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RedHat 9 (Linux i386) - man page for ctgevc (redhat section l)

CTGEVC(l)					)					CTGEVC(l)

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 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.

       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 eigen-
	       vectors.   If HOWMNY = 'A' or 'B', M is set to N.  Each selected eigenvector occu-
	       pies 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 version 3.0			   15 June 2000 				CTGEVC(l)


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