NAME

       stgex2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine stgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK,
           LWORK, INFO)
           STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
           orthogonal equivalence transformation.

Function/Subroutine Documentation

   subroutine stgex2 (logicalWANTQ, logicalWANTZ, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldq, * )Q,
       integerLDQ, real, dimension( ldz, * )Z, integerLDZ, integerJ1, integerN1, integerN2, real,
       dimension( * )WORK, integerLWORK, integerINFO)
       STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an
       orthogonal equivalence transformation.

       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

       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 REAL 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 REAL 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 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

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

           Z

                     Z is 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

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

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >=  MAX( 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 stgex2.f.

Author

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