STREXC - 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
SYNOPSIS
SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST,
WORK, INFO )
CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
PURPOSE
STREXC 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 SHSEQR),
that is, block upper triangular with 1-by-1 and 2-by-2
diagonal blocks; each 2-by-2 diagonal block has its diago
nal elements equal and its off-diagonal elements of oppo
site 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) REAL 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) REAL 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.
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) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal 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.
Man(1) output converted with
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