DTREXC(l)		LAPACK routine (version	1.1)		    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 similarity transforma-
  tion 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 diago-
  nal 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	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 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 reordering	of the diago-
	  nal 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 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.