.TH DTREXC 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DTREXC - 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 .SH SYNOPSIS .TP 19 SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO ) .TP 19 .ti +4 CHARACTER COMPQ .TP 19 .ti +4 INTEGER IFST, ILST, INFO, LDQ, LDT, N .TP 19 .ti +4 DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) .SH 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. .br 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. .br .SH ARGUMENTS .TP 8 COMPQ (input) CHARACTER*1 = \(aqV\(aq: update the matrix Q of Schur vectors; .br = \(aqN\(aq: do not update Q. .TP 8 N (input) INTEGER The order of the matrix T. N >= 0. .TP 8 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. .TP 8 LDT (input) INTEGER The leading dimension of the array T. LDT >= max(1,N). .TP 8 Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) On entry, if COMPQ = \(aqV\(aq, the matrix Q of Schur vectors. On exit, if COMPQ = \(aqV\(aq, Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = \(aqN\(aq, Q is not referenced. .TP 8 LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,N). .TP 8 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. .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br = 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.