added examples to integrate methods

src/amdis/gridfunctions/Integrate.hpp

@@ -8,12 +8,13 @@ namespace AMDiS
 {
   namespace Impl
   {
-    template <class GridFct, class GridView, class QuadProvider>
-    auto integrateImpl(GridFct&& gridFct, GridView const& gridView, QuadProvider makeQuad)
+    template <class GF, class GridView, class QuadProvider>
+    auto integrateImpl(GF&& gf, GridView const& gridView, QuadProvider makeQuad)
     {
-      auto localFct = localFunction(gridFct);
+      auto localFct = localFunction(std::forward<GF>(gf));
 
-      using Range = typename std::decay_t<GridFct>::Range;
+      using GridFct = std::decay_t<GF>;
+      using Range = typename GridFct::Range;
       Range result(0);
 
       for (auto const& element : elements(gridView)) {
@@ -33,7 +34,15 @@ namespace AMDiS
   } // end namespace Impl
 
 
-  /// Integrate expression with quadrature rule determined by polynomial order of expression
+  /// \brief Integrate expression with quadrature rule determined by polynomial order of expression
+  /**
+   * **Example:**
+   * ```
+   * double i1 = integrate(prob.solution(0), prob.gridView());
+   * double i2 = integrate(X(0) + X(1), prob.gridView());
+   * double i3 = integrate([](auto const& x) { return x[0] + x[1]; }, prob.gridView()); // ERROR
+   * ```
+   **/
   template <class Expr, class GridView>
   auto integrate(Expr&& expr, GridView const& gridView)
   {
@@ -47,17 +56,24 @@ namespace AMDiS
 
 #if AMDIS_HAS_CXX_CONSTEXPR_IF
     if constexpr(expr_has_order)
-      return Impl::integrateImpl(gridFct, gridView, makeQuad);
+      return Impl::integrateImpl(std::forward<decltype(gridFct)>(gridFct), gridView, makeQuad);
     else
       return 0.0;
 #else
     return Dune::Hybrid::ifElse(bool_<expr_has_order>,
-      [&](auto) { return Impl::integrateImpl(gridFct, gridView, makeQuad); },
+      [&](auto) { return Impl::integrateImpl(std::forward<decltype(gridFct)>(gridFct), gridView, makeQuad); },
       [ ](auto) { return 0.0; });
 #endif
   }
 
   /// Integrate expression with quadrature rule provided
+  /**
+   * **Example:**
+   * ```
+   * auto quad = Dune::QuadratureRules<double,DIM>::rule(Dune::GeometryTypes::triangle, 1);
+   * double i4 = integrate([](auto const& x) { return x[0]; }, prob.gridView(), quad); // OK
+   * ```
+   **/
   template <class Expr, class GridView,
     class QuadratureRule = Dune::QuadratureRule<typename GridView::ctype, GridView::dimension>>
   auto integrate(Expr&& expr, GridView const& gridView, QuadratureRule const& quad)
@@ -68,6 +84,12 @@ namespace AMDiS
   }
 
   /// Integrate expression with quadrature rule determined by provided polynomial `degree`
+  /**
+   * **Example:**
+   * ```
+   * double i5 = integrate([](auto const& x) { return x[0]; }, prob.gridView(), 1); // OK
+   * ```
+   **/
   template <class Expr, class GridView>
   auto integrate(Expr&& expr, GridView const& gridView, int degree,
                  Dune::QuadratureType::Enum qt = Dune::QuadratureType::GaussLegendre)