by CHGEQZ).  On exit, if SIDE =  'R'  or
	       'B', VR contains: if HOWMNY = 'A', the matrix X of right eigen‐
	       vectors 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 array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (2*N)

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

 LAPACK routine (version 3.2)	 November 2008			     CTGEVC(1)
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