quadrature(7rheolef)						    rheolef-6.1 					      quadrature(7rheolef)

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 refer-
       ence elements and orders are yet implemented. This class will be completed in the future.

IMPLEMENTATION

       template<class T>
       class quadrature {
       public:

       // typedefs:

	   typedef typename quadrature_on_geo<T>::size_type		    size_type;
	   typedef quadrature_option_type::family_type			    family_type;
	   typedef typename std::vector<weighted_point<T> >::const_iterator const_iterator;

       // allocators:

	   quadrature (quadrature_option_type opt = quadrature_option_type());

       // modifiers:

	   void set_order  (size_type order);
	   void set_family (family_type ft);

       // accessors:

	   size_type	  get_order() const;
	   family_type	  get_family() const;
	   std::string	  get_family_name() const;
	   size_type	  size	(reference_element hat_K) const;
	   const_iterator begin (reference_element hat_K) const;
	   const_iterator end	(reference_element hat_K) const;
	   template<class U>
	   friend std::ostream& operator<< (std::ostream&, const quadrature<U>&);
       protected:
	   quadrature_option_type	 _options;
	   mutable quadrature_on_geo<T>  _quad [reference_element::max_variant];
	   mutable std::vector<bool>	 _initialized;
	   void _initialize (reference_element hat_K) const;
       private:
	   quadrature (const quadrature<T>&);
	   quadrature operator= (const quadrature<T>&);
       };

SEE ALSO

       reference_element(2)

rheolef-6.1							    rheolef-6.1 					      quadrature(7rheolef)