dtgexc(3)

NAME

DTGEXC - reorder the generalized real Schur decomposition

of a real matrix pair (A,B) using an orthogonal equivalence

transformation (A, B) = Q * (A, B) * Z',

SYNOPSIS

SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A,  LDA,  B,  LDB,  Q,
LDQ, Z, LDZ, IFST, ILST, WORK, LWORK, INFO )
    LOGICAL        WANTQ, WANTZ
    INTEGER         IFST,  ILST, INFO, LDA, LDB, LDQ, LDZ,
LWORK, N
    DOUBLE         PRECISION A( LDA, * ), B( LDB, * ),  Q(
LDQ, * ), WORK( * ), Z( LDZ, * )

PURPOSE

DTGEXC reorders the generalized real Schur decomposition

of a real matrix pair (A,B) using an orthogonal equivalence

transformation (A, B) = Q * (A, B) * Z', so that the diagonal

block of (A, B) with row index IFST is moved to row ILST.

(A, B) must be in generalized real Schur canonical form

(as returned by DGGES), i.e. A is block upper triangular with

1-by-1 and 2-by-2 diagonal blocks. B is upper triangular.

Optionally, the matrices Q and Z of generalized Schur vec

tors are updated.

Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'

ARGUMENTS

WANTQ (input) LOGICAL

WANTZ (input) LOGICAL

N (input) INTEGER

The order of the matrices A and B. N >= 0.

A (input/output) DOUBLE PRECISION array, dimension

(LDA,N)

On entry, the matrix A in generalized real Schur

canonical form. On exit, the updated matrix A, again in general

ized real Schur canonical form.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

B (input/output) DOUBLE PRECISION array, dimension

(LDB,N)

On entry, the matrix B in generalized real Schur

canonical form (A,B). On exit, the updated matrix B, again in

generalized real Schur canonical form (A,B).

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

Q (input/output) DOUBLE PRECISION array, dimension

(LDZ,N)

On entry, if WANTQ = .TRUE., the orthogonal matrix

Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not

referenced.

LDQ (input) INTEGER

The leading dimension of the array Q. LDQ >= 1.

If WANTQ = .TRUE., LDQ >= N.

Z (input/output) DOUBLE PRECISION array, dimension

(LDZ,N)

On entry, if WANTZ = .TRUE., the orthogonal matrix

Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not

referenced.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1.

If WANTZ = .TRUE., LDZ >= N.

IFST (input/output) INTEGER

ILST (input/output) INTEGER Specify the re

ordering of the diagonal blocks of (A, B). The block with row

index IFST is moved to row ILST, by a sequence of swapping 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, ILST <= N.

WORK (workspace/output) DOUBLE PRECISION array, dimen

sion (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >= 4*N +

16.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

INFO (output) INTEGER

=0: successful exit.
<0: if INFO = -i, the i-th argument had an ille

gal value.
=1: The transformed matrix pair (A, B) would be

too far from generalized Schur form; the problem is ill- condi

tioned. (A, B) may have been partially reordered, and ILST points

to the first row of the current position of the block being

moved.

FURTHER DETAILS

Based on contributions by

Bo Kagstrom and Peter Poromaa, Department of Computing

Science,
Umea University, S-901 87 Umea, Sweden.

[1] B. Kagstrom; A Direct Method for Reordering Eigenval

ues in the

Generalized Real Schur Form of a Regular Matrix Pair

(A, B), in
M.S. Moonen et al (eds), Linear Algebra for Large

Scale and
Real-Time Applications, Kluwer Academic Publ. 1993, pp

195-218.

LAPACK version 3.0 15 June 2000

DTGEXC(3)