ztgex2(3)

NAME

ZTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11)

and (A22,B22)

SYNOPSIS

SUBROUTINE  ZTGEX2(  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*16     A( LDA, * ), B( LDB, * ), Q( LDQ, *  ),
Z( LDZ, * )

PURPOSE

ZTGEX2 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 vec

tors 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.

A (input/output) COMPLEX*16 arrays, dimensions

(LDA,N)

On entry, the matrix A in the pair (A, B). On ex

it, the updated matrix A.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

B (input/output) COMPLEX*16 arrays, dimensions

(LDB,N)

On entry, the matrix B in the pair (A, B). On ex

it, the updated matrix B.

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

Q (input/output) COMPLEX*16 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*16 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- condi

tioned. (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 Eigenval

ues 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 Condi

tion
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 ap

pear in
Numerical Algorithms, 1996.

LAPACK version 3.0 15 June 2000

ZTGEX2(3)