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sgees (3)
  • >> sgees (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgees - compute for an N-by-N real  nonsymmetric  matrix  A,
         the eigenvalues, the real Schur form T, and, optionally, the
         matrix of Schur vectors Z
    
    SYNOPSIS
         SUBROUTINE SGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM,  WR,
                   WI, VS, LDVS, WORK, LWORK, BWORK, INFO )
    
         CHARACTER JOBVS, SORT
    
         INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
    
         LOGICAL BWORK( * )
    
         REAL A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), WR( * )
    
         LOGICAL SELECT
    
         EXTERNAL SELECT
    
    
    
         #include <sunperf.h>
    
         void sgees(char jobvs, char sort, int  (*select)(),  int  n,
                   float  *sa,  int  lda, int *sdim, float *wr, float
                   *wi, float *vs, int ldvs, int *info) ;
    
    PURPOSE
         SGEES computes for an N-by-N real nonsymmetric matrix A, the
         eigenvalues,  the  real  Schur  form T, and, optionally, the
         matrix of Schur vectors Z.  This gives the Schur  factoriza-
         tion A = Z*T*(Z**T).
    
         Optionally, 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  ortho-
         normal 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).
    
    
    
    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': Eigen-
                   values are not ordered;
                   = 'S': Eigenvalues are ordered (see SELECT).
    
         SELECT    (input) LOGICAL FUNCTION of two REAL arguments
                   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 refer-
                   enced.   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  eigen-
                   values  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 eigenvalues (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) REAL 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  eigenvalues  (after sorting) for which
                   SELECT is true. (Complex conjugate pairs for which
                   SELECT is true for either eigenvalue count as 2.)
    
         WR        (output) REAL array, dimension (N)
                   WI      (output) REAL array, dimension (N) WR  and
                   WI  contain  the real and imaginary parts, respec-
                   tively, of the computed eigenvalues  in  the  same
                   order that they appear on the diagonal of the out-
                   put Schur form  T.   Complex  conjugate  pairs  of
                   eigenvalues  will  appear  consecutively  with the
                   eigenvalue  having  the  positive  imaginary  part
                   first.
    
         VS        (output) REAL 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) REAL array, dimension (LWORK)
                   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 gen-
                   erally be larger.
    
         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  ille-
                   gal 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  contains  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 problem is very ill-conditioned);  =
                   N+2:  after reordering, roundoff changed values of
                   some complex eigenvalues so  that  leading  eigen-
                   values   in  the  Schur  form  no  longer  satisfy
                   SELECT=.TRUE.  This could also be caused by under-
                   flow due to scaling.
    
    
    
    


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