template class FNormalForm<int>

(Return to index)

Normal form of a truncated Taylor series map.

Compute from representation of a map which can be a nil-potent, static or dynamic symplectic map. Implementation of an algorithm described in

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

Synopsis (including inherited members):

• Public members:
  • FNormalForm (const FVps<double,N>&) ;
  • FNormalForm () ;
  • FNormalForm (const FNormalForm&) ;
  • ~FNormalForm () ;
  • int degreesOfFreedom ()const ;
  • const FTps<double,N>& normalForm ()const ;
  • const FTps<double,N>& normalisingMap ()const ;
  • const FVector<complex<double>,N>& eigenValues ()const ;
  • const FMatrix<double,N,N>& eigenVectors ()const ;
  • FMatrix<double,N/2,N/2> anharmonicity ()const ;
  • FTps<double,N> invariant (int)const ;
• Protected Members:
  • void orderModes (FVector<complex<double>,N>,FMatrix<double,N,N>) ;

Documentation:

• Public members:

  FNormalForm (const FVps<double,N>&) ;

  Constructor.
  Perform normal-form analysis of map.

  FMatrix<double,N/2,N/2> anharmonicity ()const ;

  Get anharmonicities as a matrix.

  int degreesOfFreedom ()const ;

  Get number of stable degrees of freedom.

  const FVector<complex<double>,N>& eigenValues ()const ;

  Get eigenvalues of the linear part as a complex vector.

  const FMatrix<double,N,N>& eigenVectors ()const ;

  Get eigenvectors of the linear part in packed form.

  FTps<double,N> invariant (int)const ;

  Get invariant polynomial for mode i.

  const FTps<double,N>& normalForm ()const ;

  Get normal-form map as a Lie transform.

  const FTps<double,N>& normalisingMap ()const ;

  Get normalising map as a Lie transform.

• Protected members: