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

CTREVC(l)					)					CTREVC(l)

NAME
       CTREVC - compute some or all of the right and/or left eigenvectors of a complex upper tri-
       angular matrix T

SYNOPSIS
       SUBROUTINE CTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL,	LDVL,  VR,  LDVR,  MM,	M,  WORK,
			  RWORK, INFO )

	   CHARACTER	  HOWMNY, SIDE

	   INTEGER	  INFO, LDT, LDVL, LDVR, M, MM, N

	   LOGICAL	  SELECT( * )

	   REAL 	  RWORK( * )

	   COMPLEX	  T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )

PURPOSE
       CTREVC  computes some or all of the right and/or left eigenvectors of a complex upper tri-
       angular matrix T.  The right eigenvector x and the left eigenvector y of  T  corresponding
       to an eigenvalue w are defined by:

		    T*x = w*x,	   y'*T = w*y'

       where y' denotes the conjugate transpose of the vector y.

       If  all	eigenvectors are requested, the routine may either return the matrices X and/or Y
       of right or left eigenvectors of T, or the products Q*X and/or Q*Y, where Q  is	an  input
       unitary
       matrix.	If  T was obtained from the Schur factorization of an original matrix A = Q*T*Q',
       then Q*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 matrix T. N >= 0.

       T       (input/output) COMPLEX array, dimension (LDT,N)
	       The upper triangular matrix T.  T is modified, but restored on exit.

       LDT     (input) INTEGER
	       The leading dimension of the array T. LDT >= 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 Schur vectors returned by CHSEQR).  On exit, if
	       SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors
	       of  T; VL is lower triangular. The i-th column VL(i) of VL is the eigenvector cor-
	       responding to T(i,i).  if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the  left
	       eigenvectors  of T 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 the 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 Q of Schur vectors returned by CHSEQR).  On exit, if
	       SIDE  =	'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvec-
	       tors of T; VR is upper triangular. The i-th column VR(i) of VR is the  eigenvector
	       corresponding  to  T(i,i).   if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the
	       right eigenvectors of T specified by SELECT, stored consecutively in  the  columns
	       of  VR,	in  the same order as their eigenvalues.  If SIDE = 'L', VR is not refer-
	       enced.

       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 (N)

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

FURTHER DETAILS
       The  algorithm  used  in  this  program is basically backward (forward) substitution, with
       scaling to make the the code robust against possible overflow.

       Each eigenvector is normalized so that the element of largest magnitude has  magnitude  1;
       here the magnitude of a complex number (x,y) is taken to be |x| + |y|.

LAPACK version 3.0			   15 June 2000 				CTREVC(l)


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