DTGEXC(3S)DTGEXC(3S)NAMEDTGEXC - 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, * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSEDTGEXC 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 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
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DTGEXC(3S)DTGEXC(3S)
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 position
(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.
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DTGEXC(3S)DTGEXC(3S)
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.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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