ctgevc man page on IRIX

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CTGEVC(3F)							    CTGEVC(3F)

NAME
     CTGEVC - compute some or all of the right and/or left generalized
     eigenvectors of a pair of complex upper triangular matrices (A,B)

SYNOPSIS
     SUBROUTINE CTGEVC( 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( * )

	 REAL		RWORK( * )

	 COMPLEX	A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, *
			), WORK( * )

PURPOSE
     CTGEVC computes some or all of the right and/or left generalized
     eigenvectors of a pair of complex upper triangular matrices (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 eigenvectors 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

									Page 1

CTGEVC(3F)							    CTGEVC(3F)

	     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.
	     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 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 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 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 CHGEQZ).  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 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 CHGEQZ).  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.

									Page 2

CTGEVC(3F)							    CTGEVC(3F)

     MM	     (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 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.

									Page 3

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