Previous: strevc Up: ../lapack-s.html Next: strrfs

# strexc

```
NAME
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 similar-
ity 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 diag-
onal blocks; each 2-by-2 diagonal block has its diagonal
elements equal and its off-diagonal elements of opposite
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 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 vec-
tors.  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 reorder-
ing 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 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.
```