CTGEX2(3S)CTGEX2(3S)NAME
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, * )
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
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 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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CTGEX2(3S)CTGEX2(3S)
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).
Q (input/output) COMPLEX array, dimension (LDZ,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 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.
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 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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CTGEX2(3S)CTGEX2(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.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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