CTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

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, * )

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)'

WANTQ (input) LOGICAL

WANTZ (input) LOGICAL

N (input) INTEGER

The order of the matrices A and B. N >= 0.

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.

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.