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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 transā€
       formation.

       (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  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.

LAPACK version 3.0		 15 June 2000			     CTGEX2(l)
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