dtrexc (l)  Linux Manuals
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
NAME
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 ILSTSYNOPSIS
 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 1by1 and 2by2 diagonal blocks; each 2by2 diagonal block has its diagonal elements equal and its offdiagonal elements of opposite sign.
ARGUMENTS
 COMPQ (input) CHARACTER*1

= aqVaq: update the matrix Q of Schur vectors;
= aqNaq: 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 quasitriangular matrix T, in Schur Schur canonical form. On exit, the reordered upper quasitriangular 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 = aqVaq, the matrix Q of Schur vectors. On exit, if COMPQ = aqVaq, Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = aqNaq, 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 2by2 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 ith argument had an illegal value
= 1: two adjacent blocks were too close to swap (the problem is very illconditioned); T may have been partially reordered, and ILST points to the first row of the current position of the block being moved.