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.

COMPQ

          COMPQ is CHARACTER*1


          = 'V':  update the matrix Q of Schur vectors;


          = 'N':  do not update Q.

N

          N is INTEGER


          The order of the matrix T. N >= 0.


          If N == 0 arguments ILST and IFST may be any value.

T

          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

          LDT is INTEGER


          The leading dimension of the array T. LDT >= max(1,N).

Q

          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

          LDQ is INTEGER


          The leading dimension of the array Q.  LDQ >= 1, and if


          COMPQ = 'V', LDQ >= max(1,N).

IFST

          IFST is INTEGER

ILST

          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

          WORK is DOUBLE PRECISION array, dimension (N)

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016