SRC/stgex2.f(3)

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

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 array, dimension (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 array, dimension (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 (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 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.

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 stgex2.f.

Author

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