template class DragtFinnMap<int>

(Return to index)

A Lie algebraic map, factored according to Dragt and Finn.

The type of coefficients is double, and the number of variables is N. It should be noted that some algorithms, notably concatenation of maps, are limited to maps with generators up to order 6.

Type:	Instantiable
Include file:	./FixedAlgebra/DragtFinnMap.hh

Synopsis (including inherited members):

• Public members:
  • DragtFinnMap (const DragtFinnMap&) ;
  • ~DragtFinnMap () ;
  • const DragtFinnMap& operator= (const DragtFinnMap&) ;
  • DragtFinnMap () ;
  • DragtFinnMap (const FVps<double,2*N>&) ;
  • DragtFinnMap (const FTps<double,2*N>&) ;
  • DragtFinnMap (const LinearMap<double,2*N>&) ;
  • operator ()const ;
  • void assign (const FMatrix<double,2*N,2*N>&) ;
  • void assign (const FTps<double,2*N>&) ;
  • void assign (const FLieGenerator<double,N>&) ;
  • static DragtFinnMap factorBerzForestIrwin (const FTps<double,2*N>&) ;
  • static DragtFinnMap factorDouglas (const FTps<double,2*N>&) ;
  • static DragtFinnMap factorSimple (const FTps<double,2*N>&) ;
  • const FMatrix<double,2*N,2*N>& getMatrix ()const ;
  • FMatrix<double,2*N,2*N>& getMatrix () ;
  • const FTps<double,2*N>& getGenerators ()const ;
  • const FLieGenerator<double,N> getGenerator (int)const ;
  • int getOrder ()const ;
  • DragtFinnMap inverse () ;
  • DragtFinnMap reverse () ;
  • void operator+= (const FTps<double,2*N>&) ;
  • void operator-= (const FTps<double,2*N>&) ;
  • void operator+= (const FLieGenerator<double,N>&) ;
  • void operator-= (const FLieGenerator<double,N>&) ;
  • DragtFinnMap catenate (const DragtFinnMap&) ;

Documentation:

• Public members:

  DragtFinnMap () ;

  Construct identity map.

  DragtFinnMap (const FVps<double,2*N>&) ;

  Build factored representation from a Taylor series map.

  DragtFinnMap (const FTps<double,2*N>&) ;

  Build factored representation from a pseudo-Hamiltonian.

  DragtFinnMap (const LinearMap<double,2*N>&) ;

  Build factored representation from a linear map.

  void assign (const FMatrix<double,2*N,2*N>&) ;

  Assign the matrix representing the linear transform.

  void assign (const FTps<double,2*N>&) ;

  Assign the complete set of generators.

  void assign (const FLieGenerator<double,N>&) ;

  Assign the generator for a selected order.

  DragtFinnMap catenate (const DragtFinnMap&) ;

  Substitute (concatenate) with another map in beam order.

  const FLieGenerator<double,N> getGenerator (int)const ;

  Return the generator for a selected order.

  const FTps<double,2*N>& getGenerators ()const ;

  Return the complete set of generators.

  const FMatrix<double,2*N,2*N>& getMatrix ()const ;

  Return the matrix representing the linear transform.

  FMatrix<double,2*N,2*N>& getMatrix () ;

  Return the matrix representing the linear transform.

  int getOrder ()const ;

  Return the order of the generators.

  DragtFinnMap inverse () ;

  Compute inverse map.
  The first-order generator must be zero.

  operator ()const ;

  Convert to Taylor series map. Convert to Taylor series map.

  void operator+= (const FTps<double,2*N>&) ;

  Add to set of generators.

  void operator+= (const FLieGenerator<double,N>&) ;

  Add to generator of given order.

  void operator-= (const FTps<double,2*N>&) ;

  Subtract from set of generators.

  void operator-= (const FLieGenerator<double,N>&) ;

  Subtract from generator of given order.

  DragtFinnMap reverse () ;

  Compute inverse factorisation of map.
  The first-order generator must be zero.