CTGEXC(3S)CTGEXC(3S)NAME
CTGEXC - 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 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, * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
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
WANTZ (input) LOGICAL
N (input) INTEGER
The order of the matrices A and B. N >= 0.
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CTGEXC(3S)CTGEXC(3S)
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/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 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
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CTGEXC(3S)CTGEXC(3S)
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.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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