ztgex2.f(3)

NAME
ztgex2.f -

SYNOPSIS

  Functions/Subroutines
subroutine ztgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Function/Subroutine Documentation

  subroutine ztgex2 (logicalWANTQ, logicalWANTZ, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Purpose:

     ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
     in an upper triangular matrix pair (A, B) by an unitary equivalence
     transformation.
     (A, B) must be in generalized Schur canonical form, that is, A and
     B are both upper triangular.
     Optionally, the matrices Q and Z of generalized Schur vectors are
     updated.
            Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
            Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDZ,N)
              If WANTQ = .TRUE, on entry, the unitary 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 COMPLEX*16 array, dimension (LDZ,N)
              If WANTZ = .TRUE, on entry, the unitary 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).

    INFO

              INFO is INTEGER
               =0:  Successful exit.
               =1:  The transformed matrix pair (A, B) would be too far
                    from generalized Schur form; the problem is ill-
                    conditioned.

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 190 of file ztgex2.f.

Author

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