SRC/dtgex2.f(3)            Library Functions Manual            SRC/dtgex2.f(3)

NAME
       SRC/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 (logical wantq, logical wantz, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldb, * ) b, integer ldb, double precision, dimension( ldq, *
       ) q, integer ldq, double precision, dimension( ldz, * ) z, integer ldz,
       integer j1, integer n1, integer n2, double precision, dimension( * )
       work, integer lwork, integer info)
       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.

       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 219 of file dtgex2.f.

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

LAPACK                          Version 3.12.0                 SRC/dtgex2.f(3)