Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

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

CGEESX(l)					)					CGEESX(l)

NAME
       CGEESX  -  compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur
       form T, and, optionally, the matrix of Schur vectors Z

SYNOPSIS
       SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A,  LDA,  SDIM,  W,  VS,  LDVS,  RCONDE,
			  RCONDV, WORK, LWORK, RWORK, BWORK, INFO )

	   CHARACTER	  JOBVS, SENSE, SORT

	   INTEGER	  INFO, LDA, LDVS, LWORK, N, SDIM

	   REAL 	  RCONDE, RCONDV

	   LOGICAL	  BWORK( * )

	   REAL 	  RWORK( * )

	   COMPLEX	  A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )

	   LOGICAL	  SELECT

	   EXTERNAL	  SELECT

PURPOSE
       CGEESX  computes  for  an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur
       form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization
       A  =  Z*T*(Z**H).  Optionally, it also orders the eigenvalues on the diagonal of the Schur
       form so that selected eigenvalues are at the top left;  computes  a  reciprocal	condition
       number  for  the  average  of the selected eigenvalues (RCONDE); and computes a reciprocal
       condition number for the right invariant subspace corresponding to the selected	eigenval-
       ues  (RCONDV).  The leading columns of Z form an orthonormal basis for this invariant sub-
       space.

       For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section
       4.10  of  the  LAPACK  Users'  Guide  (where these quantities are called s and sep respec-
       tively).

       A complex matrix is in Schur form if it is upper triangular.

ARGUMENTS
       JOBVS   (input) CHARACTER*1
	       = 'N': Schur vectors are not computed;
	       = 'V': Schur vectors are computed.

       SORT    (input) CHARACTER*1
	       Specifies whether or not to order the eigenvalues on the  diagonal  of  the  Schur
	       form.  = 'N': Eigenvalues are not ordered;
	       = 'S': Eigenvalues are ordered (see SELECT).

       SELECT  (input) LOGICAL FUNCTION of one COMPLEX argument
	       SELECT must be declared EXTERNAL in the calling subroutine.  If SORT = 'S', SELECT
	       is used to select eigenvalues to order to the top left of the Schur form.  If SORT
	       =  'N',	SELECT is not referenced.  An eigenvalue W(j) is selected if SELECT(W(j))
	       is true.

       SENSE   (input) CHARACTER*1
	       Determines which reciprocal condition numbers are computed.  = 'N': None are  com-
	       puted;
	       = 'E': Computed for average of selected eigenvalues only;
	       = 'V': Computed for selected right invariant subspace only;
	       = 'B': Computed for both.  If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.

       N       (input) INTEGER
	       The order of the matrix A. N >= 0.

       A       (input/output) COMPLEX array, dimension (LDA, N)
	       On entry, the N-by-N matrix A.  On exit, A is overwritten by its Schur form T.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       SDIM    (output) INTEGER
	       If  SORT  =  'N', SDIM = 0.  If SORT = 'S', SDIM = number of eigenvalues for which
	       SELECT is true.

       W       (output) COMPLEX array, dimension (N)
	       W contains the computed eigenvalues, in the same order that  they  appear  on  the
	       diagonal of the output Schur form T.

       VS      (output) COMPLEX array, dimension (LDVS,N)
	       If  JOBVS  =  'V',  VS contains the unitary matrix Z of Schur vectors.  If JOBVS =
	       'N', VS is not referenced.

       LDVS    (input) INTEGER
	       The leading dimension of the array VS.  LDVS >= 1, and if JOBVS = 'V', LDVS >= N.

       RCONDE  (output) REAL
	       If SENSE = 'E' or 'B', RCONDE contains the reciprocal  condition  number  for  the
	       average of the selected eigenvalues.  Not referenced if SENSE = 'N' or 'V'.

       RCONDV  (output) REAL
	       If  SENSE  =  'V'  or 'B', RCONDV contains the reciprocal condition number for the
	       selected right invariant subspace.  Not referenced if SENSE = 'N' or 'E'.

       WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.  LWORK >= max(1,2*N).  Also, if SENSE  =  'E'  or
	       'V'  or 'B', LWORK >= 2*SDIM*(N-SDIM), where SDIM is the number of selected eigen-
	       values computed by this routine.  Note that 2*SDIM*(N-SDIM) <=  N*N/2.	For  good
	       performance, LWORK must generally be larger.

       RWORK   (workspace) REAL array, dimension (N)

       BWORK   (workspace) LOGICAL array, dimension (N)
	       Not referenced if SORT = 'N'.

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value.
	       > 0: if INFO = i, and i is
	       <= N: the QR algorithm failed to compute all the
	       eigenvalues;  elements 1:ILO-1 and i+1:N of W contain those eigenvalues which have
	       converged; if JOBVS = 'V', VS contains the transformation which reduces A  to  its
	       partially  converged  Schur  form.   = N+1: the eigenvalues could not be reordered
	       because some eigenvalues were too close to separate (the problem is very  ill-con-
	       ditioned); = N+2: after reordering, roundoff changed values of some complex eigen-
	       values  so  that  leading  eigenvalues  in  the	Schur  form  no  longer   satisfy
	       SELECT=.TRUE.  This could also be caused by underflow due to scaling.

LAPACK version 3.0			   15 June 2000 				CGEESX(l)


All times are GMT -4. The time now is 08:50 AM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password