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
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, * )
PURPOSE
DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22,
B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangu
lar matrix pair (A, B) by an orthogonal equivalence trans
formation. (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 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).
(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-
small. Appropriate value for LWORK is returned in
WORK(1).
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 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.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with
Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condi
tion
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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