Provided by: librheolef-dev_5.93-2_i386 bug

NAME

       riesz_representer - integrate a function by using quadrature formulae

DESCRIPTION

        The function riesz_representer implements the
        approximation of an integral by using quadrature formulae.
        This is an expreimental implementation: please do not use
        yet for practical usage.

SYNOPSYS

        template <class Function>
        field riesz_representer (const space& Vh, const Function& f);

        template <class Function>
        field   riesz_representer   (const   space&  Vh,  const  Function&  f,
       quadrature_option_type qopt);

EXAMPLE

        The following code compute the Riesz representant, denoted
        by mfh of f(x), and the integral of f over the domain omega:

         Float f(const point& x);
         ...
         space Vh (omega_h, "P1");
         field mfh = riesz_representer(Vh, f);
         Float int_f = dot(mfh, field(Vh,1.0));

        The Riesz representer is the mfh vector of values:

               mfh(i) = integrate f(x) phi_i(x) dx

        where phi_i is the i-th basis function in Vh
        and the integral is evaluated by using a quadrature formulae.
        By default the quadrature formule is the Gauss one with
        the order equal to the polynomial order of Vh.
        Alternative quadrature formulae and order is available
        by passing an optional variable to riesz_representer.

IMPLEMENTATION

       template <class Function>
       field
       riesz_representer (
           const space& Vh,
           const Function& f,
           quadrature_option_type qopt
              = quadrature_option_type(quadrature_option_type::max_family,0))