Zoltan2_CoordinatePartitioningGraph.hpp

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// @HEADER
// *****************************************************************************
//   Zoltan2: A package of combinatorial algorithms for scientific computing
//
// Copyright 2012 NTESS and the Zoltan2 contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef _ZOLTAN2_COORDCOMMGRAPH_HPP_
#define _ZOLTAN2_COORDCOMMGRAPH_HPP_
 
 
#include <cmath>
#include <limits>
#include <iostream>
#include <vector>
#include <set>
#include <fstream>
#include "Teuchos_CommHelpers.hpp"
#include "Teuchos_Comm.hpp"
#include "Teuchos_ArrayViewDecl.hpp"
#include "Teuchos_RCPDecl.hpp"
#include "Zoltan2_InputTraits.hpp"
 
namespace Zoltan2{
 
 
#define Z2_ABS(x) ((x) >= 0 ? (x) : -(x))
 
class coordinateModelPartBox{
 
public:
        typedef double coord_t;
        typedef Zoltan2::default_part_t part_t;
 
        coordinateModelPartBox(part_t pid, int dim_):
            pID(pid),
            dim(dim_),
            lmins(0), lmaxs(0),
            maxScalar (std::numeric_limits<coord_t>::max()),
            epsilon(std::numeric_limits<coord_t>::epsilon()),
            minHashIndices(0),
            maxHashIndices(0),
            gridIndices(0), neighbors()
        {
            lmins = new coord_t [dim];
            lmaxs = new coord_t [dim];
 
            minHashIndices = new part_t [dim];
            maxHashIndices = new part_t [dim];
            gridIndices = new std::vector <part_t> ();
            for (int i = 0; i < dim; ++i){
                lmins[i] = -this->maxScalar;
                lmaxs[i] = this->maxScalar;
            }
        }
        template <typename scalar_t>
        coordinateModelPartBox(part_t pid, int dim_, scalar_t *lmi, scalar_t *lma):
            pID(pid),
            dim(dim_),
            lmins(0), lmaxs(0),
            maxScalar (std::numeric_limits<coord_t>::max()),
            epsilon(std::numeric_limits<coord_t>::epsilon()),
            minHashIndices(0),
            maxHashIndices(0),
            gridIndices(0), neighbors()
        {
            lmins = new coord_t [dim];
            lmaxs = new coord_t [dim];
            minHashIndices = new part_t [dim];
            maxHashIndices = new part_t [dim];
            gridIndices = new std::vector <part_t> ();
            for (int i = 0; i < dim; ++i){
                lmins[i] = static_cast<coord_t>(lmi[i]);
                lmaxs[i] = static_cast<coord_t>(lma[i]);
            }
        }
 
 
        coordinateModelPartBox(const coordinateModelPartBox &other):
            pID(other.getpId()),
            dim(other.getDim()),
            lmins(0), lmaxs(0),
            maxScalar (std::numeric_limits<coord_t>::max()),
            epsilon(std::numeric_limits<coord_t>::epsilon()),
            minHashIndices(0),
            maxHashIndices(0),
            gridIndices(0), neighbors()
        {
 
            lmins = new coord_t [dim];
            lmaxs = new coord_t [dim];
            minHashIndices = new part_t [dim];
            maxHashIndices = new part_t [dim];
            gridIndices = new std::vector <part_t> ();
            coord_t *othermins = other.getlmins();
            coord_t *othermaxs = other.getlmaxs();
            for (int i = 0; i < dim; ++i){
                lmins[i] = othermins[i];
                lmaxs[i] = othermaxs[i];
            }
        }
        ~coordinateModelPartBox(){
            delete []this->lmins;
            delete [] this->lmaxs;
            delete []this->minHashIndices;
            delete [] this->maxHashIndices;
            delete gridIndices;
        }
 
        void setpId(part_t pid){
            this->pID = pid;
        }
        part_t getpId() const{
            return this->pID;
        }
 
 
        int getDim()const{
            return this->dim;
        }
        coord_t * getlmins()const{
            return this->lmins;
        }
        coord_t * getlmaxs()const{
            return this->lmaxs;
        }
        void computeCentroid(coord_t *centroid)const {
            for (int i = 0; i < this->dim; i++)
                centroid[i] = 0.5 * (this->lmaxs[i] + this->lmins[i]);
        }
 
        std::vector <part_t> * getGridIndices () {
            return this->gridIndices;
        }
 
        std::set<part_t> *getNeighbors() {
            return &(this->neighbors);
        }
 
        template <typename scalar_t>
        bool pointInBox(int pointdim, scalar_t *point) const {
          if (pointdim != this->dim) 
            throw std::logic_error("dim of point must match dim of box");
          for (int i = 0; i < pointdim; i++) {
            if (static_cast<coord_t>(point[i]) < this->lmins[i]) return false;
            if (static_cast<coord_t>(point[i]) > this->lmaxs[i]) return false;
          }
          return true;
        }
 
        template <typename scalar_t>
        bool boxesOverlap(int cdim, scalar_t *lower, scalar_t *upper) const {
          if (cdim != this->dim) 
            throw std::logic_error("dim of given box must match dim of box");
 
          // Check for at least partial overlap
          bool found = true;
          for (int i = 0; i < cdim; i++) {
            if (!((static_cast<coord_t>(lower[i]) >= this->lmins[i] && 
                   static_cast<coord_t>(lower[i]) <= this->lmaxs[i]) 
                   // lower i-coordinate in the box
               || (static_cast<coord_t>(upper[i]) >= this->lmins[i] && 
                   static_cast<coord_t>(upper[i]) <= this->lmaxs[i]) 
                   // upper i-coordinate in the box
               || (static_cast<coord_t>(lower[i]) <  this->lmins[i] && 
                   static_cast<coord_t>(upper[i]) >  this->lmaxs[i]))) {
                   // i-coordinates straddle the box
              found = false;
              break;
            }
          }
          return found;
        }
 
        bool isNeighborWith(
            const coordinateModelPartBox &other) const{
 
            coord_t *omins = other.getlmins();
            coord_t *omaxs = other.getlmaxs();
 
            int equality = 0;
            for (int i = 0; i < dim; ++i){
 
                if (omins[i] - this->lmaxs[i] > epsilon  ||
                    this->lmins[i] - omaxs[i] > epsilon ) {
                    return false;
                }
                else if (Z2_ABS(omins[i] - this->lmaxs[i]) < epsilon ||
                         Z2_ABS(this->lmins[i] - omaxs[i]) < epsilon ){
                    if (++equality > 1){
                        return false;
                    }
                }
            }
            if (equality == 1) {
                return true;
            }
            else {
                std::cout << "something is wrong: equality:" 
                          << equality << std::endl;
                return false;
            }
        }
 
 
        void addNeighbor(part_t nIndex){
            neighbors.insert(nIndex);
        }
        bool isAlreadyNeighbor(part_t nIndex){
 
            if (neighbors.end() != neighbors.find(nIndex)){
                return true;
            }
            return false;
 
        }
 
 
        void setMinMaxHashIndices (
                coord_t *minMaxBoundaries,
                coord_t *sliceSizes,
                part_t numSlicePerDim
                ){
            for (int j = 0; j < dim; ++j){
                coord_t distance = (lmins[j] - minMaxBoundaries[j]);
                part_t minInd = 0;
                if (distance > epsilon && sliceSizes[j] > epsilon){
                    minInd = static_cast<part_t>(floor((lmins[j] - minMaxBoundaries[j])/ sliceSizes[j]));
                }
 
                if(minInd >= numSlicePerDim){
                    minInd = numSlicePerDim - 1;
                }
                part_t maxInd = 0;
                distance = (lmaxs[j] - minMaxBoundaries[j]);
                if (distance > epsilon && sliceSizes[j] > epsilon){
                    maxInd = static_cast<part_t>(ceil((lmaxs[j] - minMaxBoundaries[j])/ sliceSizes[j]));
                }
                if(maxInd >= numSlicePerDim){
                    maxInd = numSlicePerDim - 1;
                }
 
                //cout << "j:" << j << " lmins:" << lmins[j] << " lmaxs:" << lmaxs[j] << endl;
                //cout << "j:" << j << " min:" << minInd << " max:" << maxInd << endl;
                minHashIndices[j] = minInd;
                maxHashIndices[j] = maxInd;
            }
            std::vector <part_t> *in = new std::vector <part_t> ();
            in->push_back(0);
            std::vector <part_t> *out = new std::vector <part_t> ();
 
            for (int j = 0; j < dim; ++j){
 
                part_t minInd = minHashIndices[j];
                part_t maxInd = maxHashIndices[j];
 
 
                part_t pScale = part_t(pow (float(numSlicePerDim), int(dim - j -1)));
 
                part_t inSize = in->size();
 
                for (part_t k = minInd; k <= maxInd; ++k){
                    for (part_t i = 0; i < inSize; ++i){
                        out->push_back((*in)[i] + k * pScale);
                    }
                }
                in->clear();
                std::vector <part_t> *tmp = in;
                in= out;
                out= tmp;
            }
 
            std::vector <part_t> *tmp = in;
            in = gridIndices;
            gridIndices = tmp;
 
 
            delete in;
            delete out;
        }
 
        void print(){
            for(int i = 0; i < this->dim; ++i){
                std::cout << "\tbox:" << this->pID << " dim:" << i << " min:" << lmins[i] << " max:" << lmaxs[i] << std::endl;
            }
        }
 
        template <typename scalar_t>
        void updateMinMax (scalar_t newBoundary, int isMax, int dimInd){
            if (isMax){
                lmaxs[dimInd] = static_cast<coord_t>(newBoundary);
            }
            else {
                lmins[dimInd] = static_cast<coord_t>(newBoundary);
            }
        }
 
        void writeGnuPlot(std::ofstream &file,std::ofstream &mm){
            int numCorners = (int(1)<<dim);
            coord_t *corner1 = new coord_t [dim];
            coord_t *corner2 = new coord_t [dim];
 
            for (int i = 0; i < dim; ++i){
                /*
                if (-maxScalar == lmins[i]){
                    if (lmaxs[i] > 0){
                        lmins[i] = lmaxs[i] / 2;
                    }
                    else{
                        lmins[i] = lmaxs[i] * 2;
                    }
                }
                */
                //std::cout << lmins[i] << " ";
                mm << lmins[i] << " ";
            }
            //std::cout <<  std::endl;
            mm << std::endl;
            for (int i = 0; i < dim; ++i){
 
                /*
                if (maxScalar == lmaxs[i]){
                    if (lmins[i] < 0){
                        lmaxs[i] = lmins[i] / 2;
                    }
                    else{
                        lmaxs[i] = lmins[i] * 2;
                    }
                }
                */
 
                //std::cout << lmaxs[i] << " ";
                mm << lmaxs[i] << " ";
            }
            //std::cout <<  std::endl;
            mm << std::endl;
 
            for (int j = 0; j < numCorners; ++j){
                std::vector <int> neighborCorners;
                for (int i = 0; i < dim; ++i){
                    if(int(j & (int(1)<<i)) == 0){
                        corner1[i] = lmins[i];
                    }
                    else {
                        corner1[i] = lmaxs[i];
                    }
                    if (j % (int(1)<<(i + 1)) >= (int(1)<<i)){
                        int c1 = j - (int(1)<<i);
 
                        if (c1 > 0) {
                            neighborCorners.push_back(c1);
                        }
                    }
                    else {
 
                        int c1 = j + (int(1)<<i);
                        if (c1 < (int(1) << dim)) {
                            neighborCorners.push_back(c1);
                        }
                    }
                }
                //std::cout << "me:" << j << " nc:" << int (neighborCorners.size()) << std::endl;
                for (int m = 0; m < int (neighborCorners.size()); ++m){
 
                    int n = neighborCorners[m];
                    //std::cout << "me:" << j << " n:" << n << std::endl;
                    for (int i = 0; i < dim; ++i){
                        if(int(n & (int(1)<<i)) == 0){
                            corner2[i] = lmins[i];
                        }
                        else {
                            corner2[i] = lmaxs[i];
                        }
                    }
 
                    std::string arrowline = "set arrow from ";
                    for (int i = 0; i < dim - 1; ++i){
                        arrowline += 
                             Teuchos::toString<coord_t>(corner1[i]) + ",";
                    }
                    arrowline += 
                         Teuchos::toString<coord_t>(corner1[dim -1]) + " to ";
 
                    for (int i = 0; i < dim - 1; ++i){
                        arrowline += 
                             Teuchos::toString<coord_t>(corner2[i]) + ",";
                    }
                    arrowline += 
                         Teuchos::toString<coord_t>(corner2[dim -1]) + 
                                                     " nohead\n";
 
                    file << arrowline;
                }
            }
            delete []corner1;
            delete []corner2;
        }
 
private:
        part_t pID; //part Id
        int dim;    //dimension of the box
        coord_t *lmins;    //minimum boundaries of the box along all dimensions.
        coord_t *lmaxs;    //maximum boundaries of the box along all dimensions.
        coord_t maxScalar;
        coord_t epsilon;
 
        //to calculate the neighbors of the box and avoid the p^2 comparisons,
        //we use hashing. A box can be put into multiple hash buckets.
        //the following 2 variable holds the minimum and maximum of the
        //hash values along all dimensions.
        part_t *minHashIndices;
        part_t *maxHashIndices;
 
        //result hash bucket indices.
        std::vector <part_t> *gridIndices;
        //neighbors of the box.
        std::set <part_t> neighbors;
};
 
 
class GridHash{
private:
 
    typedef typename Zoltan2::coordinateModelPartBox::coord_t coord_t;
    typedef typename Zoltan2::coordinateModelPartBox::part_t part_t;
 
    const RCP<std::vector<Zoltan2::coordinateModelPartBox> > pBoxes;
 
    //minimum of the maximum box boundaries
    coord_t *minMaxBoundaries;
    //maximum of the minimum box boundaries
    coord_t *maxMinBoundaries;
    //the size of each slice along dimensions
    coord_t *sliceSizes;
    part_t nTasks;
    int dim;
    //the number of slices per dimension
    part_t numSlicePerDim;
    //the number of grids - buckets
    part_t numGrids;
    //hash vector
    std::vector <std::vector <part_t>  > grids;
    //result communication graph.
    ArrayRCP <part_t> comXAdj;
    ArrayRCP <part_t> comAdj;
public:
 
    GridHash(const RCP<std::vector<Zoltan2::coordinateModelPartBox> > &pBoxes_,
             part_t ntasks_, int dim_):
        pBoxes(pBoxes_),
        minMaxBoundaries(0),
        maxMinBoundaries(0), sliceSizes(0),
        nTasks(ntasks_),
        dim(dim_),
        numSlicePerDim(part_t(pow(double(ntasks_), 1.0 / dim))),
        numGrids(0),
        grids(),
        comXAdj(), comAdj()
    {
 
        minMaxBoundaries = new coord_t[dim];
        maxMinBoundaries = new coord_t[dim];
        sliceSizes = new coord_t[dim];
        //calculate the number of slices in each dimension.
        numSlicePerDim /= 2;
        if (numSlicePerDim == 0) numSlicePerDim = 1;
 
        numGrids = part_t(pow(float(numSlicePerDim), int(dim)));
 
        //allocate memory for buckets.
        std::vector <std::vector <part_t>  > grids_ (numGrids);
        this->grids = grids_;
        //get the boundaries of buckets.
        this->getMinMaxBoundaries();
        //insert boxes to buckets
        this->insertToHash();
        //calculate the neighbors for each bucket.
        part_t nCount = this->calculateNeighbors();
 
        //allocate memory for communication graph
        ArrayRCP <part_t> tmpComXadj(ntasks_+1);
        ArrayRCP <part_t> tmpComAdj(nCount);
        comXAdj = tmpComXadj;
        comAdj = tmpComAdj;
        //fill communication graph
        this->fillAdjArrays();
    }
 
 
    ~GridHash(){
        delete []minMaxBoundaries;
        delete []maxMinBoundaries;
        delete []sliceSizes;
    }
 
    void fillAdjArrays(){
 
        part_t adjIndex = 0;
 
        comXAdj[0] = 0;
        for(part_t i = 0; i < this->nTasks; ++i){
            std::set<part_t> *neigbors = (*pBoxes)[i].getNeighbors();
 
            part_t s = neigbors->size();
 
            comXAdj[i+1] = comXAdj[i] + s;
            typedef typename std::set<part_t> mySet;
            typedef typename mySet::iterator myIT;
            myIT it;
            for (it=neigbors->begin(); it!=neigbors->end(); ++it)
 
                comAdj[adjIndex++] = *it;
            //TODO not needed anymore.
            neigbors->clear();
        }
    }
 
 
 
    void getAdjArrays(
            ArrayRCP <part_t> &comXAdj_,
            ArrayRCP <part_t> &comAdj_){
        comXAdj_ = this->comXAdj;
        comAdj_ = this->comAdj;
    }
 
    part_t calculateNeighbors(){
        part_t nCount = 0;
        for(part_t i = 0; i < this->nTasks; ++i){
            std::vector <part_t> *gridIndices =(*pBoxes)[i].getGridIndices();
            part_t gridCount = gridIndices->size();
 
            for (part_t j = 0; j < gridCount; ++j){
                part_t grid = (*gridIndices)[j];
                part_t boxCount = grids[grid].size();
                for (part_t k = 0; k < boxCount; ++k){
                    part_t boxIndex = grids[grid][k];
                    if (boxIndex > i){
                        if((!(*pBoxes)[i].isAlreadyNeighbor(boxIndex))&& (*pBoxes)[i].isNeighborWith((*pBoxes)[boxIndex])){
                            //cout << "i:" << i << " n:" << boxIndex << " are neighbors."<< endl;
                            (*pBoxes)[i].addNeighbor(boxIndex);
                            (*pBoxes)[boxIndex].addNeighbor(i);
                            nCount += 2;
                        }
                    }
                }
            }
        }
 
        return nCount;
    }
 
    void insertToHash(){
 
        //cout << "ntasks:" << this->nTasks << endl;
        for(part_t i = 0; i < this->nTasks; ++i){
            (*pBoxes)[i].setMinMaxHashIndices(minMaxBoundaries, sliceSizes, numSlicePerDim);
 
            std::vector <part_t> *gridIndices =(*pBoxes)[i].getGridIndices();
 
            part_t gridCount = gridIndices->size();
            //cout << "i:" << i << " gridsize:" << gridCount << endl;
            for (part_t j = 0; j < gridCount; ++j){
                part_t grid = (*gridIndices)[j];
 
                //cout << "i:" << i << " is being inserted to:" << grid << endl;
                (grids)[grid].push_back(i);
            }
        }
 
 
/*
        for(part_t i = 0; i < grids.size(); ++i){
            cout << "grid:" << i << " gridsuze:" << (grids)[i].size() << " elements:";
            for(part_t j = 0; j < (grids)[i].size(); ++j){
                cout <<(grids)[i][j] << " ";
            }
            cout << endl;
 
        }
*/
    }
 
    void getMinMaxBoundaries(){
        coord_t *mins = (*pBoxes)[0].getlmins();
        coord_t *maxs = (*pBoxes)[0].getlmaxs();
 
        for (int j = 0; j < dim; ++j){
            minMaxBoundaries[j] = maxs[j];
            maxMinBoundaries[j] = mins[j];
        }
 
        for (part_t i = 1; i < nTasks; ++i){
 
            mins = (*pBoxes)[i].getlmins();
            maxs = (*pBoxes)[i].getlmaxs();
 
            for (int j = 0; j < dim; ++j){
 
                if (minMaxBoundaries[j] > maxs[j]){
                    minMaxBoundaries[j] = maxs[j];
                }
                if (maxMinBoundaries[j] < mins[j]){
                    maxMinBoundaries[j] = mins[j];
                }
            }
        }
 
 
        for (int j = 0; j < dim; ++j){
            sliceSizes[j] = (maxMinBoundaries[j] - minMaxBoundaries[j]) / numSlicePerDim;
            if (sliceSizes[j] < 0) sliceSizes[j] = 0;
                /*
            cout << "dim:" << j <<
                    " minMax:" <<  minMaxBoundaries[j] <<
                    " maxMin:" << maxMinBoundaries[j] <<
                    " sliceSizes:" << sliceSizes[j] << endl;
                    */
        }
    }
};
/*
template <typename coord_t,typename part_t>
class coordinatePartBox{
public:
        part_t pID;
        int dim;
        int numCorners;
        coord_t **corners;
        coord_t *lmins, *gmins;
        coord_t *lmaxs, *gmaxs;
        coord_t maxScalar;
        std::vector <part_t> hash_indices;
        coordinatePartBox(part_t pid, int dim_, coord_t *lMins, coord_t *gMins,
                                    coord_t *lMaxs, coord_t *gMaxs):
            pID(pid),
            dim(dim_),
            numCorners(int(pow(2, dim_))),
            corners(0),
            lmins(lMins), gmins(gMins), lmaxs(lMaxs), gmaxs(gMaxs),
            maxScalar (std::numeric_limits<coord_t>::max()){
            this->corners = new coord_t *[dim];
            for (int i = 0; i < dim; ++i){
                this->corners[i] = new coord_t[this->numCorners];
                lmins[i] = this->maxScalar;
                lmaxs[i] = -this->maxScalar;
            }
 
 
            for (int j = 0; j < this->numCorners; ++j){
                for (int i = 0; i < dim; ++i){
                    std::cout << "j:" << j << " i:" << i << " 2^i:" << pow(2,i) << " and:" << int(j & int(pow(2,i))) << std::endl;
                    if(int(j & int(pow(2,i))) == 0){
                        corners[i][j] = gmins[i];
                    }
                    else {
                        corners[i][j] = gmaxs[i];
                    }
 
                }
            }
        }
 
};
 
template <typename Adapter, typename part_t>
class CoordinateCommGraph{
private:
 
    typedef typename Adapter::lno_t lno_t;
    typedef typename Adapter::gno_t gno_t;
    typedef typename Adapter::coord_t coord_t;
 
    const Environment *env;
    const Teuchos::Comm<int> *comm;
    const Zoltan2::CoordinateModel<typename Adapter::base_adapter_t> *coords;
    const Zoltan2::PartitioningSolution<Adapter> *soln;
    std::vector<coordinatePartBox, part_t> cpb;
    int coordDim;
    part_t numParts;
 
 
public:
 
    CoordinateCommGraph(
            const Environment *env_,
            const Teuchos::Comm<int> *comm_,
            const Zoltan2::CoordinateModel<typename Adapter::base_adapter_t> *coords_,
            const Zoltan2::PartitioningSolution<Adapter> *soln_
    ):
        env(env_),
        comm(comm_),
        coords(coords_),
        soln(soln_),
        coordDim (coords_->getCoordinateDim()),
        numParts (this->soln->getActualGlobalNumberOfParts())
        {
        this->create_part_boxes();
        this->hash_part_boxes();
        this->find_neighbors();
    }
 
    void create_part_boxes(){
 
 
        size_t allocSize = numParts * coordDim;
        coord_t *lmins = new coord_t [allocSize];
        coord_t *gmins = new coord_t [allocSize];
        coord_t *lmaxs = new coord_t [allocSize];
        coord_t *gmaxs = new coord_t [allocSize];
 
        for(part_t i = 0; i < numParts; ++i){
            coordinatePartBox tmp(
                    i,
                    this->coordDim,
                    lmins + i * coordDim,
                    gmins + i * coordDim,
                    lmaxs + i * coordDim,
                    gmaxs + i * coordDim
            );
            cpb.push_back(tmp);
        }
 
        typedef StridedData<lno_t, coord_t> input_t;
        Teuchos::ArrayView<const gno_t> gnos;
        Teuchos::ArrayView<input_t>     xyz;
        Teuchos::ArrayView<input_t>     wgts;
        coords->getCoordinates(gnos, xyz, wgts);
 
        //local and global num coordinates.
        lno_t numLocalCoords = coords->getLocalNumCoordinates();
 
        coord_t **pqJagged_coordinates = new coord_t *[coordDim];
 
        for (int dim=0; dim < coordDim; dim++){
            Teuchos::ArrayRCP<const coord_t> ar;
            xyz[dim].getInputArray(ar);
            //pqJagged coordinate values assignment
            pqJagged_coordinates[dim] =  (coord_t *)ar.getRawPtr();
        }
 
        part_t *sol_part = soln->getPartList();
        for(lno_t i = 0; i < numLocalCoords; ++i){
            part_t p = sol_part[i];
            cpb[p].updateMinMax(pqJagged_coordinates, i);
        }
        delete []pqJagged_coordinates;
 
 
        reduceAll<int, gno_t>(*comm, Teuchos::REDUCE_MIN,
                dim * numParts, lmins, gmins
        );
        reduceAll<int, gno_t>(*comm, Teuchos::REDUCE_MAX,
                dim * numParts, lmaxs, gmaxs
        );
    }
 
    void hash_part_boxes (){
        part_t pSingleDim = pow(double(numParts), double(1.0 / coordDim));
        if (pSingleDim == 0) pSingleDim = 1;
        std::vector < std::vector <part_t> > hash
                (
                        part_t ( pow ( part_t (pSingleDim),
                                         part_t(coordDim)
                                       )
                                 )
                );
 
        //calculate the corners of the dataset.
        coord_t *allMins = new coord_t [coordDim];
        coord_t *allMaxs = new coord_t [coordDim];
        part_t *hash_scales= new coord_t [coordDim];
 
        for (int j = 0; j < coordDim; ++j){
            allMins[j] = cpb[0].gmins[j];
            allMaxs[j] = cpb[0].gmaxs[j];
            hash_scales[j] = part_t ( pow ( part_t (pSingleDim), part_t(coordDim - j - 1)));
        }
 
        for (part_t i = 1; i < numParts; ++i){
            for (int j = 0; j < coordDim; ++j){
                coord_t minC = cpb[i].gmins[i];
                coord_t maxC = cpb[i].gmaxs[i];
                if (minC < allMins[j]) allMins[j] = minC;
                if (maxC > allMaxs[j]) allMaxs[j] = maxC;
            }
        }
 
        //get size of each hash for each dimension
        coord_t *hash_slices_size = new coord_t [coordDim];
        for (int j = 0; j < coordDim; ++j){
            hash_slices_size[j] = (allMaxs[j] - allMins[j]) / pSingleDim;
 
        }
 
        delete []allMaxs;
        delete []allMins;
 
 
 
        std::vector <part_t> *hashIndices = new std::vector <part_t>();
        std::vector <part_t> *resultHashIndices = new std::vector <part_t>();
        std::vector <part_t> *tmp_swap;
        for (part_t i = 0; i < numParts; ++i){
            hashIndices->clear();
            resultHashIndices->clear();
 
            hashIndices->push_back(0);
 
            for (int j = 0; j < coordDim; ++j){
 
                coord_t minC = cpb[i].gmins[i];
                coord_t maxC = cpb[i].gmaxs[i];
                part_t minHashIndex = part_t ((minC - allMins[j]) / hash_slices_size[j]);
                part_t maxHashIndex  = part_t ((maxC - allMins[j]) / hash_slices_size[j]);
 
                part_t hashIndexSize = hashIndices->size();
 
                for (part_t k = minHashIndex; k <= maxHashIndex; ++k ){
 
                    for (part_t i = 0; i < hashIndexSize; ++i){
                        resultHashIndices->push_back(hashIndices[i] + k *  hash_scales[j]);
                    }
                }
                tmp_swap = hashIndices;
                hashIndices = resultHashIndices;
                resultHashIndices = tmp_swap;
            }
 
            part_t hashIndexSize = hashIndices->size();
            for (part_t j = 0; j < hashIndexSize; ++j){
                hash[(*hashIndices)[j]].push_back(i);
            }
            cpb[i].hash_indices = (*hashIndices);
        }
        delete hashIndices;
        delete resultHashIndices;
    }
 
    void find_neighbors(){
 
    }
 
 
};
 
*/
} // namespace Zoltan2
 
#endif