NAME

       basis - polynomial basis

SYNOPSYS

       The basis class defines functions that evaluates a polynomial basis and its derivatives on
       a point. The  polynomial  basis  is  designated  by  a  string,  e.g.  "P0",  "P1",  "P2",
       "bubble",...   indicating  the  basis.  The  basis  depends also of the reference element:
       triangle, square, tetrahedron (see reference_element(2)).  For instance, on a square,  the
       "P1" string designates the common Q1 four-nodes basis on the reference square.

       The nodes associated to the Lagrange polynomial basis are also available by its associated
       accessor.

IMPLEMENTATION NOTE

       The basis class is a see smart_pointer(2)) class on a  basis_rep  class  that  is  a  pure
       virtual base class for effective bases, e.g. basis_P1, basis_P1, etc.

IMPLEMENTATION

       template<class T>
       class basis_basic : public smart_pointer<basis_rep<T> > {
       public:

       // typedefs:

           typedef basis_rep<T>                           rep;
           typedef smart_pointer<rep>                     base;
           typedef typename basis_rep<T>::size_type       size_type;

       // allocators:

           basis_basic (std::string name = "");

       // accessors:

           std::string name() const;
           size_type   degree() const;
           size_type   size (reference_element hat_K) const;

           void hat_node(
               reference_element              hat_K,
               std::vector<point_basic<T> >&  hat_node) const;
           void hat_node(
               reference_element                               hat_K,
               typename std::vector<point_basic<T> >::iterator hat_node) const;

           void eval(
               reference_element     hat_K,
               const point_basic<T>& hat_x,
               std::vector<T>&       values) const;
           void eval(
               reference_element                 hat_K,
               const point_basic<T>&             hat_x,
               typename std::vector<T>::iterator values) const;

           void grad_eval(
               reference_element    hat_K,
               const point_basic<T>&         hat_x,
               std::vector<point_basic<T> >&  values) const;
           void grad_eval(
               reference_element                               hat_K,
               const point_basic<T>&                           hat_x,
               typename std::vector<point_basic<T> >::iterator values) const;
       };
       typedef basis_basic<Float> basis;

SEE ALSO

       reference_element(2), smart_pointer(2)