CTGEX2(l)								 )								 CTGEX2(l)

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, * )

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.

       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 inter-
       nal 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.

LAPACK version 3.0						   15 June 2000 							 CTGEX2(l)