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dtgex2.f(3)				      LAPACK				      dtgex2.f(3)

NAME
       dtgex2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dtgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK,
	   LWORK, INFO)
	   DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
	   orthogonal equivalence transformation.

Function/Subroutine Documentation
   subroutine dtgex2 (logicalWANTQ, logicalWANTZ, integerN, double precision, dimension( lda, *
       )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision,
       dimension( ldq, * )Q, integerLDQ, double precision, dimension( ldz, * )Z, integerLDZ,
       integerJ1, integerN1, integerN2, double precision, dimension( * )WORK, integerLWORK,
       integerINFO)
       DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
       orthogonal equivalence transformation.

       Purpose:

	    DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
	    of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
	    (A, B) by an orthogonal equivalence transformation.

	    (A, B) must be in generalized real Schur canonical form (as returned
	    by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
	    diagonal blocks. B is upper triangular.

	    Optionally, the matrices Q and Z of generalized Schur vectors are
	    updated.

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

       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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, 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 DOUBLE PRECISION array, dimension (LDQ,N)
		     On entry, if WANTQ = .TRUE., the orthogonal 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 DOUBLE PRECISION array, dimension (LDZ,N)
		     On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N.

	   N1

		     N1 is INTEGER
		     The order of the first block (A11, B11). N1 = 0, 1 or 2.

	   N2

		     N2 is INTEGER
		     The order of the second block (A22, B22). N2 = 0, 1 or 2.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.
		     LWORK >=  MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )

	   INFO

		     INFO is INTEGER
		       =0: Successful exit
		       >0: If INFO = 1, the transformed matrix (A, B) would be
			   too far from generalized Schur form; the blocks are
			   not swapped and (A, B) and (Q, Z) are unchanged.
			   The problem of swapping is too ill-conditioned.
		       <0: If INFO = -16: LWORK is too small. Appropriate value
			   for LWORK is returned in WORK(1).

       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 221 of file dtgex2.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dtgex2.f(3)
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