---
name: "quadrature"
section: "7rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.0-2+b1"
release: "Debian 10 (Buster)"
platforms: ["linux"]
url: "https://new.carta.tech/quadrature/7rheolef"
---

# quadrature(7rheolef)

quadrature formulae on the reference lement

## NAME

**quadrature** - quadrature formulae on the reference lement

## SYNOPSIS

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 opt = quadrature_option())
     : 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& 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); }
// 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)

## COPYRIGHT

Copyright (C) 2000-2018 Pierre Saramito \<Pierre.Saramito@imag.fr\> GPLv3+: GNU GPL version 3 or later \<http://gnu.org/licenses/gpl.html\>. This is free software: you are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by law.