DTGEX2(3S)DTGEX2(3S)NAMEDTGEX2 - swap adjacent diagonal blocks (A11, B11) and (A22, B22) of size
1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an
orthogonal equivalence transformation
SYNOPSIS
SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
N1, N2, WORK, LWORK, INFO )
LOGICAL WANTQ, WANTZ
INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
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.
PURPOSEDTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size
1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an
orthogonal equivalence transformation. (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
WANTZ (input) LOGICAL
N (input) INTEGER
The order of the matrices A and B. N >= 0.
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DTGEX2(3S)DTGEX2(3S)
A (input/output) DOUBLE PRECISION arrays, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B). On exit, the updated
matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) DOUBLE PRECISION arrays, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B). On exit, the updated
matrix 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. Not referenced if WANTQ = .FALSE..
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. Not referenced if WANTZ = .FALSE..
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1. If WANTZ =
.TRUE., LDZ >= N.
J1 (input) INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.
N1 (input) INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK).
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= MAX( N*(N2+N1),
(N2+N1)*(N2+N1)*2 )
INFO (output) INTEGER
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be too far
from generalized Schur form; the blocks are not swapped and (A,
B) and (Q, Z) are unchanged. The problem of swapping is too
ill-conditioned. <0: If INFO = -16: LWORK is too small.
Appropriate value for LWORK is returned in WORK(1).
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DTGEX2(3S)DTGEX2(3S)FURTHER DETAILS
Based on contributions by
Bo Kagstrom and Peter Poromaa, Department of Computing Science,
Umea University, S-901 87 Umea, Sweden.
In the current code both weak and strong stability tests are performed.
The user can omit the strong stability test by changing the internal
logical parameter WANDS to .FALSE.. See ref. [2] for details.
[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.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condition
Estimation: Theory, Algorithms and Software,
Report UMINF - 94.04, Department of Computing Science, Umea
University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
Note 87. To appear in Numerical Algorithms, 1996.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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