NAME¶

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

SYNOPSIS¶

SUBROUTINE DTREXC(

COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO )

CHARACTER COMPQ INTEGER IFST, ILST, INFO, LDQ, LDT, N DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )

PURPOSE¶

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 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) 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 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) 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-conditioned); T may have been partially reordered, and ILST points to the first row of the current position of the block being moved.