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dtrexc (3)
  • >> dtrexc (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dtrexc - reorder the real  Schur  factorization  of  a  real
         matrix  A  =  Q*T*Q**T, so that the diagonal block of T with
         row index IFST is moved to row ILST
    
    SYNOPSIS
         SUBROUTINE DTREXC( COMPQ, N, T, LDT,  Q,  LDQ,  IFST,  ILST,
                   WORK, INFO )
    
         CHARACTER COMPQ
    
         INTEGER IFST, ILST, INFO, LDQ, LDT, N
    
         DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void dtrexc(char compq, int n, double *t,  int  ldt,  double
                   *q, int ldq, int *ifst, int *ilst, int *info) ;
    
    PURPOSE
         DTREXC reorders the  real  Schur  factorization  of  a  real
         matrix  A  =  Q*T*Q**T, so that the diagonal block of T with
         row index IFST is moved to row ILST.
    
         The real Schur form T is reordered by an orthogonal similar-
         ity  transformation Z**T*T*Z, and optionally the matrix Q of
         Schur vectors is updated by postmultiplying it with Z.
    
         T must be in Schur canonical form (as returned  by  DHSEQR),
         that is, block upper triangular with 1-by-1 and 2-by-2 diag-
         onal blocks; each 2-by-2 diagonal  block  has  its  diagonal
         elements  equal  and  its  off-diagonal elements of opposite
         sign.
    
    
    ARGUMENTS
         COMPQ     (input) CHARACTER*1
                   = 'V':  update the matrix Q of Schur vectors;
                   = 'N':  do not update Q.
    
         N         (input) INTEGER
                   The order of the matrix T. N >= 0.
    
         T         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDT,N)
                   On entry, the upper quasi-triangular matrix T,  in
                   Schur  Schur  canonical  form.  On exit, the reor-
                   dered  upper  quasi-triangular  matrix,  again  in
                   Schur canonical form.
    
         LDT       (input) INTEGER
                   The leading dimension  of  the  array  T.  LDT  >=
                   max(1,N).
    
         Q         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDQ,N)
                   On entry, if COMPQ = 'V', the matrix  Q  of  Schur
                   vectors.   On  exit,  if  COMPQ  = 'V', Q has been
                   postmultiplied by  the  orthogonal  transformation
                   matrix  Z  which reorders T.  If COMPQ = 'N', Q is
                   not referenced.
    
         LDQ       (input) INTEGER
                   The leading dimension of  the  array  Q.   LDQ  >=
                   max(1,N).
    
         IFST      (input/output) INTEGER
                   ILST    (input/output) INTEGER Specify the  reord-
                   ering of the diagonal blocks of T.  The block with
                   row index IFST is moved to row ILST, by a sequence
                   of  transpositions  between  adjacent  blocks.  On
                   exit, if IFST pointed on entry to the  second  row
                   of  a  2-by-2 block, it is changed to point to the
                   first row; ILST always points to the first row  of
                   the  block in its final position (which may differ
                   from its input value by +1 or -1).  1 <=  IFST  <=
                   N; 1 <= ILST <= N.
    
         WORK      (workspace) DOUBLE PRECISION array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   = 1:  two adjacent blocks were too close  to  swap
                   (the  problem is very ill-conditioned); T may have
                   been partially reordered, and ILST points  to  the
                   first  row  of  the  current position of the block
                   being moved.
    
    
    
    


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