NearestNeighbor.hpp

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#if !defined(GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP)
#define GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP 1
 
#include <algorithm>            // for nth_element, max_element, etc.
#include <vector>
#include <queue>                // for priority_queue
#include <utility>              // for swap + pair
#include <cstring>
#include <limits>
#include <cmath>
#include <iostream>
#include <sstream>
// Only for GEOGRAPHICLIB_STATIC_ASSERT and GeographicLib::GeographicErr
#include <GeographicLib/Constants.hpp>
 
#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
  GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
#include <boost/serialization/nvp.hpp>
#include <boost/serialization/split_member.hpp>
#include <boost/serialization/array.hpp>
#include <boost/serialization/vector.hpp>
#endif
 
#if defined(_MSC_VER)
// Squelch warnings about constant conditional expressions
#  pragma warning (push)
#  pragma warning (disable: 4127)
#endif
 
namespace GeographicLib {
 
  template <typename dist_t, typename pos_t, class distfun_t>
  class NearestNeighbor {
    // For tracking changes to the I/O format
    static const int version = 1;
    // This is what we get "free"; but if sizeof(dist_t) = 1 (unlikely), allow
    // 4 slots (and this accommodates the default value bucket = 4).
    static const int maxbucket =
      (2 + ((4 * sizeof(dist_t)) / sizeof(int) >= 2 ?
            (4 * sizeof(dist_t)) / sizeof(int) : 2));
  public:
 
    NearestNeighbor() : _numpoints(0), _bucket(0), _cost(0) {}
 
    NearestNeighbor(const std::vector<pos_t>& pts, const distfun_t& dist,
                    int bucket = 4) {
      Initialize(pts, dist, bucket);
    }
 
    void Initialize(const std::vector<pos_t>& pts, const distfun_t& dist,
                    int bucket = 4) {
      GEOGRAPHICLIB_STATIC_ASSERT(std::numeric_limits<dist_t>::is_signed,
                                  "dist_t must be a signed type");
      if (!( 0 <= bucket && bucket <= maxbucket ))
        throw GeographicLib::GeographicErr
          ("bucket must lie in [0, 2 + 4*sizeof(dist_t)/sizeof(int)]");
      if (pts.size() > size_t(std::numeric_limits<int>::max()))
        throw GeographicLib::GeographicErr("pts array too big");
      // the pair contains distance+id
      std::vector<item> ids(pts.size());
      for (int k = int(ids.size()); k--;)
        ids[k] = std::make_pair(dist_t(0), k);
      int cost = 0;
      std::vector<Node> tree;
      init(pts, dist, bucket, tree, ids, cost,
           0, int(ids.size()), int(ids.size()/2));
      _tree.swap(tree);
      _numpoints = int(pts.size());
      _bucket = bucket;
      _mc = _sc = 0;
      _cost = cost; _c1 = _k = _cmax = 0;
      _cmin = std::numeric_limits<int>::max();
    }
 
    dist_t Search(const std::vector<pos_t>& pts, const distfun_t& dist,
                  const pos_t& query,
                  std::vector<int>& ind,
                  int k = 1,
                  dist_t maxdist = std::numeric_limits<dist_t>::max(),
                  dist_t mindist = -1,
                  bool exhaustive = true,
                  dist_t tol = 0) const {
      if (_numpoints != int(pts.size()))
          throw GeographicLib::GeographicErr("pts array has wrong size");
      std::priority_queue<item> results;
      if (_numpoints > 0 && k > 0 && maxdist > mindist) {
        // distance to the kth closest point so far
        dist_t tau = maxdist;
        // first is negative of how far query is outside boundary of node
        // +1 if on boundary or inside
        // second is node index
        std::priority_queue<item> todo;
        todo.push(std::make_pair(dist_t(1), int(_tree.size()) - 1));
        int c = 0;
        while (!todo.empty()) {
          int n = todo.top().second;
          dist_t d = -todo.top().first;
          todo.pop();
          dist_t tau1 = tau - tol;
          // compare tau and d again since tau may have become smaller.
          if (!( n >= 0 && tau1 >= d )) continue;
          const Node& current = _tree[n];
          dist_t dst = 0;   // to suppress warning about uninitialized variable
          bool exitflag = false, leaf = current.index < 0;
          for (int i = 0; i < (leaf ? _bucket : 1); ++i) {
            int index = leaf ? current.leaves[i] : current.index;
            if (index < 0) break;
            dst = dist(pts[index], query);
            ++c;
 
            if (dst > mindist && dst <= tau) {
              if (int(results.size()) == k) results.pop();
              results.push(std::make_pair(dst, index));
              if (int(results.size()) == k) {
                if (exhaustive)
                  tau = results.top().first;
                else {
                  exitflag = true;
                  break;
                }
                if (tau <= tol) {
                  exitflag = true;
                  break;
                }
              }
            }
          }
          if (exitflag) break;
 
          if (current.index < 0) continue;
          tau1 = tau - tol;
          for (int l = 0; l < 2; ++l) {
            if (current.data.child[l] >= 0 &&
                dst + current.data.upper[l] >= mindist) {
              if (dst < current.data.lower[l]) {
                d = current.data.lower[l] - dst;
                if (tau1 >= d)
                  todo.push(std::make_pair(-d, current.data.child[l]));
              } else if (dst > current.data.upper[l]) {
                d = dst - current.data.upper[l];
                if (tau1 >= d)
                  todo.push(std::make_pair(-d, current.data.child[l]));
              } else
                todo.push(std::make_pair(dist_t(1), current.data.child[l]));
            }
          }
        }
        ++_k;
        _c1 += c;
        double omc = _mc;
        _mc += (c - omc) / _k;
        _sc += (c - omc) * (c - _mc);
        if (c > _cmax) _cmax = c;
        if (c < _cmin) _cmin = c;
      }
 
      dist_t d = -1;
      ind.resize(results.size());
 
      for (int i = int(ind.size()); i--;) {
        ind[i] = int(results.top().second);
        if (i == 0) d = results.top().first;
        results.pop();
      }
      return d;
 
    }
 
    int NumPoints() const { return _numpoints; }
 
    void Save(std::ostream& os, bool bin = true) const {
      int realspec = std::numeric_limits<dist_t>::digits *
        (std::numeric_limits<dist_t>::is_integer ? -1 : 1);
      if (bin) {
        char id[] = "NearestNeighbor_";
        os.write(id, 16);
        int buf[6];
        buf[0] = version;
        buf[1] = realspec;
        buf[2] = _bucket;
        buf[3] = _numpoints;
        buf[4] = int(_tree.size());
        buf[5] = _cost;
        os.write(reinterpret_cast<const char *>(buf), 6 * sizeof(int));
        for (int i = 0; i < int(_tree.size()); ++i) {
          const Node& node = _tree[i];
          os.write(reinterpret_cast<const char *>(&node.index), sizeof(int));
          if (node.index >= 0) {
            os.write(reinterpret_cast<const char *>(node.data.lower),
                     2 * sizeof(dist_t));
            os.write(reinterpret_cast<const char *>(node.data.upper),
                     2 * sizeof(dist_t));
            os.write(reinterpret_cast<const char *>(node.data.child),
                     2 * sizeof(int));
          } else {
            os.write(reinterpret_cast<const char *>(node.leaves),
                     _bucket * sizeof(int));
          }
        }
      } else {
        std::stringstream ostring;
          // Ensure enough precision for type dist_t.  With C++11, max_digits10
          // can be used instead.
        if (!std::numeric_limits<dist_t>::is_integer) {
          static const int prec
            = int(std::ceil(std::numeric_limits<dist_t>::digits *
                            std::log10(2.0) + 1));
          ostring.precision(prec);
        }
        ostring << version << " " << realspec << " " << _bucket << " "
                << _numpoints << " " << _tree.size() << " " << _cost;
        for (int i = 0; i < int(_tree.size()); ++i) {
          const Node& node = _tree[i];
          ostring << "\n" << node.index;
          if (node.index >= 0) {
            for (int l = 0; l < 2; ++l)
              ostring << " " << node.data.lower[l] << " " << node.data.upper[l]
                      << " " << node.data.child[l];
          } else {
            for (int l = 0; l < _bucket; ++l)
              ostring << " " << node.leaves[l];
          }
        }
        os << ostring.str();
      }
    }
 
    void Load(std::istream& is, bool bin = true) {
      int version1, realspec, bucket, numpoints, treesize, cost;
      if (bin) {
        char id[17];
        is.read(id, 16);
        id[16] = '\0';
        if (!(std::strcmp(id, "NearestNeighbor_") == 0))
          throw GeographicLib::GeographicErr("Bad ID");
        is.read(reinterpret_cast<char *>(&version1), sizeof(int));
        is.read(reinterpret_cast<char *>(&realspec), sizeof(int));
        is.read(reinterpret_cast<char *>(&bucket), sizeof(int));
        is.read(reinterpret_cast<char *>(&numpoints), sizeof(int));
        is.read(reinterpret_cast<char *>(&treesize), sizeof(int));
        is.read(reinterpret_cast<char *>(&cost), sizeof(int));
      } else {
        if (!( is >> version1 >> realspec >> bucket >> numpoints >> treesize
               >> cost ))
          throw GeographicLib::GeographicErr("Bad header");
      }
      if (!( version1 == version ))
        throw GeographicLib::GeographicErr("Incompatible version");
      if (!( realspec == std::numeric_limits<dist_t>::digits *
             (std::numeric_limits<dist_t>::is_integer ? -1 : 1) ))
        throw GeographicLib::GeographicErr("Different dist_t types");
      if (!( 0 <= bucket && bucket <= maxbucket ))
        throw GeographicLib::GeographicErr("Bad bucket size");
      if (!( 0 <= treesize && treesize <= numpoints ))
        throw
          GeographicLib::GeographicErr("Bad number of points or tree size");
      if (!( 0 <= cost ))
        throw GeographicLib::GeographicErr("Bad value for cost");
      std::vector<Node> tree;
      tree.reserve(treesize);
      for (int i = 0; i < treesize; ++i) {
        Node node;
        if (bin) {
          is.read(reinterpret_cast<char *>(&node.index), sizeof(int));
          if (node.index >= 0) {
            is.read(reinterpret_cast<char *>(node.data.lower),
                    2 * sizeof(dist_t));
            is.read(reinterpret_cast<char *>(node.data.upper),
                    2 * sizeof(dist_t));
            is.read(reinterpret_cast<char *>(node.data.child),
                    2 * sizeof(int));
          } else {
            is.read(reinterpret_cast<char *>(node.leaves),
                    bucket * sizeof(int));
            for (int l = bucket; l < maxbucket; ++l)
              node.leaves[l] = 0;
          }
        } else {
          if (!( is >> node.index ))
            throw GeographicLib::GeographicErr("Bad index");
          if (node.index >= 0) {
            for (int l = 0; l < 2; ++l) {
              if (!( is >> node.data.lower[l] >> node.data.upper[l]
                     >> node.data.child[l] ))
                throw GeographicLib::GeographicErr("Bad node data");
            }
          } else {
            // Must be at least one valid leaf followed by a sequence end
            // markers (-1).
            for (int l = 0; l < bucket; ++l) {
              if (!( is >> node.leaves[l] ))
                throw GeographicLib::GeographicErr("Bad leaf data");
            }
            for (int l = bucket; l < maxbucket; ++l)
              node.leaves[l] = 0;
          }
        }
        node.Check(numpoints, treesize, bucket);
        tree.push_back(node);
      }
      _tree.swap(tree);
      _numpoints = numpoints;
      _bucket = bucket;
      _mc = _sc = 0;
      _cost = cost; _c1 = _k = _cmax = 0;
      _cmin = std::numeric_limits<int>::max();
    }
 
    friend std::ostream& operator<<(std::ostream& os, const NearestNeighbor& t)
    { t.Save(os, false); return os; }
 
    friend std::istream& operator>>(std::istream& is, NearestNeighbor& t)
    { t.Load(is, false); return is; }
 
    void swap(NearestNeighbor& t) {
      std::swap(_numpoints, t._numpoints);
      std::swap(_bucket, t._bucket);
      std::swap(_cost, t._cost);
      _tree.swap(t._tree);
      std::swap(_mc, t._mc);
      std::swap(_sc, t._sc);
      std::swap(_c1, t._c1);
      std::swap(_k, t._k);
      std::swap(_cmin, t._cmin);
      std::swap(_cmax, t._cmax);
    }
 
    void Statistics(int& setupcost, int& numsearches, int& searchcost,
                    int& mincost, int& maxcost,
                    double& mean, double& sd) const {
      setupcost = _cost; numsearches = _k; searchcost = _c1;
      mincost = _cmin; maxcost = _cmax;
      mean = _mc; sd = std::sqrt(_sc / (_k - 1));
    }
 
    void ResetStatistics() const {
      _mc = _sc = 0;
      _c1 = _k = _cmax = 0;
      _cmin = std::numeric_limits<int>::max();
    }
 
  private:
    // Package up a dist_t and an int.  We will want to sort on the dist_t so
    // put it first.
    typedef std::pair<dist_t, int> item;
    // \cond SKIP
    class Node {
    public:
      struct bounds {
        dist_t lower[2], upper[2]; // bounds on inner/outer distances
        int child[2];
      };
      union {
        bounds data;
        int leaves[maxbucket];
      };
      int index;
 
      Node()
        : index(-1)
      {
        for (int i = 0; i < 2; ++i) {
          data.lower[i] = data.upper[i] = 0;
          data.child[i] = -1;
        }
      }
 
      // Sanity check on a Node
      void Check(int numpoints, int treesize, int bucket) const {
        if (!( -1 <= index && index < numpoints ))
          throw GeographicLib::GeographicErr("Bad index");
        if (index >= 0) {
          if (!( -1 <= data.child[0] && data.child[0] < treesize &&
                 -1 <= data.child[1] && data.child[1] < treesize ))
            throw GeographicLib::GeographicErr("Bad child pointers");
          if (!( 0 <= data.lower[0] && data.lower[0] <= data.upper[0] &&
                 data.upper[0] <= data.lower[1] &&
                 data.lower[1] <= data.upper[1] ))
            throw GeographicLib::GeographicErr("Bad bounds");
        } else {
          // Must be at least one valid leaf followed by a sequence end markers
          // (-1).
          bool start = true;
          for (int l = 0; l < bucket; ++l) {
            if (!( (start ?
                    ((l == 0 ? 0 : -1) <= leaves[l] && leaves[l] < numpoints) :
                    leaves[l] == -1) ))
              throw GeographicLib::GeographicErr("Bad leaf data");
            start = leaves[l] >= 0;
          }
          for (int l = bucket; l < maxbucket; ++l) {
            if (leaves[l] != 0)
              throw GeographicLib::GeographicErr("Bad leaf data");
          }
        }
      }
 
#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
  GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
      friend class boost::serialization::access;
      template<class Archive>
      void save(Archive& ar, const unsigned int) const {
        ar & boost::serialization::make_nvp("index", index);
        if (index < 0)
          ar & boost::serialization::make_nvp("leaves", leaves);
        else
          ar & boost::serialization::make_nvp("lower", data.lower)
            & boost::serialization::make_nvp("upper", data.upper)
            & boost::serialization::make_nvp("child", data.child);
      }
      template<class Archive>
      void load(Archive& ar, const unsigned int) {
        ar & boost::serialization::make_nvp("index", index);
        if (index < 0)
          ar & boost::serialization::make_nvp("leaves", leaves);
        else
          ar & boost::serialization::make_nvp("lower", data.lower)
            & boost::serialization::make_nvp("upper", data.upper)
            & boost::serialization::make_nvp("child", data.child);
      }
      template<class Archive>
      void serialize(Archive& ar, const unsigned int file_version)
      { boost::serialization::split_member(ar, *this, file_version); }
#endif
    };
    // \endcond
#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
  GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
    friend class boost::serialization::access;
    template<class Archive> void save(Archive& ar, const unsigned) const {
      int realspec = std::numeric_limits<dist_t>::digits *
        (std::numeric_limits<dist_t>::is_integer ? -1 : 1);
      // Need to use version1, otherwise load error in debug mode on Linux:
      // undefined reference to GeographicLib::NearestNeighbor<...>::version.
      int version1 = version;
      ar & boost::serialization::make_nvp("version", version1)
        & boost::serialization::make_nvp("realspec", realspec)
        & boost::serialization::make_nvp("bucket", _bucket)
        & boost::serialization::make_nvp("numpoints", _numpoints)
        & boost::serialization::make_nvp("cost", _cost)
        & boost::serialization::make_nvp("tree", _tree);
    }
    template<class Archive> void load(Archive& ar, const unsigned) {
      int version1, realspec, bucket, numpoints, cost;
      ar & boost::serialization::make_nvp("version", version1);
      if (version1 != version)
        throw GeographicLib::GeographicErr("Incompatible version");
      std::vector<Node> tree;
      ar & boost::serialization::make_nvp("realspec", realspec);
      if (!( realspec == std::numeric_limits<dist_t>::digits *
             (std::numeric_limits<dist_t>::is_integer ? -1 : 1) ))
        throw GeographicLib::GeographicErr("Different dist_t types");
      ar & boost::serialization::make_nvp("bucket", bucket);
      if (!( 0 <= bucket && bucket <= maxbucket ))
        throw GeographicLib::GeographicErr("Bad bucket size");
      ar & boost::serialization::make_nvp("numpoints", numpoints)
        & boost::serialization::make_nvp("cost", cost)
        & boost::serialization::make_nvp("tree", tree);
      if (!( 0 <= int(tree.size()) && int(tree.size()) <= numpoints ))
        throw
          GeographicLib::GeographicErr("Bad number of points or tree size");
      for (int i = 0; i < int(tree.size()); ++i)
        tree[i].Check(numpoints, int(tree.size()), bucket);
      _tree.swap(tree);
      _numpoints = numpoints;
      _bucket = bucket;
      _mc = _sc = 0;
      _cost = cost; _c1 = _k = _cmax = 0;
      _cmin = std::numeric_limits<int>::max();
    }
    template<class Archive>
    void serialize(Archive& ar, const unsigned int file_version)
    { boost::serialization::split_member(ar, *this, file_version); }
#endif
 
    int _numpoints, _bucket, _cost;
    std::vector<Node> _tree;
    // Counters to track stastistics on the cost of searches
    mutable double _mc, _sc;
    mutable int _c1, _k, _cmin, _cmax;
 
    int init(const std::vector<pos_t>& pts, const distfun_t& dist, int bucket,
             std::vector<Node>& tree, std::vector<item>& ids, int& cost,
             int l, int u, int vp) {
 
      if (u == l)
        return -1;
      Node node;
 
      if (u - l > (bucket == 0 ? 1 : bucket)) {
 
        // choose a vantage point and move it to the start
        int i = vp;
        std::swap(ids[l], ids[i]);
 
        int m = (u + l + 1) / 2;
 
        for (int k = l + 1; k < u; ++k) {
          ids[k].first = dist(pts[ids[l].second], pts[ids[k].second]);
          ++cost;
        }
        // partition around the median distance
        std::nth_element(ids.begin() + l + 1,
                         ids.begin() + m,
                         ids.begin() + u);
        node.index = ids[l].second;
        if (m > l + 1) {        // node.child[0] is possibly empty
          typename std::vector<item>::iterator
            t = std::min_element(ids.begin() + l + 1, ids.begin() + m);
          node.data.lower[0] = t->first;
          t = std::max_element(ids.begin() + l + 1, ids.begin() + m);
          node.data.upper[0] = t->first;
          // Use point with max distance as vantage point; this point act as a
          // "corner" point and leads to a good partition.
          node.data.child[0] = init(pts, dist, bucket, tree, ids, cost,
                                    l + 1, m, int(t - ids.begin()));
        }
        typename std::vector<item>::iterator
          t = std::max_element(ids.begin() + m, ids.begin() + u);
        node.data.lower[1] = ids[m].first;
        node.data.upper[1] = t->first;
        // Use point with max distance as vantage point here too
        node.data.child[1] = init(pts, dist, bucket, tree, ids, cost,
                                  m, u, int(t - ids.begin()));
      } else {
        if (bucket == 0)
          node.index = ids[l].second;
        else {
          node.index = -1;
          // Sort the bucket entries so that the tree is independent of the
          // implementation of nth_element.
          std::sort(ids.begin() + l, ids.begin() + u);
          for (int i = l; i < u; ++i)
            node.leaves[i-l] = ids[i].second;
          for (int i = u - l; i < bucket; ++i)
            node.leaves[i] = -1;
          for (int i = bucket; i < maxbucket; ++i)
            node.leaves[i] = 0;
        }
      }
 
      tree.push_back(node);
      return int(tree.size()) - 1;
    }
 
  };
 
} // namespace GeographicLib
 
namespace std {
 
  template <typename dist_t, typename pos_t, class distfun_t>
  void swap(GeographicLib::NearestNeighbor<dist_t, pos_t, distfun_t>& a,
            GeographicLib::NearestNeighbor<dist_t, pos_t, distfun_t>& b) {
    a.swap(b);
  }
 
} // namespace std
 
#if defined(_MSC_VER)
#  pragma warning (pop)
#endif
 
#endif  // GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP