ZTGEXC - reorder the generalized Schur decomposition of a
complex matrix pair (A,B), using an unitary 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
SYNOPSIS
SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q,
LDQ, Z, LDZ, IFST, ILST, INFO )
LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
Z( LDZ, * )
PURPOSE
ZTGEXC reorders the generalized Schur decomposition of a
complex matrix pair (A,B), using an unitary 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 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*16 array, dimension (LDA,N)
On entry, the upper triangular 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*16 array, dimension (LDB,N)
On entry, the upper triangular matrix B in the
pair (A, B). On exit, the updated matrix B.
The leading dimension of the array B. LDB >=
max(1,N).
Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
On entry, if WANTQ = .TRUE., the unitary 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) COMPLEX*16 array, dimension (LDZ,N)
On entry, if WANTZ = .TRUE., the unitary 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.
INFO (output) INTEGER
=0: Successful exit.
<0: if INFO = -i, the i-th argument had an ille
gal 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 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.
[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
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.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms
and Software
for Solving the Generalized Sylvester Equation and
Estimating the
Separation between Regular Matrix Pairs, Report UMINF
- 93.23,
Department of Computing Science, Umea University,
S-901 87 Umea,
Sweden, December 1993, Revised April 1994, Also as
LAPACK working
Note 75. To appear in ACM Trans. on Math. Software,
Vol 22, No 1,
1996.
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