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dtrexc examples
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Man Page Details
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NAME
       DTREXC - 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.

