MB03WA

Swapping two adjacent diagonal blocks in a periodic real Schur canonical form

Purpose

  To swap adjacent diagonal blocks A11*B11 and A22*B22 of size
  1-by-1 or 2-by-2 in an upper (quasi) triangular matrix product
  A*B by an orthogonal equivalence transformation.

  (A, B) must be in periodic real Schur canonical form (as returned
  by SLICOT Library routine MB03XP), i.e., A is block upper
  triangular with 1-by-1 and 2-by-2 diagonal blocks, and B is upper
  triangular.

  Optionally, the matrices Q and Z of generalized Schur vectors are
  updated.

      Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)',
      Z(in) * B(in) * Q(in)' = Z(out) * B(out) * Q(out)'.

  This routine is largely based on the LAPACK routine DTGEX2
  developed by Bo Kagstrom and Peter Poromaa.

      SUBROUTINE MB03WA( WANTQ, WANTZ, N1, N2, A, LDA, B, LDB, Q, LDQ,
     $                   Z, LDZ, INFO )
C     .. Scalar Arguments ..
      LOGICAL            WANTQ, WANTZ
      INTEGER            INFO, LDA, LDB, LDQ, LDZ, N1, N2
C     .. Array Arguments ..
      DOUBLE PRECISION   A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)

Mode Parameters

  WANTQ   LOGICAL
          Indicates whether or not the user wishes to accumulate
          the matrix Q as follows:
          = .TRUE. :  The matrix Q is updated;
          = .FALSE.:  the matrix Q is not required.

  WANTZ   LOGICAL
          Indicates whether or not the user wishes to accumulate
          the matrix Z as follows:
          = .TRUE. :  The matrix Z is updated;
          = .FALSE.:  the matrix Z is not required.

  N1      (input) INTEGER
          The order of the first block A11*B11. N1 = 0, 1 or 2.

  N2      (input) INTEGER
          The order of the second block A22*B22. N2 = 0, 1 or 2.

  A       (input/output) DOUBLE PRECISION array, dimension
          (LDA,N1+N2)
          On entry, the leading (N1+N2)-by-(N1+N2) part of this
          array must contain the matrix A.
          On exit, the leading (N1+N2)-by-(N1+N2) part of this array
          contains the matrix A of the reordered pair.

  LDA     INTEGER
          The leading dimension of the array A. LDA >= MAX(1,N1+N2).

  B       (input/output) DOUBLE PRECISION array, dimension
          (LDB,N1+N2)
          On entry, the leading (N1+N2)-by-(N1+N2) part of this
          array must contain the matrix B.
          On exit, the leading (N1+N2)-by-(N1+N2) part of this array
          contains the matrix B of the reordered pair.

  LDB     INTEGER
          The leading dimension of the array B. LDB >= MAX(1,N1+N2).

  Q       (input/output) DOUBLE PRECISION array, dimension
          (LDQ,N1+N2)
          On entry, if WANTQ = .TRUE., the leading
          (N1+N2)-by-(N1+N2) part of this array must contain the
          orthogonal matrix Q.
          On exit, the leading (N1+N2)-by-(N1+N2) part of this array
          contains the updated matrix Q. Q will be a rotation
          matrix for N1=N2=1.
          This array is not referenced if WANTQ = .FALSE..

  LDQ     INTEGER
          The leading dimension of the array Q. LDQ >= 1.
          If WANTQ = .TRUE., LDQ >= N1+N2.

  Z       (input/output) DOUBLE PRECISION array, dimension
          (LDZ,N1+N2)
          On entry, if WANTZ = .TRUE., the leading
          (N1+N2)-by-(N1+N2) part of this array must contain the
          orthogonal matrix Z.
          On exit, the leading (N1+N2)-by-(N1+N2) part of this array
          contains the updated matrix Z. Z will be a rotation
          matrix for N1=N2=1.
          This array is not referenced if WANTZ = .FALSE..

  LDZ     INTEGER
          The leading dimension of the array Z. LDZ >= 1.
          If WANTZ = .TRUE., LDZ >= N1+N2.

  INFO    INTEGER
          = 0:  successful exit;
          = 1:  the transformed matrix (A, B) would be
                too far from periodic Schur form; the blocks are
                not swapped and (A,B) and (Q,Z) are unchanged.

  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.

  [1] Kagstrom, B.
      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] Kagstrom, B., and Poromaa, P.
      Computing eigenspaces with specified eigenvalues of a regular
      matrix pair (A, B) and condition estimation: Theory,
      algorithms and software, Numer. Algorithms, 1996, vol. 12,
      pp. 369-407.

  None

Program Text

  None

  None

  None