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ctgex2.f(3)				      LAPACK				      ctgex2.f(3)

NAME
       ctgex2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ctgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
	   CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
	   unitary equivalence transformation.

Function/Subroutine Documentation
   subroutine ctgex2 (logicalWANTQ, logicalWANTZ, integerN, complex, dimension( lda, * )A,
       integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldq, * )Q,
       integerLDQ, complex, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)
       CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
       unitary equivalence transformation.

       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)**H = Q(out) * A(out) * Z(out)**H
		   Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

       Parameters:
	   WANTQ

		     WANTQ is LOGICAL
		     .TRUE. : update the left transformation matrix Q;
		     .FALSE.: do not update Q.

	   WANTZ

		     WANTZ is LOGICAL
		     .TRUE. : update the right transformation matrix Z;
		     .FALSE.: do not update Z.

	   N

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

	   A

		     A is COMPLEX arrays, dimensions (LDA,N)
		     On entry, the matrix A in the pair (A, B).
		     On exit, the updated matrix A.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A. LDA >= max(1,N).

	   B

		     B is COMPLEX arrays, dimensions (LDB,N)
		     On entry, the matrix B in the pair (A, B).
		     On exit, the updated matrix B.

	   LDB

		     LDB is INTEGER
		     The leading dimension of the array B. LDB >= max(1,N).

	   Q

		     Q is 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

		     LDQ is INTEGER
		     The leading dimension of the array Q. LDQ >= 1;
		     If WANTQ = .TRUE., LDQ >= N.

	   Z

		     Z is 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

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

	   J1

		     J1 is INTEGER
		     The index to the first block (A11, B11).

	   INFO

		     INFO is INTEGER
		      =0:  Successful exit.
		      =1:  The transformed matrix pair (A, B) would be too far
			   from generalized Schur form; the problem is ill-
			   conditioned.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:
	   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.

       Contributors:
	   Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
	   87 Umea, Sweden.

       References:
	   [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.

       Definition at line 190 of file ctgex2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ctgex2.f(3)
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