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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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