dgees man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

DGEES(1)	      LAPACK driver routine (version 3.2)	      DGEES(1)

       DGEES  -	 computes for an N-by-N real nonsymmetric matrix A, the eigen‐
       values, the real Schur form T, and, optionally,	the  matrix  of	 Schur
       vectors Z





	   DOUBLE	 PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ),	 WORK(
			 * ), WR( * )



       DGEES  computes for an N-by-N real nonsymmetric matrix A, the eigenval‐
       ues, the real Schur form T, and, optionally, the matrix of  Schur  vec‐
       tors  Z.	  This	gives the Schur factorization A = Z*T*(Z**T).  Option‐
       ally, it also orders the eigenvalues on the diagonal of the real	 Schur
       form  so	 that  selected	 eigenvalues are at the top left.  The leading
       columns of Z then form an orthonormal basis for the invariant  subspace
       corresponding  to  the selected eigenvalues.  A matrix is in real Schur
       form if it is upper quasi-triangular with  1-by-1  and  2-by-2  blocks.
       2-by-2 blocks will be standardized in the form
	       [  a  b	]
	       [  c  a	]
       where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).

       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 diago‐
	       nal of the Schur form.  = 'N': Eigenvalues are not ordered;
	       = 'S': Eigenvalues are ordered (see SELECT).

       SELECT  (external procedure) LOGICAL FUNCTION of two  DOUBLE  PRECISION
	       SELECT must be declared EXTERNAL in the calling subroutine.  If
	       SORT = 'S', SELECT is used to select eigenvalues to sort to the
	       top  left of the Schur form.  If SORT = 'N', SELECT is not ref‐
	       erenced.	 An eigenvalue	WR(j)+sqrt(-1)*WI(j)  is  selected  if
	       SELECT(WR(j),WI(j))  is	true; i.e., if either one of a complex
	       conjugate pair of eigenvalues is selected,  then	 both  complex
	       eigenvalues  are selected.  Note that a selected complex eigen‐
	       value may no longer satisfy SELECT(WR(j),WI(j)) = .TRUE.	 after
	       ordering, since ordering may change the value of complex eigen‐
	       values (especially if the eigenvalue  is	 ill-conditioned);  in
	       this case INFO is set to N+2 (see INFO below).

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

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the N-by-N matrix A.  On exit, A has been overwritten
	       by its real 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  ei‐
	       genvalues  (after  sorting)  for which SELECT is true. (Complex
	       conjugate pairs for which SELECT is true for either  eigenvalue
	       count as 2.)

       WR      (output) DOUBLE PRECISION array, dimension (N)
	       WI	(output)  DOUBLE PRECISION array, dimension (N) WR and
	       WI contain the real and imaginary parts, respectively,  of  the
	       computed	 eigenvalues in the same order that they appear on the
	       diagonal of the output Schur form T.  Complex  conjugate	 pairs
	       of  eigenvalues	will  appear consecutively with the eigenvalue
	       having the positive imaginary part first.

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

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

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

       LWORK   (input) INTEGER
	       The  dimension  of  the	array WORK.  LWORK >= max(1,3*N).  For
	       good performance, LWORK must generally be larger.  If  LWORK  =
	       -1,  then a workspace query is assumed; the routine only calcu‐
	       lates the optimal size of the WORK array, returns this value as
	       the first entry of the WORK array, and no error message related
	       to LWORK is issued by XERBLA.

       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 WR  and  WI  contain
	       those eigenvalues which have converged; if JOBVS = 'V', VS con‐
	       tains the matrix 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	 prob‐
	       lem is very ill-conditioned); = N+2: after reordering, roundoff
	       changed values of some complex eigenvalues so that leading  ei‐
	       genvalues  in  the  Schur  form no longer satisfy SELECT=.TRUE.
	       This could also be caused by underflow due to scaling.

 LAPACK driver routine (version 3November 2008			      DGEES(1)

List of man pages available for Scientific

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
Vote for polarhome
Free Shell Accounts :: the biggest list on the net