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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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dtgex2(l) |
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DTGEX2 - 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
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SUBROUTINE DTGEX2( |
WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK, LWORK, INFO ) | ||
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LOGICAL |
WANTQ, WANTZ | ||
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INTEGER |
INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 | ||
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DOUBLE |
PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * ) |
DTGEX2 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)’
WANTQ (input)
LOGICAL
WANTZ (input) LOGICAL
N (input) INTEGER
The order of the matrices A and B. N >= 0.
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).
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.
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dtgex2(l) | |