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/*
 * CartDecomposition.hpp
 *
 *  Created on: Aug 15, 2014
 *      Author: Pietro Incardona
 */

#ifndef CARTDECOMPOSITION_HPP
#define CARTDECOMPOSITION_HPP

#include "config.h"
#include "Decomposition.hpp"
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#include "Vector/map_vector.hpp"
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#include <vector>
#include "global_const.hpp"
#include <initializer_list>
#include "SubdomainGraphNodes.hpp"
#include "metis_util.hpp"
#include "dec_optimizer.hpp"
#include "Space/Shape/Box.hpp"
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#include "Space/Shape/Point.hpp"
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#include "NN/CellList/CellDecomposer.hpp"
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#include <unordered_map>
#include "NN/CellList/CellList.hpp"
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#include "Space/Ghost.hpp"
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/**
 * \brief This class decompose a space into subspaces
 *
 * \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 layout to use
 * \tparam Memory Memory factory used to allocate memory
 * \tparam Domain Structure that contain the information of your physical domain
 * \tparam data type of structure that store the sub-domain decomposition can be an openfpm structure like
 *        vector, ...
 *
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 * Given an N-dimensional space, this class decompose the space into a Cartesian grid of small
 * sub-sub-domain. At each sub-sub-domain is assigned  an id that identify which processor is
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 * going to take care of that part of space (in general the space assigned to a processor is
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 * simply connected), a second step merge several sub-sub-domain with same id into bigger region
 *  sub-domain with the id. 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 sub-domain: all the sub-domain with id == 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)
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 * * Local ghosts interal or external are all the ghosts that does not involve inter-processor communications
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 *
 * \see calculateGhostBoxes() for a visualization of internal and external ghost boxes
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 *
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 */

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template<unsigned int dim, typename T, template<typename> class device_l=openfpm::device_cpu, typename Memory=HeapMemory, template<unsigned int, typename> class Domain=Box, template<typename, typename, typename, typename, unsigned int> class data_s = openfpm::vector>
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class CartDecomposition
{
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	struct N_box
	{
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		// id of the processor in the nn_processor list (local processor id)
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		size_t id;

		// Near processor sub-domains
		typename openfpm::vector<::Box<dim,T>> bx;
	};

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	struct Box_proc
	{
		// Intersection between the local sub-domain enlarged by the ghost and the contiguous processor
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		// sub-domains (External ghost)
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		openfpm::vector<::Box<dim,T>> bx;

		// Intersection between the contiguous processor sub-domain enlarged by the ghost with the
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		// local sub-domain (Internal ghost)
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		openfpm::vector<::Box<dim,T>> nbx;


		// processor
		size_t proc;
	};

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	/*! It contain a box definition and from witch sub-domain it come from (in the local processor)
	 * and an unique across adjacent processors (for communication)
	 *
	 * If the box come from the intersection of an expanded sub-domain and a sub-domain
	 *
	 * Assuming we are considering the adjacent processor i (0 to getNNProcessors())
	 *
	 * ### external ghost box
	 *
	 * id = id_exp + N_non_exp + id_non_exp
	 *
	 * id_exp = the id in the vector proc_adj_box.get(i) of the expanded sub-domain
	 *
	 * id_non_exp = the id in the vector nn_processor_subdomains[i] of the sub-domain
	 *
	 * ### internal ghost box
	 *
	 * id = id_exp + N_non_exp + id_non_exp
	 *
	 * id_exp = the id in the vector nn_processor_subdomains[i] of the expanded sub-domain
	 *
	 * id_non_exp = the id in the vector proc_adj_box.get(i) of the sub-domain
	 *
	 */
	/*
	*/
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	struct Box_sub : public Box<dim,T>
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	{
		// Domain id
		size_t sub;
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		// Id
		size_t id;

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		Box_sub operator=(const Box<dim,T> & box)
		{
			::Box<dim,T>::operator=(box);

			return *this;
		}
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	};

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	//! Particular case for local internal ghost boxes
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	struct Box_sub_k : public Box<dim,T>
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	{
		// Domain id
		size_t sub;

		//! k \see getLocalGhostIBoxE
		long int k;

		Box_sub_k operator=(const Box<dim,T> & box)
		{
			::Box<dim,T>::operator=(box);

			return *this;
		}
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		// encap interface to make compatible with OpenFPM_IO
		template <int i> auto get() -> decltype( static_cast<Box<dim,T> *>(this)->template get<i>())
		{
			return ::Box<dim,T>::template get<i>();
		}
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	};

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	struct Box_dom
	{
		// Intersection between the local sub-domain enlarged by the ghost and the contiguous processor
		// sub-domains (External ghost)
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		openfpm::vector_std< Box_sub > ebx;
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		// Intersection between the contiguous processor sub-domain enlarged by the ghost with the
		// local sub-domain (Internal ghost)
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		openfpm::vector_std< Box_sub> ibx;
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	};

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	//! Case for local ghost box
	struct lBox_dom
	{
		// Intersection between the local sub-domain enlarged by the ghost and the contiguous processor
		// sub-domains (External ghost)
		openfpm::vector_std< Box_sub > ebx;

		// Intersection between the contiguous processor sub-domain enlarged by the ghost with the
		// local sub-domain (Internal ghost)
		openfpm::vector_std< Box_sub_k> ibx;
	};

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public:
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	//! 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;

private:

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

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

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	//! for each sub-domain (first vector), contain the list (nested vector) of the neighborhood processors
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	//! and for each processor contain the boxes calculated from the intersection
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	//! of the sub-domains + ghost with the near-by processor sub-domain () and the other way around
	//! \see calculateGhostBoxes
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	openfpm::vector< openfpm::vector< Box_proc > > box_nn_processor_int;

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	//! It store the same information of box_nn_processor_int organized by processor id
	openfpm::vector< Box_dom > proc_int_box;

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

	// for each near-processor store the sub-domain of the near processor
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	std::unordered_map<size_t, N_box> nn_processor_subdomains;
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	// for each processor store the set of the sub-domains sent to the adjacent processors
	openfpm::vector<openfpm::vector<size_t>> proc_adj_box;

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	//! it contain the internal ghosts of the local processor
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	openfpm::vector<lBox_dom> loc_ghost_box;
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	//! Structure that contain for each sub-domain box the processor id
	//! exist for efficient global communication
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	openfpm::vector<size_t> fine_s;

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	//! Structure that store the cartesian grid information
	grid_sm<dim,void> gr;
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	//! Structure that decompose your structure into cell without creating them
	//! useful to convert positions to CellId or sub-domain id in this case
	CellDecomposer_sm<dim,T> cd;
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	//! rectangular domain to decompose
	Domain<dim,T> domain;

	//! Box Spacing
	T spacing[dim];

	//! Runtime virtual cluster machine
	Vcluster & v_cl;

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	//! Cell-list that store the geometrical information of the internal ghost boxes
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	CellList<dim,T,FAST> geo_cell;

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	//! Cell-list that store the geometrical information of the local internal ghost boxes
	CellList<dim,T,FAST> lgeo_cell;

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	/*! \brief Create internally the decomposition
	 *
     * \param v_cl Virtual cluster, used internally to handle or pipeline communication
	 *
	 */
	void CreateDecomposition(Vcluster & v_cl)
	{
		// 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
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			spacing[i] = (bs.getHigh(i) - bs.getLow(i)) / gr.size(i);
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		}

		// Here we use METIS
		// Create a cartesian grid graph
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		CartesianGraphFactory<dim,Graph_CSR<nm_part_v,nm_part_e>> g_factory_part;
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		// Processor graph
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		Graph_CSR<nm_part_v,nm_part_e> gp = g_factory_part.template construct<NO_EDGE,T,dim-1>(gr.getSize(),domain);
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		// Get the number of processing units
		size_t Np = v_cl.getProcessingUnits();

		// Get the processor id
		long int p_id = v_cl.getProcessUnitID();

		// Convert the graph to metis
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		Metis<Graph_CSR<nm_part_v,nm_part_e>> met(gp,Np);
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		// decompose
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		met.decompose<nm_part_v::id>();
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		// fill the structure that store the processor id for each sub-domain
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		fine_s.resize(gr.size());
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		// Optimize the decomposition creating bigger spaces
		// And reducing Ghost over-stress
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		dec_optimizer<dim,Graph_CSR<nm_part_v,nm_part_e>> d_o(gp,gr.getSize());
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		// set of Boxes produced by the decomposition optimizer
		openfpm::vector<::Box<dim,size_t>> loc_box;

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		// optimize the decomposition
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		d_o.template optimize<nm_part_v::sub_id,nm_part_v::id>(gp,p_id,loc_box,box_nn_processor);

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		// produce the list of the contiguous processor (nn_processors) and link nn_processor_subdomains to the
		// processor list
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		for (size_t i = 0 ;  i < box_nn_processor.size() ; i++)
		{
			for (size_t j = 0 ; j < box_nn_processor.get(i).size() ; j++)
			{
				nn_processors.add(box_nn_processor.get(i).get(j));
			}
		}

		// make the list sorted and unique
	    std::sort(nn_processors.begin(), nn_processors.end());
	    auto last = std::unique(nn_processors.begin(), nn_processors.end());
	    nn_processors.erase(last, nn_processors.end());
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		// produce the list of the contiguous processor (nn_processors) and link nn_processor_subdomains to the
		// processor list
		for (size_t i = 0 ;  i < box_nn_processor.size() ; i++)
		{
			for (size_t j = 0 ; j < box_nn_processor.get(i).size() ; j++)
			{
				// processor id near to this sub-domain
				size_t proc_id = box_nn_processor.get(i).get(j);

				size_t k = 0;
				// search inside near processor list
				for (k = 0 ; k < nn_processors.size() ; k++)
					if (nn_processors.get(k) == proc_id)	break;

				nn_processor_subdomains[proc_id].id = k;
			}
		}

		// Initialize ss_box and bbox
		if (loc_box.size() >= 0)
		{
			SpaceBox<dim,T> sub_d(loc_box.get(0));
			sub_d.mul(spacing);
			sub_d.expand(spacing);

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

			ss_box = sub_d;
			bbox = sub_d;
		}

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

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			// re-scale and add spacing (the end is the starting point of the next domain + spacing)
			sub_d.mul(spacing);
			sub_d.expand(spacing);
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			// add the sub-domain
			sub_domains.add(sub_d);
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			// Calculate the bound box
			bbox.enclose(sub_d);

			// Create the smallest box contained in all sub-domain
			ss_box.contained(sub_d);
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		}
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		// fill fine_s structure
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		// 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)
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		auto it = gp.getVertexIterator();

		while (it.isNext())
		{
			size_t key = it.get();

			// fill with the fine decomposition
			fine_s.get(key) = gp.template vertex_p<nm_part_v::id>(key);

			++it;
		}
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		// Get the smallest sub-division on each direction
		::Box<dim,T> unit = getSmallestSubdivision();
		// Get the processor bounding Box
		::Box<dim,T> bound = getProcessorBounds();

		// calculate the sub-divisions (0.5 for rounding error)
		size_t div[dim];
		for (size_t i = 0 ; i < dim ; i++)
			div[i] = (size_t)((bound.getHigh(i) - bound.getLow(i)) / unit.getHigh(i) + 0.5);

		// Create shift
		Point<dim,T> orig;

		// p1 point of the Processor bound box is the shift
		for (size_t i = 0 ; i < dim ; i++)
			orig.get(i) = bound.getLow(i);

		// Initialize the geo_cell structure
		geo_cell.Initialize(domain,div,orig);
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		lgeo_cell.Initialize(domain,div,orig);
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	}

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	// Save the ghost boundaries
	Ghost<dim,T> ghost;

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	/*! \brief Create the external local ghost boxes
	 *
	 * \param ghost margin to enlarge
	 *
	 */
	void create_loc_ghost_ebox(Ghost<dim,T> & ghost)
	{
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		// Save the ghost
		this->ghost = ghost;

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		loc_ghost_box.resize(sub_domains.size());

		// For each sub-domain
		for (size_t i = 0 ; i < sub_domains.size() ; i++)
		{
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			SpaceBox<dim,T> sub_with_ghost = sub_domains.get(i);

			// enlarge the sub-domain with the ghost
			sub_with_ghost.enlarge(ghost);
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			// intersect with the other local sub-domains
			for (size_t j = 0 ; j < sub_domains.size() ; j++)
			{
				if (i == j)
					continue;

				::Box<dim,T> bi;

				bool intersect = sub_with_ghost.Intersect(::SpaceBox<dim,T>(sub_domains.get(j)),bi);

				if (intersect == true)
				{
					Box_sub b;
					b.sub = j;
					b = bi;

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					// local external ghost box
					loc_ghost_box.get(i).ebx.add(b);

					// search this box in the internal box of the sub-domain j
					for (size_t k = 0; k < loc_ghost_box.get(j).ibx.size() ; k++)
					{
						if (loc_ghost_box.get(j).ibx.get(k).sub == i)
						{
							loc_ghost_box.get(j).ibx.get(k).k = loc_ghost_box.get(i).ebx.size()-1;
							break;
						}
					}
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				}
			}
		}
	}

	/*! \brief Create the internal local ghost boxes
	 *
	 * \param ghost margin to enlarge
	 *
	 */
	void create_loc_ghost_ibox(Ghost<dim,T> & ghost)
	{
		loc_ghost_box.resize(sub_domains.size());

		// For each sub-domain
		for (size_t i = 0 ; i < sub_domains.size() ; i++)
		{
			// intersect with the others local sub-domains
			for (size_t j = 0 ; j < sub_domains.size() ; j++)
			{
				if (i == j)
					continue;

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				SpaceBox<dim,T> sub_with_ghost = sub_domains.get(j);
				// enlarge the sub-domain with the ghost
				sub_with_ghost.enlarge(ghost);

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				::Box<dim,T> bi;

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				bool intersect = sub_with_ghost.Intersect(::SpaceBox<dim,T>(sub_domains.get(i)),bi);
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				if (intersect == true)
				{
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					Box_sub_k b;
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					b.sub = j;
					b = bi;
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					b.k = -1;
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					loc_ghost_box.get(i).ibx.add(b);
				}
			}
		}
	}

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	/*! \brief Create the subspaces that decompose your domain
	 *
	 * Create the subspaces that decompose your domain
	 *
	 */

	void CreateSubspaces()
	{
		// Create a grid where each point is a space
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		grid_sm<dim,void> g(div);
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		// 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);

			// add the iterator
			++gk_it;
		}
	}

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	/*! \brief Create the box_nn_processor_int (bx part)  structure
	 *
	 * This structure store for each sub-domain of this processors enlarged by the ghost size the boxes that
	 *  come from the intersection with the near processors sub-domains (External ghost box)
	 *
	 * \param ghost margins
	 *
	 * \note Are the G8_0 G9_0 G9_1 G5_0 boxes in calculateGhostBoxes
	 * \see calculateGhostBoxes
	 *
	 */
	void create_box_nn_processor_ext(Ghost<dim,T> & ghost)
	{
		box_nn_processor_int.resize(sub_domains.size());
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		proc_int_box.resize(getNNProcessors());
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		// For each sub-domain
		for (size_t i = 0 ; i < sub_domains.size() ; i++)
		{
			SpaceBox<dim,T> sub_with_ghost = sub_domains.get(i);

			// enlarge the sub-domain with the ghost
			sub_with_ghost.enlarge(ghost);

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			// resize based on the number of adjacent processors
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			box_nn_processor_int.get(i).resize(box_nn_processor.get(i).size());

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			// For each processor adjacent to this sub-domain
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			for (size_t j = 0 ; j < box_nn_processor.get(i).size() ; j++)
			{
				// Contiguous processor
				size_t p_id = box_nn_processor.get(i).get(j);

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				// store the box in proc_int_box storing from which sub-domain they come from
				Box_dom & proc_int_box_g = proc_int_box.get(ProctoID(p_id));

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				// get the set of sub-domains of the adjacent processor p_id
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				openfpm::vector< ::Box<dim,T> > & nn_processor_subdomains_g = nn_processor_subdomains[p_id].bx;
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				// near processor sub-domain intersections
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				openfpm::vector< ::Box<dim,T> > & box_nn_processor_int_gg = box_nn_processor_int.get(i).get(j).bx;
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				// for each near processor sub-domain intersect with the enlarged local sub-domain and store it
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				for (size_t b = 0 ; b < nn_processor_subdomains_g.size() ; b++)
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				{
					::Box<dim,T> bi;

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					bool intersect = sub_with_ghost.Intersect(::Box<dim,T>(nn_processor_subdomains_g.get(b)),bi);
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					if (intersect == true)
					{
						struct p_box pb;

						pb.box = bi;
						pb.proc = p_id;
						pb.lc_proc = ProctoID(p_id);

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						//
						// Updating
						//
						// vb_ext
						// box_nn_processor_int
						// proc_int_box
						//
						// They all store the same information but organized in different ways
						// read the description of each for more information
						//
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						vb_ext.add(pb);
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						box_nn_processor_int_gg.add(bi);
						proc_int_box_g.ebx.add();
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						proc_int_box_g.ebx.last() = bi;
						proc_int_box_g.ebx.last().sub = i;
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						// Search for the correct id
						size_t k = 0;
						size_t p_idp = ProctoID(p_id);
						for (k = 0 ; k < proc_adj_box.get(p_idp).size() ; k++)
						{
							if (proc_adj_box.get(p_idp).get(k) == i)
								break;
						}
						if (k == proc_adj_box.get(p_idp).size())
							std::cerr << "Error: " << __FILE__ << ":" << __LINE__ << " sub-domain not found\n";

						proc_int_box_g.ebx.last().id = (k * nn_processor_subdomains_g.size() + b) * v_cl.getProcessingUnits() + p_id;
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					}
				}
			}
		}
	}

	/*! \brief Create the box_nn_processor_int (nbx part) structure, the geo_cell list and proc_int_box
	 *
	 * This structure store for each sub-domain of this processors the boxes that come from the intersection
	 * of the near processors sub-domains enlarged by the ghost size (Internal ghost box). These boxes
	 * fill a geometrical cell list. The proc_int_box store the same information ordered by near processors
	 *
	 * \param ghost margins
	 *
	 * \note Are the B8_0 B9_0 B9_1 B5_0 boxes in calculateGhostBoxes
	 * \see calculateGhostBoxes
	 *
	 */
	void create_box_nn_processor_int(Ghost<dim,T> & ghost)
	{
		box_nn_processor_int.resize(sub_domains.size());
		proc_int_box.resize(getNNProcessors());

		// For each sub-domain
		for (size_t i = 0 ; i < sub_domains.size() ; i++)
		{
			// For each processor contiguous to this sub-domain
			for (size_t j = 0 ; j < box_nn_processor.get(i).size() ; j++)
			{
				// Contiguous processor
				size_t p_id = box_nn_processor.get(i).get(j);

				// get the set of sub-domains of the contiguous processor p_id
				openfpm::vector< ::Box<dim,T> > & nn_p_box = nn_processor_subdomains[p_id].bx;

				// get the local processor id
				size_t lc_proc = nn_processor_subdomains[p_id].id;

				// For each near processor sub-domains enlarge and intersect with the local sub-domain and store the result
				for (size_t k = 0 ; k < nn_p_box.size() ; k++)
				{

					// enlarge the near-processor sub-domain
					::Box<dim,T> n_sub = nn_p_box.get(k);

					// local sub-domain
					::SpaceBox<dim,T> l_sub = sub_domains.get(i);

					// Create a margin of ghost size around the near processor sub-domain
					n_sub.enlarge(ghost);

					// Intersect with the local sub-domain
					p_box b_int;
					bool intersect = n_sub.Intersect(l_sub,b_int.box);

					// store if it intersect
					if (intersect == true)
					{
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						// the box fill with the processor id
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						b_int.proc = p_id;

						// fill the local processor id
						b_int.lc_proc = lc_proc;

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						//
						// Updating
						//
						// vb_int
						// box_nn_processor_int
						// proc_int_box
						//
						// They all store the same information but organized in different ways
						// read the description of each for more information
						//

						// add the box to the near processor sub-domain intersections
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						openfpm::vector< ::Box<dim,T> > & p_box_int = box_nn_processor_int.get(i).get(j).nbx;
						p_box_int.add(b_int.box);
						vb_int.add(b_int);

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						// store the box in proc_int_box storing from which sub-domain they come from
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						Box_dom & pr_box_int = proc_int_box.get(ProctoID(p_id));
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						Box_sub sb;
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						sb = b_int.box;
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						sb.sub = i;
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						// Search for the correct id
						size_t s = 0;
						size_t p_idp = ProctoID(p_id);
						for (s = 0 ; s < proc_adj_box.get(p_idp).size() ; s++)
						{
							if (proc_adj_box.get(p_idp).get(s) == i)
								break;
						}
						if (s == proc_adj_box.get(p_idp).size())
							std::cerr << "Error: " << __FILE__ << ":" << __LINE__ << " sub-domain not found\n";

						sb.id = (k * proc_adj_box.get(p_idp).size() + s) * v_cl.getProcessingUnits() + v_cl.getProcessUnitID();

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						pr_box_int.ibx.add(sb);
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						// update the geo_cell list

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

						// Get the grid and the sub-iterator
						auto & gi = geo_cell.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();
							geo_cell.addCell(gi.LinId(key),vb_int.size()-1);
							++g_sub;
						}
					}
				}
			}
		}
	}

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	// Heap memory receiver
	HeapMemory hp_recv;

	// vector v_proc
	openfpm::vector<size_t> v_proc;

	// Receive counter
	size_t recv_cnt;

	/*! \brief Message allocation
	 *
	 * \param message size required to receive from i
	 * \param total message size to receive from all the processors
	 * \param the total number of processor want to communicate with you
	 * \param i processor id
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	 * \param ri request id (it is an id that goes from 0 to total_p, and is unique
	 *           every time message_alloc is called)
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	 * \param ptr a pointer to the vector_dist structure
	 *
	 * \return the pointer where to store the message
	 *
	 */
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	static void * message_alloc(size_t msg_i ,size_t total_msg, size_t total_p, size_t i, size_t ri, void * ptr)
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	{
		// cast the pointer
		CartDecomposition<dim,T,device_l,Memory,Domain,data_s> * cd = static_cast< CartDecomposition<dim,T,device_l,Memory,Domain,data_s> *>(ptr);

		// Resize the memory
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		cd->nn_processor_subdomains[i].bx.resize(msg_i / sizeof(::Box<dim,T>) );
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		// Return the receive pointer
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		return cd->nn_processor_subdomains[i].bx.getPointer();
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	}

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public:

	/*! \brief Cartesian decomposition copy constructor
	 *
     * \param v_cl Virtual cluster, used internally to handle or pipeline communication
	 *
	 */
	CartDecomposition(CartDecomposition<dim,T,device_l,Memory,Domain,data_s> && cd)
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	:sub_domain(cd.sub_domain),gr(cd.gr),cd(cd.cd),domain(cd.domain),v_cl(cd.v_cl)
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	{
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		// Reset the box to zero
		bbox.zero();

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		//! the set of all local sub-domain as vector
		sub_domains.swap(cd.sub_domains);

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		for (size_t i = 0 ; i < dim ; i++)
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		{
			//! Box Spacing
			this->spacing[i] = spacing[i];
		}
	}

	/*! \brief Cartesian decomposition constructor
	 *
     * \param v_cl Virtual cluster, used internally to handle or pipeline communication
	 *
	 */
	CartDecomposition(Vcluster & v_cl)
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	:v_cl(v_cl)
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	{
		// Reset the box to zero
		bbox.zero();
	}
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	//! Cartesian decomposition destructor
	~CartDecomposition()
	{}

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	// It store all the boxes of the near processors in a linear array
	struct p_box
	{
		//! Box that identify the intersection of the ghost of the near processor with the
		//! processor sub-domain
		::Box<dim,T> box;
		//! local processor id
		size_t lc_proc;
		//! processor id
		size_t proc;

		/*! \brief Check if two p_box are the same
		 *
		 * \param pb box to check
		 *
		 */
		bool operator==(const p_box & pb)
		{
			return pb.lc_proc == lc_proc;
		}
	};

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	openfpm::vector<size_t> ids;

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	/*! \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 & 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 & 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 & p, size_t b_id)
		{
			return p.lc_proc;
		}
	};

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	/*! /brief Given a point it return the set of boxes in which the point fall
	 *
	 * \param p Point to check
	 * \return An iterator with the id's of the internal boxes in which the point fall
	 *
	 */
	auto getInternalIDBoxes(Point<dim,T> & p) -> decltype(geo_cell.getIterator(geo_cell.getCell(p)))
	{
		return geo_cell.getIterator(geo_cell.getCell(p));
	}

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#define UNIQUE 1
#define MULTIPLE 2

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	/*! \brief Given a position it return if the position belong to any neighborhood processor ghost
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	 * (Internal ghost)
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	 *
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	 * \tparam id type of if to get box_id processor_id lc_processor_id
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	 * \param p Particle position
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	 * \param opt intersection boxes of the same processor can overlap, so in general the function
	 *        can produce more entry with the same processor, the UNIQUE option eliminate double entries
	 *        (UNIQUE) is for particle data (MULTIPLE) is for grid data [default MULTIPLE]
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	 *
	 * \param return the processor ids
	 *
	 */
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	template <typename id> inline const openfpm::vector<size_t> ghost_processorID(Point<dim,T> & p, const int opt = MULTIPLE)
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	{
		ids.clear();

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		// Check with geo-cell if a particle is inside one Cell containing boxes
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		auto cell_it = geo_cell.getIterator(geo_cell.getCell(p));
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		// For each element in the cell, check if the point is inside the box
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		// if it is, store the processor id
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		while (cell_it.isNext())
		{
			size_t bid = cell_it.get();

			if (vb_int.get(bid).box.isInside(p) == true)
			{
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				ids.add(id::id(vb_int.get(bid),bid));
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			}
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			++cell_it;
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		}

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		// Make the id unique
		if (opt == UNIQUE)
			ids.unique();

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		return ids;
	}

	/*! \brief Given a position it return if the position belong to any neighborhood processor ghost
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	 * (Internal ghost)
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	 *
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	 * \tparam id type of if to get box_id processor_id lc_processor_id
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	 * \param p Particle position
	 *
	 * \param return the processor ids
	 *
	 */
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	template<typename id, typename Mem> inline const openfpm::vector<size_t> ghost_processorID(const encapc<1,Point<dim,T>,Mem> & p, const int opt = MULTIPLE)
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	{
		ids.clear();

		// Check with geo-cell if a particle is inside one Cell containing boxes

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		auto cell_it = geo_cell.getIterator(geo_cell.getCell(p));
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		// For each element in the cell, check if the point is inside the box
		// if it is, store the processor id
		while (cell_it.isNext())
		{
			size_t bid = cell_it.get();

			if (vb_int.get(bid).box.isInside(p) == true)
			{
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				ids.add(id::id(vb_int.get(bid),bid));
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			}
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			++cell_it;
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		}

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		// Make the id unique
		if (opt == UNIQUE)
			ids.unique();

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		return ids;
	}

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	// External ghost boxes for this processor, indicated with G8_0 G9_0 ...
	openfpm::vector<p_box> vb_ext;
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	// Internal ghost boxes for this processor domain, indicated with B8_0 B9_0 ..... in the figure
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	// below as a linear vector
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	openfpm::vector<p_box> vb_int;
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	/*! It calculate the internal ghost boxes
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	 *
	 * Example: Processor 10 calculate
	 * B8_0 B9_0 B9_1 and B5_0
	 *
	 *
+----------------------------------------------------+
|                                                    |
|                 Processor 8                        |
|                 Sub-domain 0                       +-----------------------------------+
|                                                    |                                   |
|                                                    |                                   |
++--------------+---+---------------------------+----+        Processor 9                |
 |              |   |     B8_0                  |    |        Subdomain 0                |
 |              +------------------------------------+                                   |
 |              |   |                           |    |                                   |
 |              |   |  XXXXXXXXXXXXX XX         |B9_0|                                   |
 |              | B |  X Processor 10 X         |    |                                   |
 | Processor 5  | 5 |  X Sub-domain 0 X         |    |                                   |
 | Subdomain 0  | _ |  X              X         +----------------------------------------+
 |              | 0 |  XXXXXXXXXXXXXXXX         |    |                                   |
 |              |   |                           |    |                                   |
 |              |   |                           |    |        Processor 9                |
 |              |   |                           |B9_1|        Subdomain 1                |
 |              |   |                           |    |                                   |
 |              |   |                           |    |                                   |
 |              |   |                           |    |                                   |
 +--------------+---+---------------------------+----+                                   |
                                                     |                                   |
                                                     +-----------------------------------+

       and also
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       G8_0 G9_0 G9_1 G5_0 (External ghost boxes)
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+----------------------------------------------------+
|                                                    |
|                 Processor 8                        |
|                 Sub-domain 0                       +-----------------------------------+
|           +---------------------------------------------+                              |
|           |         G8_0                           |    |                              |
++--------------+------------------------------------+    |   Processor 9                |
 |          |   |                                    |    |   Subdomain 0                |
 |          |   |                                    |G9_0|                              |
 |          |   |                                    |    |                              |
 |          |   |      XXXXXXXXXXXXX XX              |    |                              |
 |          |   |      X Processor 10 X              |    |                              |
 | Processor|5  |      X Sub-domain 0 X              |    |                              |
 | Subdomain|0  |      X              X              +-----------------------------------+
 |          |   |      XXXXXXXXXXXXXXXX              |    |                              |
 |          | G |                                    |    |                              |
 |          | 5 |                                    |    |   Processor 9                |
 |          | | |                                    |    |   Subdomain 1                |
 |          | 0 |                                    |G9_1|                              |
 |          |   |                                    |    |                              |
 |          |   |                                    |    |                              |
 +--------------+------------------------------------+    |                              |
            |                                        |    |                              |
            +----------------------------------------+----+------------------------------+


	 *
	 *
	 *
	 * \param ghost margins for each dimensions (p1 negative part) (p2 positive part)
	 *
                ^ p2[1]
                |
                |
           +----+----+
           |         |
           |         |
p1[0]<-----+         +----> p2[0]
           |         |
           |         |
           +----+----+
                |
                v  p1[1]

	 *
	 *
	 */
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	void calculateGhostBoxes()
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	{
#ifdef DEBUG
		// the ghost margins are assumed to be smaller
		// than one sub-domain

		for (size_t i = 0 ; i < dim ; i++)
		{
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			if (ghost.template getLow(i) >= domain.template getHigh(i) / gr.size(i) || ghost.template getHigh(i)  >= domain.template getHigh(i) / gr.size(i))
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			{
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				std::cerr << "Error " << __FILE__ << ":" << __LINE__  << " : Ghost are bigger than one domain" << "\n";
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			}
		}
#endif

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		// create a buffer with the sub-domains of this processor, the informations ( the boxes )
		// of the sub-domains contiguous to the processor A are sent to the processor A and
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		// the information of the contiguous sub-domains in the near processors are received
		//
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		proc_adj_box.resize(getNNProcessors());
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		openfpm::vector< openfpm::vector< ::SpaceBox<dim,T>> > boxes(nn_processors.size());
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		for (size_t b = 0 ; b < box_nn_processor.size() ; b++)
		{
			for (size_t p = 0 ; p < box_nn_processor.get(b).size() ; p++)
			{
				size_t prc = box_nn_processor.get(b).get(p);

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				// id of the processor in the processor list
				// [value between 0 and the number of the near processors]
				size_t id = nn_processor_subdomains[prc].id;

				boxes.get(id).add(sub_domains.get(b));
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				proc_adj_box.get(id).add(b);
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			}
		}

		// Intersect all the local sub-domains with the sub-domains of the contiguous processors

		// Get the sub-domains of the near processors
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		v_cl.sendrecvMultipleMessagesNBX(nn_processors,boxes,CartDecomposition<dim,T,device_l,Memory,Domain,data_s>::message_alloc, this ,NEED_ALL_SIZE);
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		// create the internal structures that store ghost information
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		create_box_nn_processor_ext(ghost);
		create_box_nn_processor_int(ghost);
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		// ebox must come after ibox (in this case)
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		create_loc_ghost_ibox(ghost);
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		create_loc_ghost_ebox(ghost);
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	}

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	/*! \brief processorID return in which processor the particle should go
	 *
	 * \return processorID
	 *
	 */

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	template<typename Mem> size_t inline processorID(encapc<1, Point<dim,T>, Mem> p)
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	{
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		return fine_s.get(cd.getCell(p));
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	}

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	// Smallest subdivision on each direction
	::Box<dim,T> ss_box;

	/*! \brief Get the smallest subdivision of the domain on each direction
	 *
	 * \return a box p1 is set to zero
	 *
	 */
	const ::Box<dim,T> & getSmallestSubdivision()
	{
		return ss_box;
	}

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	/*! \brief processorID return in which processor the particle should go
	 *
	 * \return processorID
	 *
	 */

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	size_t inline processorID(const T (&p)[dim]) const
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	{
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		return fine_s.get(cd.getCell(p));
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	}

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	/*! \brief Set the parameter of the decomposition
	 *
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     * \param div_ storing into how many domain to decompose on each dimension
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     * \param domain_ domain to decompose
	 *
	 */
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	void setParameters(const size_t (& div_)[dim], Domain<dim,T> domain_, Ghost<dim,T> ghost = Ghost<dim,T>())
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	{
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		// set the ghost
		this->ghost = ghost;
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		// Set the decomposition parameters

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		gr.setDimensions(div_);
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		domain = domain_;
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		cd.setDimensions(domain,div_,0);
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		//! Create the decomposition

		CreateDecomposition(v_cl);
	}

	/*! \brief Get the number of local local hyper-cubes or sub-domains
	 *
	 * \return the number of sub-domains
	 *
	 */
	size_t getNLocalHyperCube()
	{
		return sub_domains.size();
	}

	/*! \brief Get the number of one set of hyper-cube enclosing one particular
	 *         subspace, the hyper-cube enclose your space, even if one box is enough
	 *         can be more that one to increase occupancy
	 *
     * In case of Cartesian decomposition it just return 1, each subspace
	 * has one hyper-cube, and occupancy 1
	 *
	 * \param id of the subspace
	 * \return the number of hyper-cube enclosing your space
	 *
	 */
	size_t getNHyperCube(size_t id)
	{
		return 1;
	}

	/*! \brief Get the hyper-cube margins id_c has to be 0
	 *
	 * Get the hyper-cube margins id_c has to be 0, each subspace
	 * has one hyper-cube
	 *
	 * \param id of the subspace
	 * \param id_c
	 * \return The specified hyper-cube space
	 *
	 */
	SpaceBox<dim,T> & getHyperCubeMargins(size_t id, size_t id_c)
	{
#ifdef DEBUG
		// Check if this subspace exist
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		if (id >= gr.size())
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		{
			std::cerr << "Error CartDecomposition: id > N_tot";
		}
		else if (id_c > 0)
		{
			// Each subspace is an hyper-cube so return error if id_c > 0
			std::cerr << "Error CartDecomposition: id_c > 0";
		}
#endif

		return sub_domains.get<Object>(id);
	}

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	/*! \brief Get the total number of sub-domain for the local processor
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	 *
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	 * \return The total number of sub-domains