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( ∗ )

#include <sunperf.h>

void strexc(char compq, int n, float ∗t, int ldt, float ∗q, int ldq, int ∗ifst, int ∗ilst, int ∗info) ;

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 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 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.

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 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.

SunOS WorkShop_5.0  —  Last change: 10 Dec 1998