DTREXC(3)      LAPACK routine of NEC Numeric Library Collection      DTREXC(3)



NAME
       DTREXC

SYNOPSIS
       SUBROUTINE DTREXC (COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, 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 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)
                     COMPQ is CHARACTER*1
                     = 'V':  update the matrix Q of Schur vectors;
                     = 'N':  do not update Q.

           N         (input)
                     N is INTEGER
                     The order of the matrix T. N >= 0.

           T         (input/output)
                     T is 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)
                     LDT is INTEGER
                     The leading dimension of the array T. LDT >= max(1,N).

           Q         (input/output)
                     Q is 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)
                     LDQ is INTEGER
                     The leading dimension of the array Q.  LDQ >= max(1,N).

           IFST      (input/output)
                     IFST is INTEGER

           ILST      (input/output)
                     ILST is 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      (output)
                     WORK is DOUBLE PRECISION array, dimension (N)

           INFO      (output)
                     INFO is 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 routine                  31 October 2017                      DTREXC(3)