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

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

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:
    November 2011

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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