dtgex2.f(3)

NAME
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 (logicalWANTQ, logicalWANTZ, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( ldz, * )Z, integerLDZ, integerJ1, integerN1, integerN2, double precision, dimension( * )WORK, integerLWORK, integerINFO)

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.

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 dtgex2.f.

Author

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