MB04DB

Inverse of a balancing transformation for a real skew-Hamiltonian/Hamiltonian pencil

Purpose

  To apply from the left the inverse of a balancing transformation,
  computed by the SLICOT Library routine MB04DP, to the matrix

            [   V1   ]
            [        ],
            [ sgn*V2 ]

  where sgn is either +1 or -1.

      SUBROUTINE MB04DB( JOB, SGN, N, ILO, LSCALE, RSCALE, M, V1, LDV1,
     $                   V2, LDV2, INFO )
C     .. Scalar Arguments ..
      CHARACTER         JOB, SGN
      INTEGER           ILO, INFO, LDV1, LDV2, M, N
C     .. Array Arguments ..
      DOUBLE PRECISION  LSCALE(*), RSCALE(*), V1(LDV1,*), V2(LDV2,*)

Mode Parameters

  JOB     CHARACTER*1
          Specifies the type of inverse transformation required:
          = 'N':  do nothing, return immediately;
          = 'P':  do inverse transformation for permutation only;
          = 'S':  do inverse transformation for scaling only;
          = 'B':  do inverse transformations for both permutation
                  and scaling.
          JOB must be the same as the argument JOB supplied to
          MB04DP.

  SGN     CHARACTER*1
          Specifies the sign to use for V2:
          = 'P':  sgn = +1;
          = 'N':  sgn = -1.

  N       (input) INTEGER
          The number of rows of the matrices V1 and V2. N >= 0.

  ILO     (input) INTEGER
          The integer ILO determined by MB04DP.
          1 <= ILO <= N+1.

  LSCALE  (input) DOUBLE PRECISION array, dimension (N)
          Details of the permutation and scaling factors applied
          from the left, as returned by MB04DP.

  RSCALE  (input) DOUBLE PRECISION array, dimension (N)
          Details of the permutation and scaling factors applied
          from the right, as returned by MB04DP.

  M       (input) INTEGER
          The number of columns of the matrices V1 and V2.  M >= 0.

  V1      (input/output) DOUBLE PRECISION array, dimension (LDV1,M)
          On entry, the leading N-by-M part of this array must
          contain the matrix V1.
          On exit, the leading N-by-M part of this array is
          overwritten by the updated matrix V1 of the transformed
          matrix.

  LDV1    INTEGER
          The leading dimension of the array V1. LDV1 >= max(1,N).

  V2      (input/output) DOUBLE PRECISION array, dimension (LDV2,M)
          On entry, the leading N-by-M part of this array must
          contain the matrix V2.
          On exit, the leading N-by-M part of this array is
          overwritten by the updated matrix V2 of the transformed
          matrix.

  LDV2    INTEGER
          The leading dimension of the array V2. LDV2 >= max(1,N).

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

  [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J.,
      Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A.,
      Ostrouchov, S., and Sorensen, D.
      LAPACK Users' Guide: Second Edition.
      SIAM, Philadelphia, 1995.

  [2] Benner, P.
      Symplectic balancing of Hamiltonian matrices.
      SIAM J. Sci. Comput., 22 (5), pp. 1885-1904, 2001.

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