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DTREXC(l)			       )			     DTREXC(l)

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( * )

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 simi‐
       larity 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  diagonal	 blocks;  each
       2-by-2 diagonal block has its diagonal elements equal and its off-diag‐
       onal 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 reordered 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 orthogo‐
	       nal 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 reordering 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	 posi‐
	       tion (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 illegal 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.

LAPACK version 3.0		 15 June 2000			     DTREXC(l)
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