strexc(3)

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 in

dex 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 ma

trix 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 COM

PQ = '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 re

ordering of the diagonal blocks of T. The block with row index

IFST is moved to row ILST, by a sequence of transpositions be

tween 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 fi

nal 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 posi

tion of the block being moved.

LAPACK version 3.0 15 June 2000

STREXC(3)