Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

SYNOPSIS

       SUBROUTINE ZTGEX2( 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*16     A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )

PURPOSE

       ZTGEX2 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

ARGUMENTS

        WANTQ   (input) LOGICAL
                .TRUE. : update the left transformation matrix Q;
                .FALSE.: do not update Q.

        WANTZ   (input) LOGICAL
                .TRUE. : update the right transformation matrix Z;
                .FALSE.: do not update Z.

        N       (input) INTEGER
                The order of the matrices A and B. N >= 0.

        A       (input/output) COMPLEX*16 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*16 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*16 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*16 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.

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 auxiliary routine (version 3.3.1)   April 2011                            ZTGEX2(3lapack)