MB04WP

Generating an orthogonal symplectic matrix which performed the reduction in MB04PU

Purpose

  To generate an orthogonal symplectic matrix U, which is defined as
  a product of symplectic reflectors and Givens rotations

  U = diag( H(1),H(1) )      G(1)  diag( F(1),F(1) )
      diag( H(2),H(2) )      G(2)  diag( F(2),F(2) )
                             ....
      diag( H(n-1),H(n-1) ) G(n-1) diag( F(n-1),F(n-1) ).

  as returned by MB04PU. The matrix U is returned in terms of its
  first N rows

                   [  U1   U2 ]
               U = [          ].
                   [ -U2   U1 ]

      SUBROUTINE MB04WP( N, ILO, U1, LDU1, U2, LDU2, CS, TAU, DWORK,
     $                   LDWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           ILO, INFO, LDU1, LDU2, LDWORK, N
C     .. Array Arguments ..
      DOUBLE PRECISION  CS(*), DWORK(*), U1(LDU1,*), U2(LDU2,*), TAU(*)

Input/Output Parameters

  N       (input) INTEGER
          The order of the matrices U1 and U2.  N >= 0.

  ILO     (input) INTEGER
          ILO must have the same value as in the previous call of
          MB04PU. U is equal to the unit matrix except in the
          submatrix
          U([ilo+1:n n+ilo+1:2*n], [ilo+1:n n+ilo+1:2*n]).
          1 <= ILO <= N, if N > 0; ILO = 1, if N = 0.

  U1      (input/output) DOUBLE PRECISION array, dimension (LDU1,N)
          On entry, the leading N-by-N part of this array must
          contain in its i-th column the vector which defines the
          elementary reflector F(i).
          On exit, the leading N-by-N part of this array contains
          the matrix U1.

  LDU1    INTEGER
          The leading dimension of the array U1.  LDU1 >= MAX(1,N).

  U2      (input/output) DOUBLE PRECISION array, dimension (LDU2,N)
          On entry, the leading N-by-N part of this array must
          contain in its i-th column the vector which defines the
          elementary reflector H(i) and, on the subdiagonal, the
          scalar factor of H(i).
          On exit, the leading N-by-N part of this array contains
          the matrix U2.

  LDU2    INTEGER
          The leading dimension of the array U2.  LDU2 >= MAX(1,N).

  CS      (input) DOUBLE PRECISION array, dimension (2N-2)
          On entry, the first 2N-2 elements of this array must
          contain the cosines and sines of the symplectic Givens
          rotations G(i).

  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
          On entry, the first N-1 elements of this array must
          contain the scalar factors of the elementary reflectors
          F(i).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0,  DWORK(1)  returns the optimal
          value of LDWORK.
          On exit, if  INFO = -10,  DWORK(1)  returns the minimum
          value of LDWORK.

  LDWORK  INTEGER
          The length of the array DWORK. LDWORK >= MAX(1,2*(N-ILO)).
          For optimum performance LDWORK should be larger. (See
          SLICOT Library routine MB04WD).

          If LDWORK = -1, then a workspace query is assumed;
          the routine only calculates the optimal size of the
          DWORK array, returns this value as the first entry of
          the DWORK array, and no error message related to LDWORK
          is issued by XERBLA.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The algorithm requires O(N**3) floating point operations and is
  strongly backward stable.

  [1] C. F. VAN LOAN:
      A symplectic method for approximating all the eigenvalues of
      a Hamiltonian matrix.
      Linear Algebra and its Applications, 61, pp. 233-251, 1984.

  [2] D. KRESSNER:
      Block algorithms for orthogonal symplectic factorizations.
      BIT, 43 (4), pp. 775-790, 2003.

  None

Program Text

  None

  None

  None