From 5e304636549cf27fd266aaf3e459d4861d4ff096 Mon Sep 17 00:00:00 2001
From: Pietro Incardona <incardon@mpi-cbg.de>
Date: Tue, 21 Feb 2017 15:04:20 +0100
Subject: [PATCH] Adding left type expression and right type expression

---
 src/Draw/DrawParticles.hpp                    |    72 +-
 src/Draw/DrawParticles_unit_tests.hpp         |     4 +
 src/Draw/PointIterator.hpp                    |    10 +-
 src/Draw/PointIteratorSkin.hpp                |     8 +-
 src/FiniteDifference/Derivative.hpp           |    78 +-
 src/FiniteDifference/FDScheme.hpp             |    74 +-
 src/FiniteDifference/eq_unit_test_3d.hpp      |     5 +
 src/FiniteDifference/mul.hpp                  |    26 +-
 .../Vector/vector_dist_operator_assign.hpp    |    70 +-
 .../Vector/vector_dist_operators.hpp          |    67 +-
 .../vector_dist_operators_apply_kernel.hpp    |     2 +-
 ...dist_operators_apply_kernel_unit_tests.hpp |    12 +-
 .../vector_dist_operators_unit_tests.hpp      |    12 +-
 src/PSE/Kernels_test_util.hpp                 |     8 +-
 src/main.cpp                                  |     2 +-
 ...d_driven_cavity_3d_p2_grid_0_test_GCC6.vtk | 12972 ++++++++++++++++
 ...d_driven_cavity_3d_p2_grid_1_test_GCC6.vtk | 12972 ++++++++++++++++
 ...d_driven_cavity_3d_p3_grid_0_test_GCC6.vtk |  7757 +++++++++
 ...d_driven_cavity_3d_p3_grid_1_test_GCC6.vtk |  8827 +++++++++++
 ...d_driven_cavity_3d_p3_grid_2_test_GCC6.vtk |  9372 +++++++++++
 ...d_driven_cavity_3d_p2_grid_0_test_GCC6.vtk | 12972 ++++++++++++++++
 ...d_driven_cavity_3d_p2_grid_1_test_GCC6.vtk | 12972 ++++++++++++++++
 ...d_driven_cavity_3d_p3_grid_0_test_GCC6.vtk |  7757 +++++++++
 ...d_driven_cavity_3d_p3_grid_1_test_GCC6.vtk |  8827 +++++++++++
 ...d_driven_cavity_3d_p3_grid_2_test_GCC6.vtk |  9372 +++++++++++
 25 files changed, 104133 insertions(+), 117 deletions(-)
 create mode 100644 test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
 create mode 100644 test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
 create mode 100644 test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
 create mode 100644 test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
 create mode 100644 test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk
 create mode 100644 test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
 create mode 100644 test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
 create mode 100644 test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
 create mode 100644 test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
 create mode 100644 test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk

diff --git a/src/Draw/DrawParticles.hpp b/src/Draw/DrawParticles.hpp
index fad4345..12d46dc 100644
--- a/src/Draw/DrawParticles.hpp
+++ b/src/Draw/DrawParticles.hpp
@@ -12,10 +12,37 @@
 #include "PointIteratorSkin.hpp"
 #include "Vector/vector_dist.hpp"
 
+/*! \brief A class to draw/create particles based on simple shaped
+ *
+ * ## Draw box example
+ *
+ * \snippet Draw/DrawParticles_unit_tests.hpp DrawBox_example
+ *
+ */
 class DrawParticles
 {
 public:
 
+	/*! \brief Draw particles in a box B excluding the area of a second box A (B - A)
+	 *
+	 * The function return an iterator over particles defined on a virtual grid in the simulation domain.
+	 *
+	 * \param vd particles where we are creating the particles
+	 * \param sz indicate the grid size of the virtual grid.
+	 * \param domain Domain where the virtual grid is defined (Must match the domain of vd)
+	 * \param sub_B box contained in domain that define where the particle iterator must iterate,
+	 *            particles are placed strictly inside this box
+	 * \param sub_A box contained in the domain that define where the particle iterator should not
+	 *              iterate (excluding area)
+	 *
+	 * \note Suppose to have a simulation domain of 1.5 on x and we use sz = 16. Consider now
+	 * to have particles with spacing 0.1 on x. if we define a sub_A that on extend from 0.65
+	 *  to 0.95 the first fluid particle
+	 * is at 0.70 and the last is at 0.90
+	 *
+	 * \return an iterator to the selected particles
+	 *
+	 */
 	template<unsigned int dim, typename T, typename aggr, typename Decomposition> static PointIteratorSkin<dim,T,Decomposition>
 	DrawSkin(vector_dist<dim,T,aggr,Decomposition> & vd,
 			 size_t (& sz)[dim],
@@ -28,9 +55,30 @@ public:
 		for (size_t i = 0 ; i < dim ; i++)
 			bc[i] = NON_PERIODIC;
 
-		return PointIteratorSkin<dim,T,Decomposition>(vd.getDecomposition(),sz,domain,sub_A, sub_B, bc);
+		return PointIteratorSkin<dim,T,Decomposition>(vd.getDecomposition(),sz,vd.getDecomposition().getDomain(),sub_A, sub_B, bc);
 	}
 
+
+	/*! \brief Draw particles in a box B excluding the areas of an array of boxes A_n
+	 *
+	 * The function return an iterator over particles defined on a virtual grid in the simulation domain.
+	 *
+	 * \param vd particles where we are creating the particles
+	 * \param sz indicate the grid size of the virtual grid.
+	 * \param domain Domain where the virtual grid is defined (Must match the domain of vd)
+	 * \param sub_B box contained in domain that define where the particle iterator must iterate,
+	 *            particles are placed strictly inside this box
+	 * \param sub_A array of boxes contained in the domain that define where the particle iterator should not
+	 *              iterate (excluding areas)
+	 *
+	 * \note Suppose to have a simulation domain of 1.5 on x and we use sz = 16. Consider now
+	 * to have particles with spacing 0.1 on x. if we define a sub_A that on extend from 0.65
+	 *  to 0.95 the first fluid particle
+	 * is at 0.70 and the last is at 0.90
+	 *
+	 * \return an iterator to the selected particles
+	 *
+	 */
 	template<unsigned int dim, typename T, typename aggr, typename Decomposition> static PointIteratorSkin<dim,T,Decomposition>
 	DrawSkin(vector_dist<dim,T,aggr,Decomposition> & vd,
 			 size_t (& sz)[dim],
@@ -43,7 +91,7 @@ public:
 		for (size_t i = 0 ; i < dim ; i++)
 			bc[i] = NON_PERIODIC;
 
-		PointIteratorSkin<dim,T,Decomposition> it(vd.getDecomposition(),sz,domain,sub_A.get(0), sub_B, bc);
+		PointIteratorSkin<dim,T,Decomposition> it(vd.getDecomposition(),sz,vd.getDecomposition().getDomain(),sub_A.get(0), sub_B, bc);
 
 		for (size_t i = 1 ; i < sub_A.size() ; i++)
 			it.addBoxA(Box<dim,T>(sub_A.get(i)));
@@ -51,13 +99,31 @@ public:
 		return it;
 	}
 
+	/*! \brief Draw particles in a box
+	 *
+	 * The function return an iterator over particles defined on a virtual grid in the simulation domain.
+	 *
+	 * \param vd particles where we are creating the particles
+	 * \param sz indicate the grid size of the virtual grid.
+	 * \param domain Domain where the virtual grid is defined (Must match the domain of vd)
+	 * \param sub box contained in domain that define where the particle iterator must iterate,
+	 *            particles are placed strictly inside this box
+	 *
+	 * \note Suppose to have a simulation domain of 1.5 on x and we use sz = 16. Consider now
+	 * to have particles with spacing 0.1 on x. if we define a sub box that on extend from 0.65
+	 *  to 0.95 the first fluid particle
+	 * is at 0.70 and the last is at 0.90
+	 *
+	 * \return an iterator to the selected particles
+	 *
+	 */
 	template<unsigned int dim, typename T, typename aggr, typename Decomposition> static PointIterator<dim,T,Decomposition>
 	DrawBox(vector_dist<dim,T,aggr,Decomposition> & vd,
 			 size_t (& sz)[dim],
 			 Box<dim,T> & domain,
 			 Box<dim,T> & sub)
 	{
-		return PointIterator<dim,T,Decomposition>(vd.getDecomposition(),sz,domain,sub);
+		return PointIterator<dim,T,Decomposition>(vd.getDecomposition(),sz,vd.getDecomposition().getDomain(),sub);
 	}
 
 };
diff --git a/src/Draw/DrawParticles_unit_tests.hpp b/src/Draw/DrawParticles_unit_tests.hpp
index 9423e63..b3355bd 100644
--- a/src/Draw/DrawParticles_unit_tests.hpp
+++ b/src/Draw/DrawParticles_unit_tests.hpp
@@ -16,6 +16,8 @@ BOOST_AUTO_TEST_SUITE( draw_particles )
 
 BOOST_AUTO_TEST_CASE(point_iterator)
 {
+	//! [DrawBox_example]
+
 	size_t sz[] = {23,27,20};
 
 	Box<3,double> domain({-1.2,0.5,-0.6},{1.0,3.1,1.3});
@@ -52,6 +54,8 @@ BOOST_AUTO_TEST_CASE(point_iterator)
 		++p;
 	}
 
+	//! [DrawBox_example]
+
 	Vcluster & v_cl = create_vcluster();
 
 	v_cl.sum(cnt);
diff --git a/src/Draw/PointIterator.hpp b/src/Draw/PointIterator.hpp
index c753e7d..b64a735 100644
--- a/src/Draw/PointIterator.hpp
+++ b/src/Draw/PointIterator.hpp
@@ -69,7 +69,7 @@ class PointIterator: protected grid_dist_id_iterator_dec<Decomposition>
 	//! Spacing
 	T sp[dim];
 
-	static grid_key_dx<dim> getStart(size_t (& gs)[dim], Box<dim,T> & dom, Box<dim,T> & sub_dom, T (& sp)[dim])
+	static grid_key_dx<dim> getStart(size_t (& gs)[dim], const Box<dim,T> & dom, Box<dim,T> & sub_dom, T (& sp)[dim])
 	{
 		for (size_t i = 0 ; i < dim ; i++)
 			sp[i] = (dom.getHigh(i) - dom.getLow(i)) / (gs[i] -1);
@@ -82,7 +82,7 @@ class PointIterator: protected grid_dist_id_iterator_dec<Decomposition>
 		return pkey;
 	}
 
-	static grid_key_dx<dim> getStop(size_t (& gs)[dim], Box<dim,T> & dom, Box<dim,T> & sub_dom, T (& sp)[dim])
+	static grid_key_dx<dim> getStop(size_t (& gs)[dim], const Box<dim,T> & dom, Box<dim,T> & sub_dom, T (& sp)[dim])
 	{
 		for (size_t i = 0 ; i < dim ; i++)
 			sp[i] = (dom.getHigh(i) - dom.getLow(i)) / (gs[i] - 1);
@@ -97,6 +97,9 @@ class PointIterator: protected grid_dist_id_iterator_dec<Decomposition>
 
 	void calculateAp()
 	{
+		if (grid_dist_id_iterator_dec<Decomposition>::isNext() == false)
+			return;
+
 		grid_key_dx<dim> key = grid_dist_id_iterator_dec<Decomposition>::get();
 
 		for (size_t i = 0 ; i < dim ; i++)
@@ -110,7 +113,7 @@ public:
 	 * \param sp grid spacing
 	 *
 	 */
-	PointIterator( Decomposition & dec, size_t (& sz)[dim], Box<dim,T> & domain, Box<dim,T> & sub_domain)
+	PointIterator( Decomposition & dec, size_t (& sz)[dim], const Box<dim,T> & domain, Box<dim,T> & sub_domain)
 	:grid_dist_id_iterator_dec<Decomposition>(dec, sz, getStart(sz,domain,sub_domain,sp), getStop(sz,domain,sub_domain,sp)),sub_domain(sub_domain),domain(domain)
 	{
 		calculateAp();
@@ -133,6 +136,7 @@ public:
 	PointIterator & operator++()
 	{
 		grid_dist_id_iterator_dec<Decomposition>::operator++();
+
 		calculateAp();
 
 		return *this;
diff --git a/src/Draw/PointIteratorSkin.hpp b/src/Draw/PointIteratorSkin.hpp
index d1c9979..fc5e7fd 100644
--- a/src/Draw/PointIteratorSkin.hpp
+++ b/src/Draw/PointIteratorSkin.hpp
@@ -101,6 +101,9 @@ class PointIteratorSkin: protected grid_dist_id_iterator_dec_skin<Decomposition>
 
 	void calculateAp()
 	{
+		if (grid_dist_id_iterator_dec_skin<Decomposition>::isNext() == false)
+			return;
+
 		grid_key_dx<dim> key = grid_dist_id_iterator_dec_skin<Decomposition>::get();
 
 		for (size_t i = 0 ; i < dim ; i++)
@@ -133,7 +136,7 @@ public:
 	 * \param sp grid spacing
 	 *
 	 */
-	PointIteratorSkin( Decomposition & dec, size_t (& sz)[dim], Box<dim,T> & domain, const Box<dim,T> & sub_A, const Box<dim,T> & sub_B, size_t (& bc)[dim])
+	PointIteratorSkin( Decomposition & dec, size_t (& sz)[dim], const Box<dim,T> & domain, const Box<dim,T> & sub_A, const Box<dim,T> & sub_B, size_t (& bc)[dim])
 	:grid_dist_id_iterator_dec_skin<Decomposition>(dec, sz, getAB(sz,domain,sub_A,sub_B,sp,RETURN_A), getAB(sz,domain,sub_A,sub_B,sp,RETURN_B), bc),domain(domain)
 	{
 		sub_domainA.add(sub_A);
@@ -142,6 +145,7 @@ public:
 
 	/*! \Return the actual point
 	 *
+	 * \return the actual point
 	 *
 	 */
 	Point<dim,T> & get()
@@ -157,11 +161,13 @@ public:
 	PointIteratorSkin & operator++()
 	{
 		grid_dist_id_iterator_dec_skin<Decomposition>::operator++();
+
 		calculateAp();
 
 		while (grid_dist_id_iterator_dec_skin<Decomposition>::isNext() && isValidPoint() == false)
 		{
 			grid_dist_id_iterator_dec_skin<Decomposition>::operator++();
+
 			calculateAp();
 		}
 
diff --git a/src/FiniteDifference/Derivative.hpp b/src/FiniteDifference/Derivative.hpp
index c3795f6..8f2ae94 100644
--- a/src/FiniteDifference/Derivative.hpp
+++ b/src/FiniteDifference/Derivative.hpp
@@ -52,14 +52,20 @@ class D
 	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
 	 *  it calculate how the operator shift the calculation in the cell
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
+	 * \return where (in which cell) the derivative is calculated
+	 *
 	 */
-	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
+	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
+			                                          const grid_sm<Sys_eqs::dims,void> & gs,
+													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
 		std::cerr << "Error " << __FILE__ << ":" << __LINE__ << " only CENTRAL, FORWARD, BACKWARD derivative are defined";
+
+		return pos;
 	}
 };
 
@@ -80,8 +86,10 @@ class D<d,arg,Sys_eqs,CENTRAL>
 
 	/*! \brief Calculate which colums of the Matrix are non zero
 	 *
-	 * \param pos position where the derivative is calculated
+	 * \param g_map mapping grid
+	 * \param kmap position where the derivative is calculated
 	 * \param gs Grid info
+	 * \param spacing grid spacing
 	 * \param cols non-zero colums calculated by the function
 	 * \param coeff coefficent (constant in front of the derivative)
 	 *
@@ -90,7 +98,12 @@ class D<d,arg,Sys_eqs,CENTRAL>
 	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
 	 *
 	 */
-	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
+	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
+			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
+							 const grid_sm<Sys_eqs::dims,void> & gs,
+							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
+							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
+							 typename Sys_eqs::stype coeff)
 	{
 		// if the system is staggered the CENTRAL derivative is equivalent to a forward derivative
 		if (is_grid_staggered<Sys_eqs>::value())
@@ -141,12 +154,16 @@ class D<d,arg,Sys_eqs,CENTRAL>
 	 *
 	 * \f$ \frac{\partial v_x}{\partial y} \f$ is calculated on position (*), so the function return the grid_key {0,0}
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
+	 * \return where (in which cell grid) the derivative is calculated
+	 *
 	 */
-	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
+	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
+			                                          const grid_sm<Sys_eqs::dims,void> & gs,
+													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
 		auto arg_pos = arg::position(pos,gs,s_pos);
 		if (is_grid_staggered<Sys_eqs>::value())
@@ -195,8 +212,10 @@ public:
 
 	/*! \brief Calculate which colums of the Matrix are non zero
 	 *
-	 * \param pos position where the derivative is calculated
+	 * \param g_map mapping grid points
+	 * \param kmap position where the derivative is calculated
 	 * \param gs Grid info
+	 * \param spacing of the grid
 	 * \param cols non-zero colums calculated by the function
 	 * \param coeff coefficent (constant in front of the derivative)
 	 *
@@ -205,7 +224,12 @@ public:
 	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
 	 *
 	 */
-	static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
+	static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
+			          grid_dist_key_dx<Sys_eqs::dims> & kmap,
+					  const grid_sm<Sys_eqs::dims,void> & gs,
+					  typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
+					  std::unordered_map<long int,typename Sys_eqs::stype > & cols,
+					  typename Sys_eqs::stype coeff)
 	{
 #ifdef SE_CLASS1
 		if (Sys_eqs::boundary[d] == PERIODIC)
@@ -279,10 +303,12 @@ public:
 	 * outside the boundary is simply the central scheme, at the boundary it is simply the
 	 * staggered position of the property
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
+	 * \return where (in which cell grid) the derivative is calculated
+	 *
 	 */
 	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
@@ -308,8 +334,10 @@ class D<d,arg,Sys_eqs,FORWARD>
 
 	/*! \brief Calculate which colums of the Matrix are non zero
 	 *
-	 * \param pos position where the derivative is calculated
+	 * \param g_map mapping grid
+	 * \param kmap position where the derivative is calculated
 	 * \param gs Grid info
+	 * \param spacing grid spacing
 	 * \param cols non-zero colums calculated by the function
 	 * \param coeff coefficent (constant in front of the derivative)
 	 *
@@ -318,7 +346,12 @@ class D<d,arg,Sys_eqs,FORWARD>
 	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
 	 *
 	 */
-	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] ,std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
+	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
+			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
+							 const grid_sm<Sys_eqs::dims,void> & gs,
+							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
+							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
+							 typename Sys_eqs::stype coeff)
 	{
 
 		long int old_val = kmap.getKeyRef().get(d);
@@ -336,12 +369,16 @@ class D<d,arg,Sys_eqs,FORWARD>
 	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
 	 * the FORWARD scheme return the position of the staggered property
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
+	 * \return where (in which cell grid) the derivative is calculated
+	 *
 	 */
-	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
+	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
+			                                          const grid_sm<Sys_eqs::dims,void> & gs,
+													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
 		return arg::position(pos,gs,s_pos);
 	}
@@ -364,8 +401,10 @@ class D<d,arg,Sys_eqs,BACKWARD>
 
 	/*! \brief Calculate which colums of the Matrix are non zero
 	 *
-	 * \param pos position where the derivative is calculated
+	 * \param g_map mapping grid
+	 * \param kmap position where the derivative is calculated
 	 * \param gs Grid info
+	 * \param spacing of the grid
 	 * \param cols non-zero colums calculated by the function
 	 * \param coeff coefficent (constant in front of the derivative)
 	 *
@@ -374,7 +413,12 @@ class D<d,arg,Sys_eqs,BACKWARD>
 	 * \snippet FDScheme_unit_tests.hpp Usage of stencil derivative
 	 *
 	 */
-	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap , const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims], std::unordered_map<long int,typename Sys_eqs::stype > & cols , typename Sys_eqs::stype coeff)
+	inline static void value(const typename stub_or_real<Sys_eqs,Sys_eqs::dims,typename Sys_eqs::stype,typename Sys_eqs::b_grid::decomposition::extended_type>::type & g_map,
+			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
+							 const grid_sm<Sys_eqs::dims,void> & gs,
+							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
+							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
+							 typename Sys_eqs::stype coeff)
 	{
 
 		long int old_val = kmap.getKeyRef().get(d);
@@ -392,10 +436,12 @@ class D<d,arg,Sys_eqs,BACKWARD>
 	 * In case of non staggered case this function just return a null grid_key, in case of staggered,
 	 * the BACKWARD scheme return the position of the staggered property
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
+	 * \return where (in which cell grid) the derivative is calculated
+	 *
 	 */
 	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
diff --git a/src/FiniteDifference/FDScheme.hpp b/src/FiniteDifference/FDScheme.hpp
index 93eda7e..b2e5543 100644
--- a/src/FiniteDifference/FDScheme.hpp
+++ b/src/FiniteDifference/FDScheme.hpp
@@ -126,59 +126,67 @@ class FDScheme
 {
 public:
 
-	// Distributed grid map
+	//! Distributed grid map
 	typedef grid_dist_id<Sys_eqs::dims,typename Sys_eqs::stype,scalar<size_t>,typename Sys_eqs::b_grid::decomposition::extended_type> g_map_type;
 
+	//! Type that specify the properties of the system of equations
 	typedef Sys_eqs Sys_eqs_typ;
 
 private:
 
-	// Padding
+	//! Padding
 	Padding<Sys_eqs::dims> pd;
 
+	//! Sparse matrix triplet type
 	typedef typename Sys_eqs::SparseMatrix_type::triplet_type triplet;
 
-	// Vector b
+	//! Vector b
 	typename Sys_eqs::Vector_type b;
 
-	// Domain Grid informations
+	//! Domain Grid informations
 	const grid_sm<Sys_eqs::dims,void> & gs;
 
-	// Get the grid spacing
+	//! Get the grid spacing
 	typename Sys_eqs::stype spacing[Sys_eqs::dims];
 
-	// mapping grid
+	//! mapping grid
 	g_map_type g_map;
 
-	// row of the matrix
+	//! row of the matrix
 	size_t row;
 
-	// row on b
+	//! row on b
 	size_t row_b;
 
-	// Grid points that has each processor
+	//! Grid points that has each processor
 	openfpm::vector<size_t> pnt;
 
-	// Staggered position for each property
+	//! Staggered position for each property
 	comb<Sys_eqs::dims> s_pos[Sys_eqs::nvar];
 
-	// Each point in the grid has a global id, to decompose correctly the Matrix each processor contain a
-	// contiguos range of global id, example processor 0 can have from 0 to 234 and processor 1 from 235 to 512
-	// no processors can have holes in the sequence, this number indicate where the sequence start for this
-	// processor
+	//! Each point in the grid has a global id, to decompose correctly the Matrix each processor contain a
+	//! contiguos range of global id, example processor 0 can have from 0 to 234 and processor 1 from 235 to 512
+	//! no processors can have holes in the sequence, this number indicate where the sequence start for this
+	//! processor
 	size_t s_pnt;
 
+	/*! \brief Equation id + space position
+	 *
+	 */
 	struct key_and_eq
 	{
+		//! space position
 		grid_key_dx<Sys_eqs::dims> key;
+
+		//! equation id
 		size_t eq;
 	};
 
 	/*! \brief From the row Matrix position to the spatial position
 	 *
-	 * \param row Matrix
+	 * \param row Matrix row
 	 *
-	 * \return spatial position
+	 * \return spatial position + equation id
 	 *
 	 */
 	inline key_and_eq from_row_to_key(size_t row)
@@ -205,9 +213,10 @@ private:
 		return ke;
 	}
 
-	/* \brief calculate the mapping grid size with padding
+	/*! \brief calculate the mapping grid size with padding
 	 *
-	 * \param gs original grid size
+	 * \param sz original grid size
+	 * \param pd padding
 	 *
 	 * \return padded grid size
 	 *
@@ -323,7 +332,7 @@ public:
 
 	/*! \brief set the staggered position for each property
 	 *
-	 * \param vector containing the staggered position for each property
+	 * \param sp vector containing the staggered position for each property
 	 *
 	 */
 	void setStagPos(comb<Sys_eqs::dims> (& sp)[Sys_eqs::nvar])
@@ -335,10 +344,8 @@ public:
 	/*! \brief compute the staggered position for each property
 	 *
 	 * This is compute from the value_type stored by Sys_eqs::b_grid::value_type
+	 * the position of the staggered properties
 	 *
-	 * ### Example
-	 *
-	 * \snippet eq_unit_test.hpp Compute staggered properties
 	 *
 	 */
 	void computeStag()
@@ -377,13 +384,17 @@ public:
 	/*! \brief Constructor
 	 *
 	 * \param pd Padding, how many points out of boundary are present
-	 * \param domain extension of the domain
+	 * \param stencil how many ghost points are required for this calculation
+	 * \param domain the domain
 	 * \param gs grid infos where Finite differences work
-	 * \param stencil maximum extension of the stencil on each directions
-	 * \param dec Decomposition of the domain
+	 * \param b_g maximum extension of the stencil on each directions
 	 *
 	 */
-	FDScheme(Padding<Sys_eqs::dims> & pd, const Ghost<Sys_eqs::dims,long int> & stencil, const Box<Sys_eqs::dims,typename Sys_eqs::stype> & domain, const grid_sm<Sys_eqs::dims,void> & gs, const typename Sys_eqs::b_grid & b_g)
+	FDScheme(Padding<Sys_eqs::dims> & pd,
+			 const Ghost<Sys_eqs::dims,long int> & stencil,
+			 const Box<Sys_eqs::dims,typename Sys_eqs::stype> & domain,
+			 const grid_sm<Sys_eqs::dims,void> & gs,
+			 const typename Sys_eqs::b_grid & b_g)
 	:pd(pd),gs(gs),g_map(b_g,stencil,pd),row(0),row_b(0)
 	{
 		Vcluster & v_cl = b_g.getDecomposition().getVC();
@@ -450,9 +461,15 @@ public:
 	 * \param id Equation id in the system that we are imposing
 	 * \param start starting point of the box
 	 * \param stop stop point of the box
+	 * \param skip_first skip the first point
 	 *
 	 */
-	template<typename T> void impose(const T & op , typename Sys_eqs::stype num ,long int id ,const long int (& start)[Sys_eqs::dims], const long int (& stop)[Sys_eqs::dims], bool skip_first = false)
+	template<typename T> void impose(const T & op,
+			                         typename Sys_eqs::stype num,
+									 long int id,
+									 const long int (& start)[Sys_eqs::dims],
+									 const long int (& stop)[Sys_eqs::dims],
+									 bool skip_first = false)
 	{
 		grid_key_dx<Sys_eqs::dims> start_k;
 		grid_key_dx<Sys_eqs::dims> stop_k;
@@ -557,6 +574,7 @@ public:
 		}
 	}
 
+	//! type of the sparse matrix
 	typename Sys_eqs::SparseMatrix_type A;
 
 	/*! \brief produce the Matrix
@@ -598,7 +616,7 @@ public:
 	 * \tparam Grid_dst type of the target grid
 	 * \tparam pos target properties
 	 *
-	 * \param scheme Discretization scheme
+	 * \param v Vector that contain the solution of the system
 	 * \param start point
 	 * \param stop point
 	 * \param g_dst Destination grid
diff --git a/src/FiniteDifference/eq_unit_test_3d.hpp b/src/FiniteDifference/eq_unit_test_3d.hpp
index f8b4bc3..b515558 100644
--- a/src/FiniteDifference/eq_unit_test_3d.hpp
+++ b/src/FiniteDifference/eq_unit_test_3d.hpp
@@ -216,6 +216,11 @@ template<typename solver_type,typename lid_nn_3d> void lid_driven_cavity_3d()
         std::string file1 = std::string("test/") + s + "lid_driven_cavity_3d_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC5.vtk";
         std::string file2 = s + "lid_driven_cavity_3d_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";
 
+    #elif __GNUC__ == 6
+
+        std::string file1 = std::string("test/") + s + "lid_driven_cavity_3d_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC6.vtk";
+        std::string file2 = s + "lid_driven_cavity_3d_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";
+
 	#else
 
         std::string file1 = std::string("test/") + s + "lid_driven_cavity_3d_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC4.vtk";
diff --git a/src/FiniteDifference/mul.hpp b/src/FiniteDifference/mul.hpp
index 759e2a6..84d481b 100644
--- a/src/FiniteDifference/mul.hpp
+++ b/src/FiniteDifference/mul.hpp
@@ -72,8 +72,8 @@ struct const_mul_functor_value
 	 * \param kmap grid point (row) where we evaluate the non-zero colums
 	 * \param gs grid size
 	 * \param spacing grid spacing
-	 * \param col non zero colums
-	 * \param coefficent
+	 * \param cols non zero colums
+	 * \param coeff multiplication coefficent
 	 *
 	 */
 	const_mul_functor_value(const grid_dist_id<last::dims,typename last::stype,scalar<size_t>,typename last::b_grid::decomposition::extended_type> & g_map,
@@ -118,23 +118,31 @@ struct const_mul_functor_value
 template<typename ... expr >
 struct mul
 {
-	// Transform from variadic template to boost mpl vector
+	//! Transform from variadic template to boost mpl vector
 	typedef boost::mpl::vector<expr... > v_expr;
 
-	// size of v_expr
+	//! size of v_expr
 	typedef typename boost::mpl::size<v_expr>::type v_sz;
 
+	//! type on which this expression operate
 	typedef typename boost::mpl::at<v_expr, boost::mpl::int_<v_sz::type::value - 1> >::type Sys_eqs;
 
 	/*! \brief Calculate which colums of the Matrix are non zero
 	 *
-	 * \param pos position where the multiplication is calculated
+	 * \param g_map mapping grid
+	 * \param kmap position where the multiplication is calculated
 	 * \param gs Grid info
+	 * \param spacing of the grid
 	 * \param cols non-zero colums calculated by the function
 	 * \param coeff coefficent (constant in front of the derivative)
 	 *
 	 */
-	inline static void value(const grid_dist_id<Sys_eqs::dims,typename Sys_eqs::stype,scalar<size_t>,typename Sys_eqs::b_grid::decomposition::extended_type> & g_map, grid_dist_key_dx<Sys_eqs::dims> & kmap, const grid_sm<Sys_eqs::dims,void> & gs, typename Sys_eqs::stype (& spacing )[Sys_eqs::dims] , std::unordered_map<long int,typename Sys_eqs::stype > & cols, typename Sys_eqs::stype coeff)
+	inline static void value(const grid_dist_id<Sys_eqs::dims,typename Sys_eqs::stype,scalar<size_t>,typename Sys_eqs::b_grid::decomposition::extended_type> & g_map,
+			                 grid_dist_key_dx<Sys_eqs::dims> & kmap,
+							 const grid_sm<Sys_eqs::dims,void> & gs,
+							 typename Sys_eqs::stype (& spacing )[Sys_eqs::dims],
+							 std::unordered_map<long int,typename Sys_eqs::stype > & cols,
+							 typename Sys_eqs::stype coeff)
 	{
 		const_mul_functor_value<v_expr> mfv(g_map,kmap,gs,spacing,cols,coeff);
 
@@ -151,12 +159,14 @@ struct mul
 	 *
 	 * it just return the position of the staggered property in the last expression
 	 *
-	 * \param position where we are calculating the derivative
+	 * \param pos position where we are calculating the derivative
 	 * \param gs Grid info
 	 * \param s_pos staggered position of the properties
 	 *
 	 */
-	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos, const grid_sm<Sys_eqs::dims,void> & gs, const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
+	inline static grid_key_dx<Sys_eqs::dims> position(grid_key_dx<Sys_eqs::dims> & pos,
+			                                          const grid_sm<Sys_eqs::dims,void> & gs,
+													  const comb<Sys_eqs::dims> (& s_pos)[Sys_eqs::nvar])
 	{
 		return boost::mpl::at<v_expr, boost::mpl::int_<v_sz::type::value - 2> >::type::position(pos,gs,s_pos);
 	}
diff --git a/src/Operators/Vector/vector_dist_operator_assign.hpp b/src/Operators/Vector/vector_dist_operator_assign.hpp
index 44a3701..5f26a50 100644
--- a/src/Operators/Vector/vector_dist_operator_assign.hpp
+++ b/src/Operators/Vector/vector_dist_operator_assign.hpp
@@ -56,8 +56,8 @@ template<typename prp1, typename expr1, typename prp2, typename expr2> void assi
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
 
 		++it;
 	}
@@ -79,9 +79,9 @@ template<typename prp1, typename expr1, typename prp2, typename expr2, typename
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
 
 		++it;
 	}
@@ -112,10 +112,10 @@ void assign(prp1 & p1, const expr1 & v_e1,
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
-		pos_or_prop<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
 
 		++it;
 	}
@@ -151,11 +151,11 @@ void assign(prp1 & p1, const expr1 & v_e1,
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
-		pos_or_prop<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
-		pos_or_prop<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
+		pos_or_propL<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
 
 		++it;
 	}
@@ -194,12 +194,12 @@ void assign(prp1 & p1, const expr1 & v_e1,
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
-		pos_or_prop<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
-		pos_or_prop<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
-		pos_or_prop<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
+		pos_or_propL<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
+		pos_or_propL<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
 
 		++it;
 	}
@@ -244,13 +244,13 @@ void assign(prp1 & p1, const expr1 & v_e1,
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
-		pos_or_prop<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
-		pos_or_prop<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
-		pos_or_prop<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
-		pos_or_prop<typename prp7::vtype,prp7::prop>::value(p7.getVector(),key) = v_exp7.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
+		pos_or_propL<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
+		pos_or_propL<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
+		pos_or_propL<typename prp7::vtype,prp7::prop>::value(p7.getVector(),key) = v_exp7.value(key);
 
 		++it;
 	}
@@ -298,14 +298,14 @@ void assign(prp1 & p1, const expr1 & v_e1,
 	{
 		auto key = it.get();
 
-		pos_or_prop<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
-		pos_or_prop<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
-		pos_or_prop<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
-		pos_or_prop<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
-		pos_or_prop<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
-		pos_or_prop<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
-		pos_or_prop<typename prp7::vtype,prp7::prop>::value(p7.getVector(),key) = v_exp7.value(key);
-		pos_or_prop<typename prp8::vtype,prp8::prop>::value(p8.getVector(),key) = v_exp8.value(key);
+		pos_or_propL<typename prp1::vtype,prp1::prop>::value(p1.getVector(),key) = v_exp1.value(key);
+		pos_or_propL<typename prp2::vtype,prp2::prop>::value(p2.getVector(),key) = v_exp2.value(key);
+		pos_or_propL<typename prp3::vtype,prp3::prop>::value(p3.getVector(),key) = v_exp3.value(key);
+		pos_or_propL<typename prp4::vtype,prp4::prop>::value(p4.getVector(),key) = v_exp4.value(key);
+		pos_or_propL<typename prp5::vtype,prp5::prop>::value(p5.getVector(),key) = v_exp5.value(key);
+		pos_or_propL<typename prp6::vtype,prp6::prop>::value(p6.getVector(),key) = v_exp6.value(key);
+		pos_or_propL<typename prp7::vtype,prp7::prop>::value(p7.getVector(),key) = v_exp7.value(key);
+		pos_or_propL<typename prp8::vtype,prp8::prop>::value(p8.getVector(),key) = v_exp8.value(key);
 
 		++it;
 	}
diff --git a/src/Operators/Vector/vector_dist_operators.hpp b/src/Operators/Vector/vector_dist_operators.hpp
index 9e0a9a5..6d8f7d8 100644
--- a/src/Operators/Vector/vector_dist_operators.hpp
+++ b/src/Operators/Vector/vector_dist_operators.hpp
@@ -167,7 +167,8 @@ public:
 	 * \return return the result of the expression
 	 *
 	 */
-	template<typename r_type=typename std::remove_reference<decltype(o1.value(vect_dist_key_dx(0)) + o2.value(vect_dist_key_dx(0)))>::type > inline r_type value(const vect_dist_key_dx & key) const
+	template<typename r_type=typename std::remove_reference<decltype(o1.value(vect_dist_key_dx(0)) + o2.value(vect_dist_key_dx(0)))>::type >
+	inline r_type value(const vect_dist_key_dx & key) const
 	{
 		return o1.value(key) + o2.value(key);
 	}
@@ -312,7 +313,7 @@ public:
 	}
 };
 
-/*! \brief selector for position or properties
+/*! \brief selector for position or properties left side expression
  *
  * \tparam vector type of the original vector
  *
@@ -320,7 +321,7 @@ public:
  *
  */
 template <typename vector, unsigned int prp>
-struct pos_or_prop
+struct pos_or_propL
 {
 	//! return the value (position or property) of the particle k in the vector v
 	static inline auto value(vector & v, const vect_dist_key_dx & k) -> decltype(v.template getProp<prp>(k))
@@ -329,7 +330,24 @@ struct pos_or_prop
 	}
 };
 
-/*! \brief selector for position or properties
+/*! \brief selector for position or properties right side position
+ *
+ * \tparam vector type of the original vector
+ *
+ * \tparam prp property id
+ *
+ */
+template <typename vector, unsigned int prp>
+struct pos_or_propR
+{
+	//! return the value (position or property) of the particle k in the vector v
+	static inline auto value(vector & v, const vect_dist_key_dx & k) -> decltype(v.template getProp<prp>(k))
+	{
+		return v.template getProp<prp>(k);
+	}
+};
+
+/*! \brief selector for position or properties left side
  *
  * \tparam vector type of the original vector
  *
@@ -337,13 +355,42 @@ struct pos_or_prop
  *
  */
 template <typename vector>
-struct pos_or_prop<vector,PROP_POS>
+struct pos_or_propL<vector,PROP_POS>
 {
+#ifdef SE_CLASS3
+
+	//! return the value (position or property) of the particle k in the vector v
+	static inline auto value(vector & v, const vect_dist_key_dx & k) -> decltype(getExpr(v.getPos(k).getReference()))
+	{
+		return getExpr(v.getPos(k).getReference());
+	}
+
+#else
+
 	//! return the value (position or property) of the particle k in the vector v
 	static inline auto value(vector & v, const vect_dist_key_dx & k) -> decltype(getExpr(v.getPos(k)))
 	{
 		return getExpr(v.getPos(k));
 	}
+
+#endif
+};
+
+/*! \brief selector for position or properties right side
+ *
+ * \tparam vector type of the original vector
+ *
+ * \tparam prp property id
+ *
+ */
+template <typename vector>
+struct pos_or_propR<vector,PROP_POS>
+{
+	//! return the value (position or property) of the particle k in the vector v
+	static inline auto value(vector & v, const vect_dist_key_dx & k) -> decltype(getExprR(v.getPos(k)))
+	{
+		return getExprR(v.getPos(k));
+	}
 };
 
 /*! \brief it take an expression and create the negatove of this expression
@@ -428,9 +475,9 @@ public:
 	 * \return the result of the expression
 	 *
 	 */
-	inline auto value(const vect_dist_key_dx & k) const -> decltype(pos_or_prop<vector,prp>::value(v,k))
+	inline auto value(const vect_dist_key_dx & k) const -> decltype(pos_or_propR<vector,prp>::value(v,k))
 	{
-		return pos_or_prop<vector,prp>::value(v,k);
+		return pos_or_propR<vector,prp>::value(v,k);
 	}
 
 	/*! \brief Fill the vector property with the evaluated expression
@@ -450,7 +497,7 @@ public:
 		{
 			auto key = it.get();
 
-			pos_or_prop<vector,prp>::value(v,key) = v_exp.value(key);
+			pos_or_propL<vector,prp>::value(v,key) = v_exp.value(key);
 
 			++it;
 		}
@@ -475,7 +522,7 @@ public:
 		{
 			auto key = it.get();
 
-			pos_or_prop<vector,prp>::value(v,key) = v_exp.value(key);
+			pos_or_propL<vector,prp>::value(v,key) = v_exp.value(key);
 
 			++it;
 		}
@@ -498,7 +545,7 @@ public:
 		{
 			auto key = it.get();
 
-			pos_or_prop<vector,prp>::value(v,key) = d;
+			pos_or_propL<vector,prp>::value(v,key) = d;
 
 			++it;
 		}
diff --git a/src/Operators/Vector/vector_dist_operators_apply_kernel.hpp b/src/Operators/Vector/vector_dist_operators_apply_kernel.hpp
index e2e1aea..ea89f7b 100644
--- a/src/Operators/Vector/vector_dist_operators_apply_kernel.hpp
+++ b/src/Operators/Vector/vector_dist_operators_apply_kernel.hpp
@@ -202,7 +202,7 @@ struct apply_kernel_is_number_or_expression_gen
 	    rtype prp_p = v_exp.value(key);
 
 	    // position of particle p
-	    auto & p = vd.getPos(key);
+	    Point<vector::dims,typename vector::stype> p = vd.getPos(key);
 
 	    // Get the neighborhood of the particle
 	    auto NN = cl.template getNNIterator<NO_CHECK>(cl.getCell(p));
diff --git a/src/Operators/Vector/vector_dist_operators_apply_kernel_unit_tests.hpp b/src/Operators/Vector/vector_dist_operators_apply_kernel_unit_tests.hpp
index 28a4994..f45954d 100644
--- a/src/Operators/Vector/vector_dist_operators_apply_kernel_unit_tests.hpp
+++ b/src/Operators/Vector/vector_dist_operators_apply_kernel_unit_tests.hpp
@@ -30,7 +30,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		float prp_x = vd.template getProp<VC>(p) * vd.template getProp<VB>(p) + norm(vd.template getProp<VB>(p));
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
@@ -81,7 +81,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		float prp_x = vd.template getProp<VC>(p) * vd.template getProp<VB>(p) + norm(vd.template getProp<VB>(p));
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
@@ -145,7 +145,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		Point<3,float> prp_x = 2.0 * vd.template getProp<VC>(p) + vd.template getProp<VB>(p);
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
@@ -198,7 +198,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		Point<3,float> prp_x = vd.template getProp<VC>(p);
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
@@ -249,7 +249,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		Point<3,float> prp_x = 2.0f*vd.template getProp<VC>(p) + vd.template getProp<VB>(p);
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
@@ -307,7 +307,7 @@ template <typename vector,typename Kernel, typename NN_type> bool check_values_a
 		Point<2,float> ker_accu = 0.0;
 
 		// For each neighborhood particle
-		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(vd.getPos(p)));
+		auto Np = NN.template getNNIterator<NO_CHECK>(NN.getCell(xp));
 
 		while (Np.isNext())
 		{
diff --git a/src/Operators/Vector/vector_dist_operators_unit_tests.hpp b/src/Operators/Vector/vector_dist_operators_unit_tests.hpp
index f1f5e5e..d2d7a12 100644
--- a/src/Operators/Vector/vector_dist_operators_unit_tests.hpp
+++ b/src/Operators/Vector/vector_dist_operators_unit_tests.hpp
@@ -70,7 +70,9 @@ template <typename rtype, typename vector, unsigned int A, unsigned int B, unsig
 	{
 		auto key = it.get();
 
-		rtype base1 = rtype(vd.getPos(key)) + p;
+		Point<vector::dims,typename vector::stype> xp = vd.getPos(key);
+
+		rtype base1 = rtype(xp) + p;
 		rtype base2 = vd.template getProp<A>(key);
 
 		ret &=  base1 == base2;
@@ -92,7 +94,9 @@ template <typename rtype, typename vector, unsigned int A, unsigned int B, unsig
 	{
 		auto key = it.get();
 
-		rtype base1 = rtype(vd.getPos(key)) - p;
+		Point<vector::dims,typename vector::stype> xp = vd.getPos(key);
+
+		rtype base1 = rtype(xp) - p;
 		rtype base2 = vd.template getProp<A>(key);
 
 		ret &=  base1 == base2;
@@ -114,7 +118,9 @@ template <typename rtype, typename vector, unsigned int A, unsigned int B, unsig
 	{
 		auto key = it.get();
 
-		rtype base1 = -(rtype(vd.getPos(key)) - p);
+		Point<vector::dims,typename vector::stype> xp = vd.getPos(key);
+
+		rtype base1 = -(rtype(xp) - p);
 		rtype base2 = vd.template getProp<A>(key);
 
 		ret &=  base1 == base2;
diff --git a/src/PSE/Kernels_test_util.hpp b/src/PSE/Kernels_test_util.hpp
index d61c2fe..f74682b 100644
--- a/src/PSE/Kernels_test_util.hpp
+++ b/src/PSE/Kernels_test_util.hpp
@@ -97,7 +97,9 @@ template<typename T, typename Kernel> void PSE_test(size_t Npart, size_t overlap
 		// set the position of the particles
 		vd.getPos(key)[0] = 0.448000 - ((long int)key.getKey() - mp) * spacing;
 		//set the property of the particles
-		vd.template getProp<0>(key) = f_xex2(vd.getPos(key)[0]);
+		T d = vd.getPos(key)[0];
+
+		vd.template getProp<0>(key) = f_xex2(d);
 
 		++it2;
 	}
@@ -130,8 +132,10 @@ template<typename T, typename Kernel> void PSE_test(size_t Npart, size_t overlap
     	// given by the Near particle, exclude itself
     	if (nnp != key.getKey())
     	{
+    		Point<1,T> xp = vd.getPos(nnp);
+
     		// W(x-y)
-    		T ker = lker.value(p,vd.getPos(nnp));
+    		T ker = lker.value(p,xp);
 
     		// f(y)
     		T prp_y = vd.template getProp<0>(nnp);
diff --git a/src/main.cpp b/src/main.cpp
index 6fd91c3..6f3c913 100755
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -15,4 +15,4 @@
 #include "util/util_num_unit_tests.hpp"
 #include "PSE/Kernels_unit_tests.hpp"
 #include "Operators/Vector/vector_dist_operators_unit_tests.hpp"
-//#include "Draw/DrawParticles_unit_tests.hpp"
+#include "Draw/DrawParticles_unit_tests.hpp"
diff --git a/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk b/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
new file mode 100644
index 0000000..d4a22c4
--- /dev/null
+++ b/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
@@ -0,0 +1,12972 @@
+# vtk DataFile Version 3.0
+grids
+ASCII
+DATASET POLYDATA
+POINTS 2592 float
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diff --git a/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk b/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
new file mode 100644
index 0000000..8b4b390
--- /dev/null
+++ b/test/petsc_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
@@ -0,0 +1,12972 @@
+# vtk DataFile Version 3.0
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diff --git a/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
new file mode 100644
index 0000000..296645c
--- /dev/null
+++ b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
@@ -0,0 +1,7757 @@
+# vtk DataFile Version 3.0
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diff --git a/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
new file mode 100644
index 0000000..4f32f27
--- /dev/null
+++ b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
@@ -0,0 +1,8827 @@
+# vtk DataFile Version 3.0
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diff --git a/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk
new file mode 100644
index 0000000..db7ea3d
--- /dev/null
+++ b/test/petsc_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk
@@ -0,0 +1,9372 @@
+# vtk DataFile Version 3.0
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diff --git a/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk b/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
new file mode 100644
index 0000000..495a410
--- /dev/null
+++ b/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_0_test_GCC6.vtk
@@ -0,0 +1,12972 @@
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diff --git a/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk b/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
new file mode 100644
index 0000000..f7a9317
--- /dev/null
+++ b/test/umfpack_solver<double>_lid_driven_cavity_3d_p2_grid_1_test_GCC6.vtk
@@ -0,0 +1,12972 @@
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diff --git a/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
new file mode 100644
index 0000000..38737ec
--- /dev/null
+++ b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_0_test_GCC6.vtk
@@ -0,0 +1,7757 @@
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diff --git a/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
new file mode 100644
index 0000000..351bb23
--- /dev/null
+++ b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_1_test_GCC6.vtk
@@ -0,0 +1,8827 @@
+# vtk DataFile Version 3.0
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diff --git a/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk
new file mode 100644
index 0000000..69a5e28
--- /dev/null
+++ b/test/umfpack_solver<double>_lid_driven_cavity_3d_p3_grid_2_test_GCC6.vtk
@@ -0,0 +1,9372 @@
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