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

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