Defining metrical transformations

Any type can represent a metrical transformation, that is, play the role of the template parameter TRAFO in the non-orthogonal classes, as long as a class quantumdata::transformation::Traits can be specialized for the type.

The general requirements on the structure of the traits class is:

class quantumdata::transformation::Traits

template <typename TRAFO> (cf. template parameters)

N_RANK

static const int N_RANK

type TrafoTypes

The Composite transformation stores the underlying elementary transformations as a Boost.Fusion vector, and this type has to represent such a vector.

type StateVectorLow

static void transform(const TRAFO& trafo, const StateVectorLow& in, StateVectorLow& out)

static const TrafoTypes& getTrafos(const TRAFO& trafo)

There is a class which helps with the specialization of quantumdata::transformation::Traits for elementary transformations. Traits specializations for elementary transformations can simply inherit from this class:

class quantumdata::transformation::ElementaryTraits

template <typename TRAFO> (cf. template parameters)

template<typename TRAFO>
struct ElementaryTraits
{
  typedef typename boost::fusion::vector<TRAFO> TrafoTypes;
  // Simply creates a single-element vector out of TRAFO, so that afterwards it can be treated in a unified way with Composites

  static const TrafoTypes getTrafos(const TRAFO& trafo) {return boost::fusion::make_vector(trafo);}
  // The same at runtime

};

Traits specializations

For the dummy transformation Identity:

template<int RANK>
struct Traits<Identity<RANK> > : ElementaryTraits<Identity<RANK> >
{
  static const int N_RANK=RANK;

  typedef typename Types<N_RANK>::StateVectorLow StateVectorLow;
  static void transform(Identity<RANK> trafo, const StateVectorLow& in, StateVectorLow& out) {out=in;}

};

(Most of the times, the dummy transform function will not be called for such classes because the Identity components are filtered out at compile time from Composite transformations.)

A TTD_CArray<2*RANK> can represent a transformation of rank RANK:

template<int TWO_TIMES_RANK>
struct Traits<TTD_CArray<TWO_TIMES_RANK> > : ElementaryTraits<TTD_CArray<TWO_TIMES_RANK> >
{
  static const int N_RANK=TWO_TIMES_RANK/2;

  typedef typename Types<N_RANK>::StateVectorLow StateVectorLow;
  static void transform(const TTD_CArray<TWO_TIMES_RANK>& trafo, const StateVectorLow& in, StateVectorLow& out);

};

In this case the transform function is implemented to represent the application of the matrix.

A pointer to a function with the appropriate signature:

template<int RANK>
struct Traits< void(*)(const TTD_CArray<RANK>&, TTD_CArray<RANK>&) > : ElementaryTraits< void(*)(const TTD_CArray<RANK>&, TTD_CArray<RANK>&) >
{
  static const int N_RANK=RANK;

  typedef typename Types<N_RANK>::StateVectorLow StateVectorLow;

  typedef void(*TRAFO)(const StateVectorLow&, StateVectorLow&);

  static void transform(const TRAFO trafo, const StateVectorLow& in, StateVectorLow& out) {trafo(in,out);}

};