gmm_domain_decomp.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2004-2020 Yves Renard
 
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/** @file gmm_domain_decomp.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date May 21, 2004.
    @brief Domain decomposition.
*/
#ifndef GMM_DOMAIN_DECOMP_H__
#define GMM_DOMAIN_DECOMP_H__
 
#include "gmm_kernel.h"
#include <map>
 
 
namespace gmm {
 
  /** This function separates into small boxes of size msize with a ratio
   * of overlap (in [0,1[) a set of points. The result is given into a
   * vector of sparse matrices vB.
   */
  template <typename Matrix, typename Point>
  void rudimentary_regular_decomposition(std::vector<Point> pts,
                                         double msize,
                                         double overlap,
                                         std::vector<Matrix> &vB) {
    typedef typename linalg_traits<Matrix>::value_type value_type;
    typedef abstract_null_type void_type;
    typedef std::map<size_type, void_type> map_type;
 
    size_type nbpts = pts.size();
    if (!nbpts || pts[0].size() == 0) { vB.resize(0); return; }
    int dim = int(pts[0].size());
 
    // computation of the global box and the number of sub-domains
    Point pmin = pts[0], pmax = pts[0];
    for (size_type i = 1; i < nbpts; ++i)
      for (int k = 0; k < dim; ++k) {
        pmin[k] = std::min(pmin[k], pts[i][k]);
        pmax[k] = std::max(pmax[k], pts[i][k]);
      }
    
    std::vector<size_type> nbsub(dim), mult(dim);
    std::vector<int> pts1(dim), pts2(dim);
    size_type nbtotsub = 1;
    for (int k = 0; k < dim; ++k) {
      nbsub[k] = size_type((pmax[k] - pmin[k]) / msize)+1;
      mult[k] = nbtotsub; nbtotsub *= nbsub[k];
    }
    
    std::vector<map_type> subs(nbtotsub);
    // points ventilation
    std::vector<size_type> ns(dim), na(dim), nu(dim);
    for (size_type i = 0; i < nbpts; ++i) {
      for (int k = 0; k < dim; ++k) {
          double a = (pts[i][k] - pmin[k]) / msize;
          ns[k] = size_type(a) - 1; na[k] = 0;
          pts1[k] = int(a + overlap); pts2[k] = int(ceil(a-1.0-overlap));
      }
      size_type sum = 0;
      do {
        bool ok = 1;
        for (int k = 0; k < dim; ++k)
          if ((ns[k] >= nbsub[k]) || (pts1[k] < int(ns[k]))
              || (pts2[k] > int(ns[k]))) { ok = false; break; }
        if (ok) {
          size_type ind = ns[0];
          for (int k=1; k < dim; ++k) ind += ns[k]*mult[k];
          subs[ind][i] = void_type();
        }
        for (int k = 0; k < dim; ++k) {
          if (na[k] < 2) { na[k]++; ns[k]++; ++sum; break; }
          na[k] = 0; ns[k] -= 2; sum -= 2;
        }
      } while (sum);
    }
    // delete too small domains.
    size_type nbmaxinsub = 0;
    for (size_type i = 0; i < nbtotsub; ++i)
      nbmaxinsub = std::max(nbmaxinsub, subs[i].size());
    
    std::fill(ns.begin(), ns.end(), size_type(0));
    for (size_type i = 0; i < nbtotsub; ++i) {
      if (subs[i].size() > 0 && subs[i].size() < nbmaxinsub / 10) {
        
        for (int k = 0; k < dim; ++k) nu[k] = ns[k];
        size_type nbmax = 0, imax = 0;
        
        for (int l = 0; l < dim; ++l) {
          nu[l]--;
          for (int m = 0; m < 2; ++m, nu[l]+=2) {
            bool ok = true;
            for (int k = 0; k < dim && ok; ++k) 
              if (nu[k] >= nbsub[k]) ok = false;
            if (ok) {
              size_type ind = ns[0];
              for (int k=1; k < dim; ++k) ind += ns[k]*mult[k];
              if (subs[ind].size() > nbmax)
                { nbmax = subs[ind].size(); imax = ind; }
            }
          }
          nu[l]--;
        }
        
        if (nbmax > subs[i].size()) {
          for (map_type::iterator it=subs[i].begin(); it!=subs[i].end(); ++it)
            subs[imax][it->first] = void_type();
          subs[i].clear();
        }
      }
      for (int k = 0; k < dim; ++k)
        { ns[k]++; if (ns[k] < nbsub[k]) break; ns[k] = 0; }
    }
    
    // delete empty domains.
    size_type effnb = 0;
    for (size_type i = 0; i < nbtotsub; ++i) {
      if (subs[i].size() > 0)
        { if (i != effnb) std::swap(subs[i], subs[effnb]); ++effnb; }
    }
 
    // build matrices
    subs.resize(effnb);
    vB.resize(effnb);
    for (size_type i = 0; i < effnb; ++i) {
      clear(vB[i]); resize(vB[i], nbpts, subs[i].size());
      size_type j = 0;
      for (map_type::iterator it=subs[i].begin(); it!=subs[i].end(); ++it, ++j)
        vB[i](it->first, j) = value_type(1);
    }
  }
  
 
}
 
 
#endif