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# basis - polynomial basis

 basis(7rheolef) rheolef-6.7 basis(7rheolef)

## 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)
 rheolef-6.7 rheolef-6.7