interpolation.hpp

/*
 * mp4_interpolation.hpp
 *
 *  Created on: May 4, 2017
 *      Author: i-bird
 */
 
#ifndef OPENFPM_NUMERICS_SRC_INTERPOLATION_INTERPOLATION_HPP_
#define OPENFPM_NUMERICS_SRC_INTERPOLATION_INTERPOLATION_HPP_
 
#include "NN/Mem_type/MemFast.hpp"
#include "NN/CellList/CellList.hpp"
#include "Grid/grid_dist_key.hpp"
#include "Vector/vector_dist_key.hpp"
 
#define INTERPOLATION_ERROR_OBJECT std::runtime_error("Runtime interpolation error");
 
constexpr int inte_m2p = 0;
constexpr int inte_p2m = 1;
 
template<unsigned int n_ele>
struct agg_arr
{
    size_t ele[n_ele];
};
 
template<typename T>
struct mul_inte
{
    inline static void value(T & result, const T & coeff, const T & src)
    {
        result += coeff * src;
    }
};
 
template<typename T, unsigned int N1>
struct mul_inte<T[N1]>
{
    inline static void value(T (& result)[N1], const T & coeff, const T (& src)[N1])
    {
        for (size_t i = 0 ; i < N1 ; i++)
            result[i] += coeff * src[i];
    }
};
 
template<typename T, unsigned int N1, unsigned int N2>
struct mul_inte<T[N1][N2]>
{
    inline static void value(T (& result)[N1][N2], const T & coeff, const T (& src)[N1][N2])
    {
        for (size_t i = 0 ; i < N1 ; i++)
            for (size_t j = 0 ; j < N2 ; j++)
                result[i][j] += coeff * src[i][j];
    }
};
 
template<unsigned int np, unsigned int prp_g, unsigned int prp_v,unsigned int m2p_or_p2m>
struct inte_template
{
    template<unsigned int np_a_int, typename grid, typename vector, typename iterator> inline static void value(grid & gd,
                                                                      vector & vd,
                                                                      const grid_dist_lin_dx & k_dist,
                                                                      iterator & key_p,
                                                                      typename vector::stype (& a_int)[np_a_int],
                                                                      const size_t & key)
    {
        mul_inte<typename std::remove_reference<decltype(gd.template get<prp_g>(k_dist))>::type>::value(gd.template get<prp_g>(k_dist),a_int[key],vd.template getProp<prp_v>(key_p));
    }
};
 
template<unsigned int np, unsigned int prp_g, unsigned int prp_v>
struct inte_template<np,prp_g,prp_v,inte_m2p>
{
    template<unsigned int np_a_int, typename grid, typename vector, typename iterator> inline static void value(grid & gd,
                                                                      vector & vd,
                                                                      const grid_dist_lin_dx & k_dist,
                                                                      iterator & key_p,
                                                                      typename vector::stype (& a_int)[np_a_int],
                                                                      const size_t & key)
    {
        mul_inte<typename std::remove_reference<decltype(gd.template get<prp_g>(k_dist))>::type>::value(vd.template getProp<prp_v>(key_p),a_int[key],gd.template get<prp_g>(k_dist));
    }
};
 
template<unsigned int dims, typename vector, unsigned int np>
struct calculate_aint
{
    static inline void value(size_t (& sz)[vector::dims],
                             typename vector::stype a_int[openfpm::math::pow(np,vector::dims)],
                             typename vector::stype (& a)[vector::dims][np])
    {
        grid_sm<vector::dims,void> gs(sz);
        grid_key_dx_iterator<vector::dims> kit(gs);
 
        size_t s = 0;
        while (kit.isNext())
        {
            auto key = kit.get();
 
            a_int[s] = 1;
 
            for (size_t i = 0 ; i < vector::dims ; i++)
                a_int[s] *= a[i][key.get(i)];
 
            s++;
            ++kit;
        }
    }
};
 
template<typename vector, unsigned int np>
struct calculate_aint<2,vector,np>
{
 
    static inline void value(size_t (& sz)[vector::dims],
                             typename vector::stype a_int[openfpm::math::pow(np,vector::dims)],
                             typename vector::stype (& a)[vector::dims][np])
    {
        size_t s = 0;
        for (size_t i = 0 ; i < np ; i++)
        {
            for (size_t j = 0 ; j < np ; j++)
            {
                a_int[s] = a[0][j]*a[1][i];
 
                s++;
            }
        }
    }
};
 
template<typename vector, unsigned int np>
struct calculate_aint<3,vector,np>
{
    static inline void value(size_t (& sz)[vector::dims],
                             typename vector::stype a_int[openfpm::math::pow(np,vector::dims)],
                             typename vector::stype (& a)[vector::dims][np])
    {
        size_t s = 0;
        for (size_t i = 0 ; i < np ; i++)
        {
            for (size_t j = 0 ; j < np ; j++)
            {
                for (size_t k = 0 ; k < np ; k++)
                {
                    a_int[s] = a[0][k]*a[1][j]*a[2][i];
 
                    s++;
                }
            }
        }
    }
};
 
template<typename vector, typename grid>
inline size_t getSub(Point<vector::dims,typename vector::stype> & p,
                     const CellList<vector::dims,typename vector::stype,Mem_fast<>,shift<vector::dims,typename vector::stype>> & geo_cell,
                     grid & gd)
{
    size_t cell = geo_cell.getCell(p);
 
    for (size_t i = 0 ; i < geo_cell.getNelements(cell) ; i++)
    {
        size_t ns = geo_cell.get(cell,i);
 
        if (gd.getDecomposition().getSubDomain(ns).isInsideNP(p))
            return ns;
    }
 
    // If we end up here it mean that the particle decomposition and the grid decomposition are at machine precision level
    // different. To recover we shift the particle of a machine precision correction inside the domain.
 
    typename vector::stype dx[vector::dims];
    typename vector::stype best_dx[vector::dims];
    typename vector::stype best_tot_dx;
    long int best_sub;
 
    Box<vector::dims,typename vector::stype> sub_dom = gd.getDecomposition().getSubDomain(0);
 
    for (size_t j = 0 ; j < vector::dims ; j++)
    {
            if (sub_dom.getLow(j) > p.get(j))
            {dx[j] = 2*(sub_dom.getLow(j) - p.get(j));}
            else if (sub_dom.getHigh(j) < p.get(j))
            {dx[j] = 2*(sub_dom.getHigh(j) - p.get(j));}
            else {dx[j] = 0;}
    }
 
    typename vector::stype tot_dx = 0.0;
 
    for (size_t j = 0 ; j < vector::dims ; j++)
    {tot_dx += fabs(dx[j]);}
 
    best_tot_dx = tot_dx;
    for (size_t j = 0 ; j < vector::dims ; j++)
    {best_dx[j] = dx[j];}
    best_sub = 0;
 
    for (size_t i = 1 ; i < gd.getDecomposition().getNSubDomain() ; i++)
    {
        Box<vector::dims,typename vector::stype> sub_dom = gd.getDecomposition().getSubDomain(i);
 
        for (size_t j = 0 ; j < vector::dims ; j++)
        {
            if (sub_dom.getLow(j) > p.get(j))
            {dx[j] = 2*(sub_dom.getLow(j) - p.get(j));}
            else if (sub_dom.getHigh(j) < p.get(j))
            {dx[j] = 2*(sub_dom.getHigh(j) - p.get(j));}
            else {dx[j] = 0;}
        }
 
        typename vector::stype tot_dx = 0.0;
 
        for (size_t j = 0 ; j < vector::dims ; j++)
        {tot_dx += fabs(dx[j]);}
 
        if (tot_dx < best_tot_dx)
        {
            best_tot_dx = tot_dx;
            for (size_t j = 0 ; j < vector::dims ; j++)
            {best_dx[j] = dx[j];}
            best_sub = i;
        }
    }
 
    // shift xp
 
    for (size_t j = 0 ; j < vector::dims ; j++)
    {p.get(j) += best_dx[j];}
 
    return best_sub;
}
 
template<typename vector,typename kernel>
struct inte_calc_impl
{
    typedef typename vector::stype arr_type;
 
    template<unsigned int prp_g, unsigned int prp_v, unsigned int m2p_or_p2m, unsigned int np_a_int, typename grid>
                                                                     static inline void inte_calc(const vect_dist_key_dx & key_p,
                                                                     vector & vd,
                                                                     const Box<vector::dims,typename vector::stype> & domain,
                                                                     int (& ip)[vector::dims][kernel::np],
                                                                     grid & gd,
                                                                     const typename vector::stype (& dx)[vector::dims],
                                                                     typename vector::stype (& xp)[vector::dims],
                                                                     typename vector::stype (& a_int)[np_a_int],
                                                                     typename vector::stype (& a)[vector::dims][kernel::np],
                                                                     typename vector::stype (& x)[vector::dims][kernel::np],
                                                                     size_t (& sz)[vector::dims],
                                                                     const CellList<vector::dims,typename vector::stype,Mem_fast<>,shift<vector::dims,typename vector::stype>> & geo_cell,
                                                                     openfpm::vector<agg_arr<openfpm::math::pow(kernel::np,vector::dims)>> & offsets)
    {
        Point<vector::dims,typename vector::stype> p = vd.getPos(key_p);
 
        // On which sub-domain we interpolate the particle
        size_t sub = getSub<vector>(p,geo_cell,gd);
 
        typename vector::stype x0[vector::dims];
 
        // calculate the position of the particle in the grid
        // coordinated
        for (size_t i = 0 ; i < vector::dims ; i++)
        {x0[i] = (p.get(i)-domain.getLow(i))*dx[i];}
 
        // convert into integer
        for (size_t i = 0 ; i < vector::dims ; i++)
        {ip[i][0] = (int)x0[i];}
 
        // convert the global grid position into local grid position
        grid_key_dx<vector::dims> base;
 
        for (size_t i = 0 ; i < vector::dims ; i++)
        {base.set_d(i,ip[i][0] - gd.getLocalGridsInfo().get(sub).origin.get(i) - (long int)kernel::np/2 + 1);}
 
        // convenient grid of points
 
        for (size_t j = 0 ; j < kernel::np-1 ; j++)
        {
            for (size_t i = 0 ; i < vector::dims ; i++)
            {ip[i][j+1] = (int)ip[i][j]+1;}
        }
 
        for (size_t i = 0 ; i < vector::dims ; i++)
            xp[i] = x0[i] - ip[i][0];
 
        for (long int j = 0 ; j < kernel::np ; j++)
        {
            for (size_t i = 0 ; i < vector::dims ; i++)
            {x[i][j] = - xp[i] + typename vector::stype((long int)j - (long int)kernel::np/2 + 1);}
        }
 
        for (size_t j = 0 ; j < kernel::np ; j++)
        {
            for (size_t i = 0 ; i < vector::dims ; i++)
            {a[i][j] = kernel::value(x[i][j],j);}
        }
 
        calculate_aint<vector::dims,vector,kernel::np>::value(sz,a_int,a);
 
        grid_dist_lin_dx k_dist_lin;
        k_dist_lin.setSub(sub);
 
        size_t k = 0;
        auto & gs_info = gd.get_loc_grid(sub).getGrid();
 
        size_t lin_base = gs_info.LinId(base);
 
        for (size_t i = 0 ; i < openfpm::math::pow(kernel::np,vector::dims) ; i++)
        {
            size_t lin = offsets.get(sub).ele[k] + lin_base;
            k_dist_lin.getKeyRef() = lin;
 
            inte_template<kernel::np,prp_g,prp_v,m2p_or_p2m>::value(gd,vd,k_dist_lin,key_p,a_int,k);
 
            k++;
        }
    }
};
 
template<typename vector,typename grid, typename kernel>
class interpolate
{
    CellList<vector::dims,typename vector::stype,Mem_fast<>,shift<vector::dims,typename vector::stype>> geo_cell;
 
    struct Box_vol
    {
        Box<vector::dims,size_t> bv;
 
        size_t vol;
 
        bool operator<(const Box_vol & bv)
        {
            return vol < bv.vol;
        }
    };
 
    vector & vd;
 
    grid & gd;
 
    typedef typename vector::stype arr_type;
 
    openfpm::vector<agg_arr<openfpm::math::pow(kernel::np,vector::dims)>> offsets;
 
    size_t sz[vector::dims];
 
    typename vector::stype dx[vector::dims];
 
    Box<vector::dims,typename vector::stype> domain;
 
    void calculate_the_offsets(openfpm::vector<agg_arr<openfpm::math::pow(kernel::np,vector::dims)>> & offsets, size_t (& sz)[vector::dims])
    {
        offsets.resize(gd.getN_loc_grid());
 
        for (size_t i = 0 ; i < offsets.size() ; i++)
        {
            auto & loc_grid = gd.get_loc_grid(i);
            const grid_sm<vector::dims,void> & gs = loc_grid.getGrid();
 
            grid_sm<vector::dims,void> gs2(sz);
            grid_key_dx_iterator<vector::dims> kit2(gs2);
 
            size_t k = 0;
 
            while (kit2.isNext())
            {
                auto key = kit2.get();
 
                long int lin = gs.LinId(key);
 
                offsets.get(i).ele[k] = lin;
 
                ++k;
                ++kit2;
            }
        }
    }
 
public:
 
    interpolate(vector & vd, grid & gd)
    :vd(vd),gd(gd)
    {
        // get the processor bounding box in grid units
        Box<vector::dims,typename vector::stype> bb = gd.getDecomposition().getProcessorBounds();
        Box<vector::dims,typename vector::stype> bunit = gd.getDecomposition().getCellDecomposer().getCellBox();
 
        size_t div[vector::dims];
 
        for (size_t i = 0 ; i < vector::dims ; i++)
            div[i] = (bb.getHigh(i) - bb.getLow(i)) / bunit.getHigh(i);
 
        geo_cell.Initialize(bb,div);
 
        // Now draw the domain into the cell list
 
        auto & dec = gd.getDecomposition();
 
        for (size_t i = 0 ; i < dec.getNSubDomain() ; i++)
        {
            const Box<vector::dims,typename vector::stype> & bx = dec.getSubDomain(i);
 
            // get the cells this box span
            const grid_key_dx<vector::dims> p1 = geo_cell.getCellGrid(bx.getP1());
            const grid_key_dx<vector::dims> p2 = geo_cell.getCellGrid(bx.getP2());
 
            // Get the grid and the sub-iterator
            auto & gi = geo_cell.getGrid();
            grid_key_dx_iterator_sub<vector::dims> 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),i);
                ++g_sub;
            }
        }
 
        for (size_t i = 0 ; i < vector::dims ; i++)
        {sz[i] = kernel::np;}
 
        calculate_the_offsets(offsets,sz);
 
        // calculate spacing
        for (size_t i = 0 ; i < vector::dims ; i++)
        {dx[i] = 1.0/gd.spacing(i);}
 
        // simulation domain
        domain = vd.getDecomposition().getDomain();
    };
 
    template<unsigned int prp_v, unsigned int prp_g> void p2m(vector & vd, grid & gd)
    {
#ifdef SE_CLASS1
 
        if (!vd.getDecomposition().is_equal_ng(gd.getDecomposition()) )
        {
            std::cerr << __FILE__ << ":" << __LINE__ << " Error: the distribution of the vector of particles" <<
                    " and the grid is different. In order to interpolate the two data structure must have the" <<
                    " same decomposition" << std::endl;
 
            ACTION_ON_ERROR(INTERPOLATION_ERROR_OBJECT)
        }
 
#endif
 
        // point position
        typename vector::stype xp[vector::dims];
 
        int ip[vector::dims][kernel::np];
        typename vector::stype x[vector::dims][kernel::np];
        typename vector::stype a[vector::dims][kernel::np];
 
        typename vector::stype a_int[openfpm::math::pow(kernel::np,vector::dims)];
 
        auto it = vd.getDomainIterator();
 
        while (it.isNext() == true)
        {
            auto key_p = it.get();
 
            inte_calc_impl<vector,kernel>::template inte_calc<prp_g,prp_v,inte_p2m,openfpm::math::pow(kernel::np,vector::dims)>(key_p,vd,domain,ip,gd,dx,xp,a_int,a,x,sz,geo_cell,offsets);
 
            ++it;
        }
    }
 
    template<unsigned int prp_g, unsigned int prp_v> void m2p(grid & gd, vector & vd)
    {
#ifdef SE_CLASS1
 
        if (!vd.getDecomposition().is_equal_ng(gd.getDecomposition()) )
        {
            std::cerr << __FILE__ << ":" << __LINE__ << " Error: the distribution of the vector of particles" <<
                    " and the grid is different. In order to interpolate the two data structure must have the" <<
                    " same decomposition" << std::endl;
 
            ACTION_ON_ERROR(INTERPOLATION_ERROR_OBJECT)
        }
 
#endif
 
        // point position
        typename vector::stype xp[vector::dims];
 
        int ip[vector::dims][kernel::np];
        typename vector::stype x[vector::dims][kernel::np];
        typename vector::stype a[vector::dims][kernel::np];
 
        //      grid_cpu<vector::dims,aggregate<typename vector::stype>> a_int(sz);
        //      a_int.setMemory();
        typename vector::stype a_int[openfpm::math::pow(kernel::np,vector::dims)];
 
        auto it = vd.getDomainIterator();
 
        while (it.isNext() == true)
        {
            auto key_p = it.get();
 
            inte_calc_impl<vector,kernel>::template inte_calc<prp_g,prp_v,inte_m2p,openfpm::math::pow(kernel::np,vector::dims)>(key_p,vd,domain,ip,gd,dx,xp,a_int,a,x,sz,geo_cell,offsets);
 
            ++it;
        }
    }
 
 
    template<unsigned int prp_v, unsigned int prp_g> inline void p2m(vector & vd, grid & gd,const vect_dist_key_dx & p)
    {
#ifdef SE_CLASS1
 
        if (!vd.getDecomposition().is_equal_ng(gd.getDecomposition()) )
        {
            std::cerr << __FILE__ << ":" << __LINE__ << " Error: the distribution of the vector of particles" <<
                    " and the grid is different. In order to interpolate the two data structure must have the" <<
                    " same decomposition" << std::endl;
 
            ACTION_ON_ERROR(INTERPOLATION_ERROR_OBJECT)
        }
 
#endif
 
        // point position
        typename vector::stype xp[vector::dims];
 
        int ip[vector::dims][kernel::np];
        typename vector::stype x[vector::dims][kernel::np];
        typename vector::stype a[vector::dims][kernel::np];
 
        typename vector::stype a_int[openfpm::math::pow(kernel::np,vector::dims)];
 
        /* coverty[uninit_use_in_call] */
        inte_calc_impl<vector,kernel>::template inte_calc<prp_g,prp_v,inte_p2m,openfpm::math::pow(kernel::np,vector::dims)>(p,vd,domain,ip,gd,dx,xp,a_int,a,x,sz,geo_cell,offsets);
    }
 
    template<unsigned int prp_g, unsigned int prp_v> inline void m2p(grid & gd, vector & vd, const vect_dist_key_dx & p)
    {
#ifdef SE_CLASS1
 
        if (!vd.getDecomposition().is_equal_ng(gd.getDecomposition()) )
        {
            std::cerr << __FILE__ << ":" << __LINE__ << " Error: the distribution of the vector of particles" <<
                    " and the grid is different. In order to interpolate the two data structure must have the" <<
                    " same decomposition" << std::endl;
 
            ACTION_ON_ERROR(INTERPOLATION_ERROR_OBJECT)
        }
 
#endif
 
        // point position
        typename vector::stype xp[vector::dims];
 
        int ip[vector::dims][kernel::np];
        typename vector::stype x[vector::dims][kernel::np];
        typename vector::stype a[vector::dims][kernel::np];
 
        //      grid_cpu<vector::dims,aggregate<typename vector::stype>> a_int(sz);
        //      a_int.setMemory();
        typename vector::stype a_int[openfpm::math::pow(kernel::np,vector::dims)];
 
        inte_calc_impl<vector,kernel>::template inte_calc<prp_g,prp_v,inte_m2p,openfpm::math::pow(kernel::np,vector::dims)>(p,vd,domain,ip,gd,dx,xp,a_int,a,x,sz,geo_cell,offsets);
    }
 
    int getSub(Point<vector::dims,typename vector::stype> & p)
    {
        return ::getSub<vector>(p,geo_cell,gd);
    }
 
};
 
#endif /* OPENFPM_NUMERICS_SRC_INTERPOLATION_INTERPOLATION_HPP_ */