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

NAME

       LAPACK-3  -  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

SYNOPSIS

       SUBROUTINE STGEX2( WANTQ,  WANTZ,  N,  A,  LDA,  B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK,
                          LWORK, INFO )

           LOGICAL        WANTQ, WANTZ

           INTEGER        INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2

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

PURPOSE

       STGEX2 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 SGGES), 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

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) REAL 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) REAL 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) REAL array, dimension (LDZ,N)
                On entry, if WANTQ = .TRUE., the orthogonal 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) REAL 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     (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). 1 <= J1 <= N.

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

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

        WORK    (workspace) REAL array, dimension (MAX(1,LWORK)).

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

        INFO    (output) 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).

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                            STGEX2(3lapack)