DTREXC(l) ) DTREXC(l)
DTREXC - 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
SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO )
INTEGER IFST, ILST, INFO, LDQ, LDT, N
DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )
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 ele-
ments equal and its off-diagonal elements of opposite sign.
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 transposi-
tions 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-condi-
tioned); T may have been partially reordered, and ILST points to the first row of
the current position of the block being moved.
LAPACK version 3.0 15 June 2000 DTREXC(l)