CartDecomposition.hpp

/*
 * CartDecomposition.hpp
 *
 *  Created on: Oct 07, 2015
 *      Author: Pietro Incardona, Antonio Leo
 */

#ifndef CARTDECOMPOSITION_HPP
#define CARTDECOMPOSITION_HPP

#include "config.h"
#include <cmath>
#include "VCluster/VCluster.hpp"
#include "Graph/CartesianGraphFactory.hpp"
#include "Decomposition.hpp"
#include "Vector/map_vector.hpp"
#include <vector>
#include <initializer_list>
#include "SubdomainGraphNodes.hpp"
#include "dec_optimizer.hpp"
#include "Space/Shape/Box.hpp"
#include "Space/Shape/Point.hpp"
#include "NN/CellList/CellDecomposer.hpp"
#include <unordered_map>
#include "NN/CellList/CellList.hpp"
#include "Space/Ghost.hpp"
#include "common.hpp"
#include "ie_loc_ghost.hpp"
#include "ie_ghost.hpp"
#include "nn_processor.hpp"
#include "GraphMLWriter/GraphMLWriter.hpp"
#include "Distribution/ParMetisDistribution.hpp"
#include "Distribution/DistParMetisDistribution.hpp"
#include "Distribution/MetisDistribution.hpp"
#include "DLB/DLB.hpp"
#include "util/se_util.hpp"
#include "util/mathutil.hpp"
#include "CartDecomposition_ext.hpp"
#include "data_type/aggregate.hpp"
#include "Domain_NN_calculator_cart.hpp"

#define CARTDEC_ERROR 2000lu

/*! \brief It spread the sub-sub-domain on a regular cartesian grid of size dim
 *
 * \warning this function only guarantee that the division on each direction is
 *          2^n with some n and does not guarantee that the number of
 *          sub-sub-domain is preserved
 *
 * \param div number of division on each direction as output
 * \param n_sub number of sub-domain
 * \param dim_r dimension reduction
 *
 */
template<unsigned int dim> static void nsub_to_div2(size_t (& div)[dim], size_t n_sub, size_t dim_r)
{
	for (size_t i = 0; i < dim; i++)
	{
		if (i < dim_r)
		{div[i] = openfpm::math::round_big_2(pow(n_sub, 1.0 / dim_r));}
		else
		{div[i] = 1;}
	}
}

/*! \brief It spread the sub-sub-domain on a regular cartesian grid of size dim
 *
 * \warning this function only guarantee that the division on each direction is
 *          2^n with some n and does not guarantee that the number of
 *          sub-sub-domain is preserved
 *
 * \param div number of division on each direction as output
 * \param n_sub number of sub-domain
 * \param dim_r dimension reduction
 *
 */
template<unsigned int dim> static void nsub_to_div(size_t (& div)[dim], size_t n_sub, size_t dim_r)
{
	for (size_t i = 0; i < dim; i++)
	{
		if (i < dim_r)
		{div[i] = std::floor(pow(n_sub, 1.0 / dim_r));}
		else
		{div[i] = 1;}
	}
}

#define COMPUTE_SKIN_SUB 1

/**
 * \brief This class decompose a space into sub-sub-domains and distribute them across processors
 *
 * \tparam dim is the dimensionality of the physical domain we are going to decompose.
 * \tparam T type of the space we decompose, Real, Integer, Complex ...
 * \tparam Memory Memory factory used to allocate memory
 * \tparam Distribution type of distribution, can be ParMetisDistribution or MetisDistribution
 *
 * Given an N-dimensional space, this class decompose the space into a Cartesian grid of small
 * sub-sub-domain. To each sub-sub-domain is assigned an id that identify at which processor is
 * assigned (in general the union of all the sub-sub-domain assigned to a processor is
 * simply connected space), a second step merge several sub-sub-domain with same id into bigger region
 *  sub-domain. Each sub-domain has an extended space called ghost part
 *
 * Assuming that VCluster.getProcessUnitID(), equivalent to the MPI processor rank, return the processor local
 * processor id, we define
 *
 * * local processor: processor rank
 * * local sub-domain: sub-domain given to the local processor
 * * external ghost box: (or ghost box) are the boxes that compose the ghost space of the processor, or the
 *   boxes produced expanding every local sub-domain by the ghost extension and intersecting with the sub-domain
 *   of the other processors
 * * Near processors are the processors adjacent to the local processor, where with adjacent we mean all the processor
 *   that has a non-zero intersection with the ghost part of the local processor, or all the processors that
 *   produce non-zero external boxes with the local processor, or all the processor that should communicate
 *   in case of ghost data synchronization
 * * internal ghost box: is the part of ghost of the near processor that intersect the space of the
 *       processor, or the boxes produced expanding the sub-domain of the near processors with the local sub-domain
 * * Near processor sub-domain: is a sub-domain that live in the a near (or contiguous) processor
 * * Near processor list: the list of all the near processor of the local processor (each processor has a list
 *                        of the near processor)
 * * Local ghosts internal or external are all the ghosts that does not involve inter-processor communications
 *
 * \see calculateGhostBoxes() for a visualization of internal and external ghost boxes
 *
 * ### Create a Cartesian decomposition object on a Box space, distribute, calculate internal and external ghost boxes
 *
 * \snippet CartDecomposition_unit_test.hpp Create CartDecomposition
 *
 */

template<unsigned int dim, typename T, typename Memory, typename Distribution>
class CartDecomposition: public ie_loc_ghost<dim, T>, public nn_prcs<dim, T>, public ie_ghost<dim, T>, public domain_nn_calculator_cart<dim>
{
public:

	//! Type of the domain we are going to decompose
	typedef T domain_type;

	//! It simplify to access the SpaceBox element
	typedef SpaceBox<dim, T> Box;

	//! This class is base of itself
	typedef CartDecomposition<dim,T,Memory,Distribution> base_type;

	//! This class admit a class defined on an extended domain
	typedef CartDecomposition_ext<dim,T,Memory,Distribution> extended_type;

protected:

	//! Indicate the communication weight has been set
	bool commCostSet = false;

	//! This is the key type to access  data_s, for example in the case of vector
	//! acc_key is size_t
	typedef typename openfpm::vector<SpaceBox<dim, T>,
			Memory,
			typename memory_traits_lin<SpaceBox<dim, T>>::type,
			memory_traits_lin,
			openfpm::vector_grow_policy_default,
			openfpm::vect_isel<SpaceBox<dim, T>>::value>::access_key acc_key;

	//! the set of all local sub-domain as vector
	openfpm::vector<SpaceBox<dim, T>> sub_domains;

	//! the remote set of all sub-domains as vector of 'sub_domains' vectors
	mutable openfpm::vector<Box_map<dim, T>> sub_domains_global;

	//! for each sub-domain, contain the list of the neighborhood processors
	openfpm::vector<openfpm::vector<long unsigned int> > box_nn_processor;

	//! Structure that contain for each sub-sub-domain box the processor id
	//! exist for efficient global communication
	CellList<dim,T,Mem_fast<>,shift<dim,T>> fine_s;

	//! Structure that store the cartesian grid information
	grid_sm<dim, void> gr;

	//! Structure that store the cartesian grid information
	grid_sm<dim, void> gr_dist;

	//! Structure that decompose the space into cells without creating them
	//! useful to convert positions to CellId or sub-domain id in this case
	CellDecomposer_sm<dim, T, shift<dim,T>> cd;

	//! rectangular domain to decompose
	::Box<dim,T> domain;

	//! Box Spacing
	T spacing[dim];

	//! Magnification factor between distribution and
	//! decomposition
	size_t magn[dim];

	//! Runtime virtual cluster machine
	Vcluster & v_cl;

	//! Create distribution
	Distribution dist;

	//! Processor bounding box
	::Box<dim,T> bbox;

	//! reference counter of the object in case is shared between object
	long int ref_cnt;

	//! ghost info
	Ghost<dim,T> ghost;

	//! Boundary condition info
	size_t bc[dim];

	//! Processor domain bounding box
	::Box<dim,size_t> proc_box;

	//! set of Boxes produced by the decomposition optimizer
	openfpm::vector<::Box<dim, size_t>> loc_box;

	/*! \brief It convert the box from the domain decomposition into sub-domain
	 *
	 * The decomposition box from the domain-decomposition contain the box in integer
	 * coordinates. This box is converted into a continuos box. It also adjust loc_box
	 * if the distribution grid and the decomposition grid are different.
	 *
	 * \param loc_box local box
	 *
	 * \return the corresponding sub-domain
	 *
	 */
	template<typename Memory_bx> SpaceBox<dim,T> convertDecBoxIntoSubDomain(encapc<1,::Box<dim,size_t>,Memory_bx> loc_box)
	{
		// A point with all coordinate to one
		size_t one[dim];
		for (size_t i = 0 ; i < dim ; i++)	{one[i] = 1;}

		SpaceBox<dim, size_t> sub_dc = loc_box;
		SpaceBox<dim, size_t> sub_dce = sub_dc;
		sub_dce.expand(one);
		sub_dce.mul(magn);

		// shrink by one
		for (size_t i = 0 ; i < dim ; i++)
		{
			loc_box.template get<Box::p1>()[i] = sub_dce.getLow(i);
			loc_box.template get<Box::p2>()[i] = sub_dce.getHigh(i) - 1;
		}

		SpaceBox<dim, T> sub_d(sub_dce);
		sub_d.mul(spacing);
		sub_d += domain.getP1();

		// we add the

		// Fixing sub-domains to cover all the domain

		// Fixing sub_d
		// if (loc_box) is at the boundary we have to ensure that the box span the full
		// domain (avoiding rounding off error)
		for (size_t i = 0; i < dim; i++)
		{
			if (sub_dc.getHigh(i) == gr.size(i) - 1)
			{sub_d.setHigh(i, domain.getHigh(i));}

			if (sub_dc.getLow(i) == 0)
			{sub_d.setLow(i,domain.getLow(i));}
		}

		return sub_d;
	}

	void collect_all_sub_domains(openfpm::vector<Box_map<dim,T>> & sub_domains_global)
	{
#ifdef SE_CLASS2
		check_valid(this,8);
#endif

		sub_domains_global.clear();
		openfpm::vector<Box_map<dim,T>> bm;

		for (size_t i = 0 ; i < sub_domains.size() ; i++)
		{
			Box_map<dim,T> tmp;
			tmp.box = ::SpaceBox<dim,T>(sub_domains.get(i));
			tmp.prc = v_cl.rank();

			bm.add(tmp);

		}

		v_cl.SGather(bm,sub_domains_global,0);

		size_t size = sub_domains_global.size();

		v_cl.max(size);
		v_cl.execute();

		sub_domains_global.resize(size);

		v_cl.Bcast(sub_domains_global,0);
		v_cl.execute();
	}

public:

	void initialize_fine_s(const ::Box<dim,T> & domain)
	{
		fine_s.clear();
		size_t div_g[dim];

		// We reduce the size of the cells by a factor 8 in 3d 4 in 2d
		for (size_t i = 0 ; i < dim ; i++)
		{div_g[i] = gr.size(i)/2;}

		fine_s.Initialize(domain,div_g);
	}

	void construct_fine_s()
	{
		collect_all_sub_domains(sub_domains_global);

		// now draw all sub-domains in fine-s

		for (size_t i = 0 ; i < sub_domains_global.size() ; i++)
		{

			// get the cells this box span
			const grid_key_dx<dim> p1 = fine_s.getCellGrid(sub_domains_global.get(i).box.getP1());
			const grid_key_dx<dim> p2 = fine_s.getCellGrid(sub_domains_global.get(i).box.getP2());

			// Get the grid and the sub-iterator
			auto & gi = fine_s.getGrid();
			grid_key_dx_iterator_sub<dim> g_sub(gi,p1,p2);

			// add the box-id to the cell list
			while (g_sub.isNext())
			{
				auto key = g_sub.get();
				fine_s.addCell(gi.LinId(key),i);
				++g_sub;
			}
		}
	}

	/*! \brief Constructor, it decompose and distribute the sub-domains across the processors
	 *
	 * \param v_cl Virtual cluster, used internally for communications
	 * \param bc boundary conditions
	 * \param opt option (one option is to construct)
	 *
	 */
	void createSubdomains(Vcluster & v_cl, const size_t (& bc)[dim], size_t opt = 0)
	{
		int p_id = v_cl.getProcessUnitID();

		// Calculate the total number of box and and the spacing
		// on each direction
		// Get the box containing the domain
		SpaceBox<dim, T> bs = domain.getBox();

		for (unsigned int i = 0; i < dim; i++)
		{
			// Calculate the spacing
			spacing[i] = (bs.getHigh(i) - bs.getLow(i)) / gr.size(i);
		}

		// fill the structure that store the processor id for each sub-domain
		initialize_fine_s(domain);

		// Optimize the decomposition creating bigger spaces
		// And reducing Ghost over-stress
		dec_optimizer<dim, Graph_CSR<nm_v, nm_e>> d_o(dist.getGraph(), gr_dist.getSize());

		// Ghost
		Ghost<dim,long int> ghe;

		// Set the ghost
		for (size_t i = 0 ; i < dim ; i++)
		{
			ghe.setLow(i,static_cast<long int>(ghost.getLow(i)/spacing[i]) - 1);
			ghe.setHigh(i,static_cast<long int>(ghost.getHigh(i)/spacing[i]) + 1);
		}

		// optimize the decomposition
		d_o.template optimize<nm_v::sub_id, nm_v::proc_id>(dist.getGraph(), p_id, loc_box, box_nn_processor,ghe,bc);

		// Initialize
		if (loc_box.size() > 0)
		{
			bbox = convertDecBoxIntoSubDomain(loc_box.get(0));
			proc_box = loc_box.get(0);
			sub_domains.add(bbox);
		}
		else
		{
			// invalidate all the boxes
			for (size_t i = 0 ; i < dim ; i++)
			{
				proc_box.setLow(i,0.0);
				proc_box.setHigh(i,0);

				bbox.setLow(i,0.0);
				bbox.setHigh(i,0);
			}
		}

		// convert into sub-domain
		for (size_t s = 1; s < loc_box.size(); s++)
		{
			SpaceBox<dim,T> sub_d = convertDecBoxIntoSubDomain(loc_box.get(s));

			// add the sub-domain
			sub_domains.add(sub_d);

			// Calculate the bound box
			bbox.enclose(sub_d);
			proc_box.enclose(loc_box.get(s));
		}

		nn_prcs<dim,T>::create(box_nn_processor, sub_domains);
		nn_prcs<dim,T>::applyBC(domain,ghost,bc);

		// fill fine_s structure
		// fine_s structure contain the processor id for each sub-sub-domain
		// with sub-sub-domain we mean the sub-domain decomposition before
		// running dec_optimizer (before merging sub-domains)

		///////////////////////////////// TODO //////////////////////////////////////////

		construct_fine_s();

		/////////////////////////////////////////////////////////////////////////////////

/*		grid_key_dx_iterator<dim> git(gr);

		while (git.isNext())
		{
			auto key = git.get();
			grid_key_dx<dim> key2;

			for (size_t i = 0 ; i < dim ; i++)
			{key2.set_d(i,key.get(i) / magn[i]);}

			size_t lin = gr_dist.LinId(key2);
			size_t lin2 = gr.LinId(key);

			// Here we draw the fine_s in the cell-list

			fine_s.get(lin2) = dist.getGraph().template vertex_p<nm_v::proc_id>(lin);

			++git;
		}*/

		Initialize_geo_cell_lists();
	}

	/*! \brief Initialize geo_cell lists
	 *
	 *
	 *
	 */
	void Initialize_geo_cell_lists()
	{
		// Get the processor bounding Box
		::Box<dim,T> bound = getProcessorBounds();

		// Check if the box is valid
		if (bound.isValidN() == true)
		{
			// Not necessary, but I prefer
			bound.enlarge(ghost);

			// calculate the sub-divisions
			size_t div[dim];
			for (size_t i = 0; i < dim; i++)
			{div[i] = (size_t) ((bound.getHigh(i) - bound.getLow(i)) / cd.getCellBox().getP2()[i]);}

			// Initialize the geo_cell structure
			ie_ghost<dim,T>::Initialize_geo_cell(bound,div);

			// Initialize shift vectors
			ie_ghost<dim,T>::generateShiftVectors(domain,bc);
		}
	}

	/*! \brief Calculate communication and migration costs
	 *
	 * \param ts how many timesteps have passed since last calculation, used to approximate the cost
	 */
	void computeCommunicationAndMigrationCosts(size_t ts)
	{
		float migration = 0;

		SpaceBox<dim, T> cellBox = cd.getCellBox();
		float b_s = static_cast<float>(cellBox.getHigh(0));
		float gh_s = static_cast<float>(ghost.getHigh(0));

		// compute the gh_area for 2 dim case
		float gh_v = (gh_s * b_s);

		// multiply for sub-sub-domain side for each domain
		for (size_t i = 2; i < dim; i++)
		{
			/* coverity[dead_error_line] */
			gh_v *= b_s;
		}

		size_t norm = (size_t) (1.0 / gh_v);

		migration = pow(b_s, dim);

		size_t prev = 0;

		for (size_t i = 0; i < dist.getNSubSubDomains(); i++)
		{
			dist.setMigrationCost(i, norm * migration /* * dist.getSubSubDomainComputationCost(i)*/ );

			for (size_t s = 0; s < dist.getNSubSubDomainNeighbors(i); s++)
			{
				// We have to remove dist.getSubSubDomainComputationCost(i) otherwise the graph is
				// not directed
				dist.setCommunicationCost(i, s, 1 /** dist.getSubSubDomainComputationCost(i)*/  *  ts);
			}
			prev += dist.getNSubSubDomainNeighbors(i);
		}

		commCostSet = true;
	}

	/*! \brief Create the sub-domain that decompose your domain
	 *
	 */
	void CreateSubspaces()
	{
		// Create a grid where each point is a space
		grid_sm<dim, void> g(div);

		// create a grid_key_dx iterator
		grid_key_dx_iterator<dim> gk_it(g);

		// Divide the space into subspaces
		while (gk_it.isNext())
		{
			//! iterate through all subspaces
			grid_key_dx<dim> key = gk_it.get();

			//! Create a new subspace
			SpaceBox<dim, T> tmp;

			//! fill with the Margin of the box
			for (int i = 0; i < dim; i++)
			{
				tmp.setHigh(i, (key.get(i) + 1) * spacing[i]);
				tmp.setLow(i, key.get(i) * spacing[i]);
			}

			//! add the space box
			sub_domains.add(tmp);

			// Next sub-domain
			++gk_it;
		}
	}


	/*! \brief It calculate the internal ghost boxes
	 *
	 * Example: Processor 10 calculate
	 * B8_0 B9_0 B9_1 and B5_0
	 *
	 *
	 *
	 \verbatim

	+----------------------------------------------------+
	|                                                    |
	|                 Processor 8                        |
	|                 Sub+domain 0                       +-----------------------------------+
	|                                                    |                                   |
	|                                                    |                                   |
	++--------------+---+---------------------------+----+        Processor 9                |
	 |              |   |     B8_0                  |    |        Subdomain 0                |
	 |              +------------------------------------+                                   |
	 |              |   |                           |    |                                   |
	 |              |   |                           |B9_0|                                   |
	 |              | B |    Local processor        |    |                                   |
	 | Processor 5  | 5 |    Subdomain 0            |    |                                   |
	 | Subdomain 0  | _ |                           +----------------------------------------+
	 |              | 0 |                           |    |                                   |
	 |              |   |                           |    |                                   |
	 |              |   |                           |    |        Processor 9                |
	 |              |   |                           |B9_1|        Subdomain 1                |
	 |              |   |                           |    |                                   |
	 |              |   |                           |    |                                   |
	 |              |   |                           |    |                                   |
	 +--------------+---+---------------------------+----+                                   |
														 |                                   |
														 +-----------------------------------+


 \endverbatim

       and also
       G8_0 G9_0 G9_1 G5_0 (External ghost boxes)

\verbatim

		  +----------------------------------------------------+
		  |                 Processor 8                        |
		  |                 Subdomain 0                        +-----------------------------------+
		  |                                                    |                                   |
		  |           +---------------------------------------------+                              |
		  |           |         G8_0                           |    |                              |
	+-----+---------------+------------------------------------+    |   Processor 9                |
	|                 |   |                                    |    |   Subdomain 0                |
	|                 |   |                                    |G9_0|                              |
	|                 |   |                                    |    |                              |
	|                 |   |                                    |    |                              |
	|                 |   |        Local processor             |    |                              |
	|  Processor 5    |   |        Sub+domain 0                |    |                              |
	|  Subdomain 0    |   |                                    +-----------------------------------+
	|                 |   |                                    |    |                              |
	|                 | G |                                    |    |                              |
	|                 | 5 |                                    |    |   Processor 9                |
	|                 | | |                                    |    |   Subdomain 1                |
	|                 | 0 |                                    |G9_1|                              |
	|                 |   |                                    |    |                              |
	|                 |   |                                    |    |                              |
	+---------------------+------------------------------------+    |                              |
					  |                                        |    |                              |
					  +----------------------------------------+----+------------------------------+

	 \endverbatim

	 *
	 * ghost margins for each dimensions (p1 negative part) (p2 positive part)
	 *
	 *
	 \verbatim

	 	 	 	 	 ^ p2[1]
	 	 	 	 	 |
	 	 	 	 	 |
	 	 	 	+----+----+
	 	 	 	|         |
	 	 	 	|         |
	 p1[0]<-----+         +----> p2[0]
	 	 	 	|         |
	 	 	 	|         |
	 	 	 	+----+----+
	 	 	 	 	 |
	 	 	 	 	 v  p1[1]

	 \endverbatim

	 *
	 *
	 */
	void calculateGhostBoxes()
	{
		// Intersect all the local sub-domains with the sub-domains of the contiguous processors

		// create the internal structures that store ghost information
		ie_ghost<dim, T>::create_box_nn_processor_ext(v_cl, ghost, sub_domains, box_nn_processor, *this);
		ie_ghost<dim, T>::create_box_nn_processor_int(v_cl, ghost, sub_domains, box_nn_processor, *this);

		ie_loc_ghost<dim,T>::create(sub_domains,domain,ghost,bc);
	}

	template<typename T2> inline size_t processorID_impl(T2 & p) const
	{
		// Get the number of elements in the cell

		size_t e = -1;
		size_t cl = fine_s.getCell(p);
		size_t n_ele = fine_s.getNelements(cl);

		for (size_t i = 0 ; i < n_ele ; i++)
		{
			e = fine_s.get(cl,i);

			if (sub_domains_global.get(e).box.isInsideNP(p) == true)
			{
				break;
			}
		}

#ifdef SE_CLASS1

		if (n_ele == 0)
		{
			std::cout << __FILE__ << ":" << __LINE__ << " I cannot detect in which processor this particle go" << std::endl;
			return -1;
		}

#endif

		return sub_domains_global.get(e).prc;
	}


public:

	//! Space dimensions
	static constexpr int dims = dim;

	//! Space type
	typedef T stype;

	//! Increment the reference counter
	void incRef()
	{ref_cnt++;}

	//! Decrement the reference counter
	void decRef()
	{ref_cnt--;}

	//! Return the reference counter
	long int ref()
	{
		return ref_cnt;
	}

	/*! \brief Cartesian decomposition constructor
	 *
	 * \param v_cl Virtual cluster, used internally to handle or pipeline communication
	 *
	 */
	CartDecomposition(Vcluster & v_cl)
	:nn_prcs<dim, T>(v_cl), v_cl(v_cl), dist(v_cl),ref_cnt(0)
	{
		// Reset the box to zero
		bbox.zero();
	}

	/*! \brief Cartesian decomposition copy constructor
	 *
     * \param cart object to copy
	 *
	 */
	CartDecomposition(const CartDecomposition<dim,T,Memory,Distribution> & cart)
	:nn_prcs<dim,T>(cart.v_cl),v_cl(cart.v_cl),dist(v_cl),ref_cnt(0)
	{
		this->operator=(cart);
	}

	/*! \brief Cartesian decomposition copy constructor
	 *
     * \param cart object to copy
	 *
	 */
	CartDecomposition(CartDecomposition<dim,T,Memory,Distribution> && cart)
	:nn_prcs<dim,T>(cart.v_cl),v_cl(cart.v_cl),dist(v_cl),ref_cnt(0)
	{
		this->operator=(cart);
	}

	//! Cartesian decomposition destructor
	~CartDecomposition()
	{
	}

	/*! \brief class to select the returned id by ghost_processorID
	 *
	 */
	class box_id
	{
	public:
		/*! \brief Return the box id
		 *
		 * \param p structure containing the id informations
		 * \param b_id box_id
		 *
		 * \return box id
		 *
		 */
		inline static size_t id(p_box<dim, T> & p, size_t b_id)
		{
			return b_id;
		}
	};

	/*! \brief class to select the returned id by ghost_processorID
	 *
	 */
	class processor_id
	{
	public:
		/*! \brief Return the processor id
		 *
		 * \param p structure containing the id informations
		 * \param b_id box_id
		 *
		 * \return processor id
		 *
		 */
		inline static size_t id(p_box<dim, T> & p, size_t b_id)
		{
			return p.proc;
		}
	};

	/*! \brief class to select the returned id by ghost_processorID
	 *
	 */
	class lc_processor_id
	{
	public:
		/*! \brief Return the near processor id
		 *
		 * \param p structure containing the id informations
		 * \param b_id box_id
		 *
		 * \return local processor id
		 *
		 */
		inline static size_t id(p_box<dim, T> & p, size_t b_id)
		{
			return p.lc_proc;
		}
	};

	/*! \brief class to select the returned id by ghost_processorID
	 *
	 */
	class shift_id
	{
	public:
		/*! \brief Return the shift id
		 *
		 * \param p structure containing the id informations
		 * \param b_id box_id
		 *
		 * \return shift_id id
		 *
		 */
		inline static size_t id(p_box<dim,T> & p, size_t b_id)
		{
			return p.shift_id;
		}
	};

	/*! \brief Apply boundary condition to the point
	 *
	 * If the particle go out to the right, bring back the particle on the left
	 * in case of periodic, nothing in case of non periodic
	 *
	 * \param pt Point to apply the boundary condition. (it's coordinated are changed according the
	 *        the explanation before)
	 *
	 */
	void applyPointBC(float (& pt)[dim]) const
	{
		for (size_t i = 0 ; i < dim ; i++)
		{
			if (bc[i] == PERIODIC)
			{pt[i] = openfpm::math::periodic_l(pt[i],domain.getHigh(i),domain.getLow(i));}
		}
	}

	/*! \brief Apply boundary condition to the point
	 *
	 * If the particle go out to the right, bring back the particle on the left
	 * in case of periodic, nothing in case of non periodic
	 *
	 * \param pt Point to apply the boundary conditions.(it's coordinated are changed according the
	 *        the explanation before)
	 *
	 */
	void applyPointBC(Point<dim,T> & pt) const
	{
		for (size_t i = 0 ; i < dim ; i++)
		{
			if (bc[i] == PERIODIC)
			{pt.get(i) = openfpm::math::periodic_l(pt.get(i),domain.getHigh(i),domain.getLow(i));}
		}
	}

	/*! \brief Apply boundary condition to the point
	 *
	 * If the particle go out to the right, bring back the particle on the left
	 * in case of periodic, nothing in case of non periodic
	 *
	 * \param pt encapsulated point object (it's coordinated are changed according the
	 *        the explanation before)
	 *
	 */
	template<typename Mem> void applyPointBC(encapc<1,Point<dim,T>,Mem> && pt) const
	{
		for (size_t i = 0 ; i < dim ; i++)
		{
			if (bc[i] == PERIODIC)
			{pt.template get<0>()[i] = openfpm::math::periodic_l(pt.template get<0>()[i],domain.getHigh(i),domain.getLow(i));}
		}
	}

	/*! \brief It create another object that contain the same decomposition information but with different ghost boxes
	 *
	 * \param g ghost
	 *
	 * \return a duplicated decomposition with different ghost boxes
	 *
	 */
	CartDecomposition<dim,T,Memory,Distribution> duplicate(const Ghost<dim,T> & g) const
	{
		CartDecomposition<dim,T,Memory,Distribution> cart(v_cl);

		cart.box_nn_processor = box_nn_processor;
		cart.sub_domains = sub_domains;
		cart.fine_s = fine_s;

		cart.gr = gr;
		cart.cd = cd;
		cart.domain = domain;
		for (size_t i = 0 ; i < dim ; i++)
		{cart.spacing[i] = spacing[i];};

		cart.bbox = bbox;
		cart.ghost = g;

		cart.dist = dist;

		for (size_t i = 0 ; i < dim ; i++)
			cart.bc[i] = bc[i];

		(static_cast<nn_prcs<dim,T> &>(cart)).create(box_nn_processor, sub_domains);
		(static_cast<nn_prcs<dim,T> &>(cart)).applyBC(domain,ghost,bc);

		cart.Initialize_geo_cell_lists();
		cart.calculateGhostBoxes();

		return cart;
	}

	/*! \brief It create another object that contain the same information and act in the same way
	 *
	 * \return a duplicated CartDecomposition object
	 *
	 */
	CartDecomposition<dim,T,Memory,Distribution> duplicate() const
	{
		CartDecomposition<dim,T,Memory,Distribution> cart(v_cl);

		(static_cast<ie_loc_ghost<dim,T>*>(&cart))->operator=(static_cast<ie_loc_ghost<dim,T>>(*this));
		(static_cast<nn_prcs<dim,T>*>(&cart))->operator=(static_cast<nn_prcs<dim,T>>(*this));
		(static_cast<ie_ghost<dim,T>*>(&cart))->operator=(static_cast<ie_ghost<dim,T>>(*this));

		cart.sub_domains = sub_domains;
		cart.box_nn_processor = box_nn_processor;
		cart.fine_s = fine_s;
		cart.gr = gr;
		cart.gr_dist = gr_dist;
		cart.dist = dist;
		cart.commCostSet = commCostSet;
		cart.cd = cd;
		cart.domain = domain;
		cart.sub_domains_global = sub_domains_global;
		for (size_t i = 0 ; i < dim ; i++)
		{cart.spacing[i] = spacing[i];};

		cart.ghost = ghost;

		cart.bbox = bbox;

		for (size_t i = 0 ; i < dim ; i++)
			cart.bc[i] = this->bc[i];

		return cart;
	}

	/*! \brief Copy the element
	 *
	 * \param cart element to copy
	 *
	 * \return itself
	 *
	 */
	CartDecomposition<dim,T,Memory, Distribution> & operator=(const CartDecomposition & cart)
	{
		static_cast<ie_loc_ghost<dim,T>*>(this)->operator=(static_cast<ie_loc_ghost<dim,T>>(cart));
		static_cast<nn_prcs<dim,T>*>(this)->operator=(static_cast<nn_prcs<dim,T>>(cart));
		static_cast<ie_ghost<dim,T>*>(this)->operator=(static_cast<ie_ghost<dim,T>>(cart));

		sub_domains = cart.sub_domains;
		box_nn_processor = cart.box_nn_processor;
		fine_s = cart.fine_s;
		gr = cart.gr;
		gr_dist = cart.gr_dist;
		dist = cart.dist;
		commCostSet = cart.commCostSet;
		cd = cart.cd;
		domain = cart.domain;
		sub_domains_global = cart.sub_domains_global;

		for (size_t i = 0 ; i < dim ; i++)
		{
			spacing[i] = cart.spacing[i];
			magn[i] = cart.magn[i];
		};

		ghost = cart.ghost;