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CTGEXC(l)			       )			     CTGEXC(l)

NAME
       CTGEXC  -  reorder  the	generalized  Schur  decomposition of a complex
       matrix pair (A,B), using an unitary equivalence transformation  (A,  B)
       := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index
       IFST is moved to row ILST

SYNOPSIS
       SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB,  Q,	LDQ,  Z,  LDZ,
			  IFST, ILST, INFO )

	   LOGICAL	  WANTQ, WANTZ

	   INTEGER	  IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N

	   COMPLEX	  A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE
       CTGEXC reorders the generalized Schur decomposition of a complex matrix
       pair (A,B), using an unitary equivalence transformation (A, B) :=  Q  *
       (A,  B)	* Z', so that the diagonal block of (A, B) with row index IFST
       is moved to row ILST.  (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 array, dimension (LDA,N)
	       On entry, the upper triangular 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 array, dimension (LDB,N)
	       On entry, the upper triangular 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)
	       On entry, if WANTQ = .TRUE., the unitary matrix	Q.   On	 exit,
	       the updated matrix Q.  If WANTQ = .FALSE., Q is not referenced.

       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)
	       On entry, if WANTZ = .TRUE., the unitary matrix	Z.   On	 exit,
	       the updated matrix Z.  If WANTZ = .FALSE., Z is not referenced.

       LDZ     (input) INTEGER
	       The  leading  dimension	of  the	 array Z. LDZ >= 1; If WANTZ =
	       .TRUE., LDZ >= N.

       IFST    (input/output) INTEGER
	       ILST    (input/output) INTEGER Specify the  reordering  of  the
	       diagonal	 blocks	 of  (A, B).  The block with row index IFST is
	       moved to row ILST, by a sequence of swapping  between  adjacent
	       blocks.

       INFO    (output) INTEGER
	       =0:  Successful exit.
	       <0:  if INFO = -i, the i-th argument had an illegal value.
	       =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.

       [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.

       [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
	   for Solving the Generalized Sylvester Equation and Estimating the
	   Separation between Regular Matrix Pairs, Report UMINF - 93.23,
	   Department of Computing Science, Umea University, S-901 87 Umea,
	   Sweden, December 1993, Revised April 1994, Also as LAPACK working
	   Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
	   1996.

LAPACK version 3.0		 15 June 2000			     CTGEXC(l)
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