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STGEX2(1) LAPACK auxiliary routine (version 3.2) STGEX2(1)

NAME

STGEX2 - swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation

SYNOPSIS

WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK, LWORK, INFO )

LOGICAL WANTQ, WANTZ INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )

PURPOSE

STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation. (A, B) must be in generalized real Schur canonical form (as returned by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is 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



The order of the matrices A and B. N >= 0.
On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
The leading dimension of the array A. LDA >= max(1,N).
On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
The leading dimension of the array B. LDB >= max(1,N).
On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE..
The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
On entry, if WANTZ =.TRUE., the orthogonal matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE..
The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
The index to the first block (A11, B11). 1 <= J1 <= N.
The order of the first block (A11, B11). N1 = 0, 1 or 2.
The order of the second block (A22, B22). N2 = 0, 1 or 2.
The dimension of the array WORK. LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be too far from generalized Schur form; the blocks are not swapped and (A, B) and (Q, Z) are unchanged. The problem of swapping is too ill-conditioned. <0: If INFO = -16: LWORK is too small. Appropriate value for LWORK is returned in WORK(1).

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
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.

November 2008 LAPACK auxiliary routine (version 3.2)