CTGEXC(1) LAPACK routine (version 3.2) CTGEXC(1)NAME
CTGEXC - 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
SYNOPSIS
SUBROUTINE CTGEXC( 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 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
PURPOSE
CTGEXC 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 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 .TRUE. : update the left transformation matrix
Q;
WANTZ (input) LOGICAL
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) COMPLEX 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 array, dimension (LDB,N)
On entry, the upper triangular 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) COMPLEX 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 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) 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 illegal 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 partially 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 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.
[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.
LAPACK routine (version 3.2) November 2008 CTGEXC(1)
