NAME

       quadrature - quadrature formulae on the reference lement

SYNOPSYS

       The  quadrature  class  defines  a  container  for  a quadrature formulae on the reference
       element (see reference_element(2)).  This container stores the nodes coordinates  and  the
       weights.

THE CONSTRUCTOR TAKES TWO ARGUMENTS

        the  reference  element  K  and  the order r of the quadrature formulae.  The formulae is
       exact when computing the integral of a polynom p that degree is less or equal to order r.

                         n
           /            ___
           | p(x) dx =      p(x_q) w_q
           / K          /__
                        q=1

LIMITATIONS

       The formulae is optimal when it uses a minimal number  of  nodes  n.   Optimal  quadrature
       formula  are  hard-coded  in  this  class.   Not all reference elements and orders are yet
       implemented. This class will be completed in the future.

IMPLEMENTATION

       template<class T>
       class quadrature : public smart_pointer<quadrature_rep<T> > {
       public:

       // typedefs:

           typedef quadrature_rep<T>              rep;
           typedef smart_pointer<rep>             base;
           typedef typename rep::size_type        size_type;
           typedef typename rep::family_type      family_type;
           typedef typename rep::const_iterator   const_iterator;
           typedef typename rep::orientation_type orientation_type;

       // allocators:

           quadrature (quadrature_option_type opt = quadrature_option_type())
            : base(new_macro(rep(opt))) {}

       // modifiers:

           void set_order  (size_type order) { base::data().set_order(order); }
           void set_family (family_type ft)  { base::data().set_family(ft); }

       // accessors:

           size_type      get_order() const { return base::data().get_order();}
           family_type    get_family() const { return base::data().get_family();}
           std::string    get_family_name() const { return base::data().get_family_name();}
           const quadrature_option_type& get_options() const { return base::data().get_options(); }
           size_type      size  (reference_element hat_K) const { return base::data().size(hat_K); }
           const_iterator begin (reference_element hat_K) const { return base::data().begin(hat_K); }
           const_iterator end   (reference_element hat_K) const { return base::data().end(hat_K); }
           const weighted_point<T>& operator() (reference_element hat_K, size_type q) const
                                                                { return base::data().operator() (hat_K,q); }
           template<class U>
           friend std::ostream& operator<< (std::ostream& os, const quadrature<U>& q) {
               return os << q.data(); }

       // side accessor:

           void side_initialize (
               reference_element             tilde_K,
               size_type                     loc_isid,
               reference_element             hat_S,
               size_type                     shift,
               orientation_type              orient) const {
                   base::data().side_initialize (tilde_K, loc_isid, hat_S, shift, orient);
           }
       };

SEE ALSO

       reference_element(2)