DTREXC (3lapack)

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
  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-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
          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 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.