CTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11)
and (A22,B22)
SYNOPSIS
SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q,
LDQ, Z, LDZ, J1, INFO )
LOGICAL WANTQ, WANTZ
INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, N
COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
Z( LDZ, * )
PURPOSE
CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and
(A22,B22) in an upper triangular matrix pair (A, B) by an
unitary equivalence transformation.
(A, B) must be in generalized Schur canonical form, that
is, A and B are both 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) COMPLEX 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) COMPLEX 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).
If WANTQ = .TRUE, on entry, the unitary 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) COMPLEX array, dimension (LDZ,N)
If WANTZ = .TRUE, on entry, the unitary 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).
INFO (output) INTEGER
=0: Successful exit.
=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 par
tially 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.
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
Department of Computing Science, Umea University,
S-901 87 Umea,
Sweden, 1994. Also as LAPACK Working Note 87. To
appear in
Numerical Algorithms, 1996.
Man(1) output converted with
man2html