DTGEXC(l) ) DTGEXC(l)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 diago‐
nal blocks. B is upper triangular.
Optionally, the matrices Q and Z of generalized Schur vectors 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 generalized 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 reordering of the
diagonal blocks of (A, B). The block with row index IFST is
moved to row ILST, by a sequence of swapping 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 posi‐
tion (which may differ from its input value by +1 or -1). 1 <=
IFST, ILST <= N.
WORK (workspace/output) DOUBLE PRECISION array, dimension (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 illegal value.
=1: The transformed matrix pair (A, B) would be too far from
generalized Schur form; the problem is ill- conditioned. (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 Eigenvalues 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(l)
