GeographicLib 2.5.2

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NearestNeighbor.hpp
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1/**
2 * \file NearestNeighbor.hpp
3 * \brief Header for GeographicLib::NearestNeighbor class
4 *
5 * Copyright (c) Charles Karney (2016-2020) <karney@alum.mit.edu> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#if !defined(GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP)
11#define GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP 1
12
13#include <algorithm> // for nth_element, max_element, etc.
14#include <vector>
15#include <queue> // for priority_queue
16#include <utility> // for swap + pair
17#include <cstring>
18#include <limits>
19#include <cmath>
20#include <sstream>
21// Only for GeographicLib::GeographicErr
22#include <GeographicLib/Constants.hpp>
23
24#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
25 GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
26#include <boost/serialization/nvp.hpp>
27#include <boost/serialization/split_member.hpp>
28#include <boost/serialization/array.hpp>
29#include <boost/serialization/vector.hpp>
30#endif
31
32 namespace GeographicLib {
33
34 /**
35 * \brief Nearest-neighbor calculations
36 *
37 * This class solves the nearest-neighbor problm using a vantage-point tree
38 * as described in \ref nearest.
39 *
40 * This class is templated so that it can handle arbitrary metric spaces as
41 * follows:
42 *
43 * @tparam dist_t the type used for measuring distances; it can be a real or
44 * signed integer type; in typical geodetic applications, \e dist_t might
45 * be <code>double</code>.
46 * @tparam pos_t the type for specifying the positions of points; geodetic
47 * application might bundle the latitude and longitude into a
48 * <code>std::pair<dist_t, dist_t></code>.
49 * @tparam distfun_t the type of a function object which takes takes two
50 * positions (of type \e pos_t) and returns the distance (of type \e
51 * dist_t); in geodetic applications, this might be a class which is
52 * constructed with a Geodesic object and which implements a member
53 * function with a signature <code>dist_t operator() (const pos_t&, const
54 * pos_t&) const</code>, which returns the geodesic distance between two
55 * points.
56 *
57 * \note The distance measure must satisfy the triangle inequality, \f$
58 * d(a,c) \le d(a,b) + d(b,c) \f$ for all points \e a, \e b, \e c. The
59 * geodesic distance (given by Geodesic::Inverse) does, while the great
60 * ellipse distance and the rhumb line distance <i>do not</i>. If you use
61 * the ordinary Euclidean distance, i.e., \f$ \sqrt{(x_a-x_b)^2 +
62 * (y_a-y_b)^2} \f$ for two dimensions, don't be tempted to leave out the
63 * square root in the interests of "efficiency"; the squared distance does
64 * not satisfy the triangle inequality!
65 *
66 * \note This is a "header-only" implementation and, as such, depends in a
67 * minimal way on the rest of GeographicLib (the only dependency is through
68 * the use of GeographicLib::GeographicErr for handling and run-time
69 * exceptions). Therefore, it is easy to extract this class from the rest of
70 * GeographicLib and use it as a stand-alone facility.
71 *
72 * The \e dist_t type must support numeric_limits queries (specifically:
73 * is_signed, is_integer, max(), digits).
74 *
75 * The NearestNeighbor object is constructed with a vector of points (type \e
76 * pos_t) and a distance function (type \e distfun_t). However the object
77 * does \e not store the points. When querying the object with Search(),
78 * it's necessary to supply the same vector of points and the same distance
79 * function.
80 *
81 * There's no capability in this implementation to add or remove points from
82 * the set. Instead Initialize() should be called to re-initialize the
83 * object with the modified vector of points.
84 *
85 * Because of the overhead in constructing a NearestNeighbor object for a
86 * large set of points, functions Save() and Load() are provided to save the
87 * object to an external file. operator<<(), operator>>() and <a
88 * href="https://www.boost.org/libs/serialization/doc"> Boost
89 * serialization</a> can also be used to save and restore a NearestNeighbor
90 * object. This is illustrated in the example.
91 *
92 * Example of use:
93 * \include example-NearestNeighbor.cpp
94 **********************************************************************/
95 template<typename dist_t, typename pos_t, class distfun_t>
96 class NearestNeighbor {
97 // For tracking changes to the I/O format
98 static const int version = 1;
99 // This is what we get "free"; but if sizeof(dist_t) = 1 (unlikely), allow
100 // 4 slots (and this accommodates the default value bucket = 4).
101 static const int maxbucket =
102 (2 + ((4 * sizeof(dist_t)) / sizeof(int) >= 2 ?
103 (4 * sizeof(dist_t)) / sizeof(int) : 2));
104 public:
105
106 /**
107 * Default constructor for NearestNeighbor.
108 *
109 * This is equivalent to specifying an empty set of points.
110 **********************************************************************/
111 NearestNeighbor() : _numpoints(0), _bucket(0), _cost(0) {}
112
113 /**
114 * Constructor for NearestNeighbor.
115 *
116 * @param[in] pts a vector of points to include in the set.
117 * @param[in] dist the distance function object.
118 * @param[in] bucket the size of the buckets at the leaf nodes; this must
119 * lie in [0, 2 + 4*sizeof(dist_t)/sizeof(int)] (default 4).
120 * @exception GeographicErr if the value of \e bucket is out of bounds or
121 * the size of \e pts is too big for an int.
122 * @exception std::bad_alloc if memory for the tree can't be allocated.
123 *
124 * \e pts may contain coincident points (i.e., the distance between them
125 * vanishes); these are treated as distinct.
126 *
127 * The choice of \e bucket is a tradeoff between space and efficiency. A
128 * larger \e bucket decreases the size of the NearestNeighbor object which
129 * scales as pts.size() / max(1, bucket) and reduces the number of distance
130 * calculations to construct the object by log2(bucket) * pts.size().
131 * However each search then requires about bucket additional distance
132 * calculations.
133 *
134 * \warning The distances computed by \e dist must satisfy the standard
135 * metric conditions. If not, the results are undefined. Neither the data
136 * in \e pts nor the query points should contain NaNs or infinities because
137 * such data violates the metric conditions.
138 *
139 * \warning The same arguments \e pts and \e dist must be provided
140 * to the Search() function.
141 **********************************************************************/
142 NearestNeighbor(const std::vector<pos_t>& pts, const distfun_t& dist,
143 int bucket = 4) {
144 Initialize(pts, dist, bucket);
145 }
146
147 /**
148 * Initialize or re-initialize NearestNeighbor.
149 *
150 * @param[in] pts a vector of points to include in the tree.
151 * @param[in] dist the distance function object.
152 * @param[in] bucket the size of the buckets at the leaf nodes; this must
153 * lie in [0, 2 + 4*sizeof(dist_t)/sizeof(int)] (default 4).
154 * @exception GeographicErr if the value of \e bucket is out of bounds or
155 * the size of \e pts is too big for an int.
156 * @exception std::bad_alloc if memory for the tree can't be allocated.
157 *
158 * See also the documentation on the constructor.
159 *
160 * If an exception is thrown, the state of the NearestNeighbor is
161 * unchanged.
162 **********************************************************************/
163 void Initialize(const std::vector<pos_t>& pts, const distfun_t& dist,
164 int bucket = 4) {
165 static_assert(std::numeric_limits<dist_t>::is_signed,
166 "dist_t must be a signed type");
167 if (!( 0 <= bucket && bucket <= maxbucket ))
168 throw GeographicLib::GeographicErr
169 ("bucket must lie in [0, 2 + 4*sizeof(dist_t)/sizeof(int)]");
170 if (pts.size() > size_t(std::numeric_limits<int>::max()))
171 throw GeographicLib::GeographicErr("pts array too big");
172 // the pair contains distance+id
173 std::vector<item> ids(pts.size());
174 for (int k = int(ids.size()); k--;)
175 ids[k] = std::make_pair(dist_t(0), k);
176 int cost = 0;
177 std::vector<Node> tree;
178 init(pts, dist, bucket, tree, ids, cost,
179 0, int(ids.size()), int(ids.size()/2));
180 _tree.swap(tree);
181 _numpoints = int(pts.size());
182 _bucket = bucket;
183 _mc = _sc = 0;
184 _cost = cost; _c1 = _k = _cmax = 0;
185 _cmin = std::numeric_limits<int>::max();
186 }
187
188 /**
189 * Search the NearestNeighbor.
190 *
191 * @param[in] pts the vector of points used for initialization.
192 * @param[in] dist the distance function object used for initialization.
193 * @param[in] query the query point.
194 * @param[out] ind a vector of indices to the closest points found.
195 * @param[in] k the number of points to search for (default = 1).
196 * @param[in] maxdist only return points with distances of \e maxdist or
197 * less from \e query (default is the maximum \e dist_t).
198 * @param[in] mindist only return points with distances of more than
199 * \e mindist from \e query (default = &minus;1).
200 * @param[in] exhaustive whether to do an exhaustive search (default true).
201 * @param[in] tol the tolerance on the results (default 0).
202 * @return the distance to the closest point found (&minus;1 if no points
203 * are found).
204 * @exception GeographicErr if \e pts has a different size from that used
205 * to construct the object.
206 *
207 * The indices returned in \e ind are sorted by distance from \e query
208 * (closest first).
209 *
210 * The simplest invocation is with just the 4 non-optional arguments. This
211 * returns the closest distance and the index to the closest point in
212 * <i>ind</i><sub>0</sub>. If there are several points equally close, then
213 * <i>ind</i><sub>0</sub> gives the index of an arbirary one of them. If
214 * there's no closest point (because the set of points is empty), then \e
215 * ind is empty and &minus;1 is returned.
216 *
217 * With \e exhaustive = true and \e tol = 0 (their default values), this
218 * finds the indices of \e k closest neighbors to \e query whose distances
219 * to \e query are in (\e mindist, \e maxdist]. If \e mindist and \e
220 * maxdist have their default values, then these bounds have no effect. If
221 * \e query is one of the points in the tree, then set \e mindist = 0 to
222 * prevent this point (and other coincident points) from being returned.
223 *
224 * If \e exhaustive = false, exit as soon as \e k results satisfying the
225 * distance criteria are found. If less than \e k results are returned
226 * then the search was exhaustive even if \e exhaustive = false.
227 *
228 * If \e tol is positive, do an approximate search; in this case the
229 * results are to be interpreted as follows: if the <i>k</i>'th distance is
230 * \e dk, then all results with distances less than or equal \e dk &minus;
231 * \e tol are correct; all others are suspect &mdash; there may be other
232 * closer results with distances greater or equal to \e dk &minus; \e tol.
233 * If less than \e k results are found, then the search is exact.
234 *
235 * \e mindist should be used to exclude a "small" neighborhood of the query
236 * point (relative to the average spacing of the data). If \e mindist is
237 * large, the efficiency of the search deteriorates.
238 *
239 * \note Only the shortest distance is returned (as as the function value).
240 * The distances to other points (indexed by <i>ind</i><sub><i>j</i></sub>
241 * for \e j > 0) can be found by invoking \e dist again.
242 *
243 * \warning The arguments \e pts and \e dist must be identical to those
244 * used to initialize the NearestNeighbor; if not, this function will
245 * return some meaningless result (however, if the size of \e pts is wrong,
246 * this function throw an exception).
247 *
248 * \warning The query point cannot be a NaN or infinite because then the
249 * metric conditions are violated.
250 **********************************************************************/
251 dist_t Search(const std::vector<pos_t>& pts, const distfun_t& dist,
252 const pos_t& query,
253 std::vector<int>& ind,
254 int k = 1,
255 dist_t maxdist = std::numeric_limits<dist_t>::max(),
256 dist_t mindist = -1,
257 bool exhaustive = true,
258 dist_t tol = 0) const {
259 if (_numpoints != int(pts.size()))
260 throw GeographicLib::GeographicErr("pts array has wrong size");
261 std::priority_queue<item> results;
262 if (_numpoints > 0 && k > 0 && maxdist > mindist) {
263 // distance to the kth closest point so far
264 dist_t tau = maxdist;
265 // first is negative of how far query is outside boundary of node
266 // +1 if on boundary or inside
267 // second is node index
268 std::priority_queue<item> todo;
269 todo.push(std::make_pair(dist_t(1), int(_tree.size()) - 1));
270 int c = 0;
271 while (!todo.empty()) {
272 int n = todo.top().second;
273 dist_t d = -todo.top().first;
274 todo.pop();
275 dist_t tau1 = tau - tol;
276 // compare tau and d again since tau may have become smaller.
277 if (!( n >= 0 && tau1 >= d )) continue;
278 const Node& current = _tree[n];
279 dist_t dst = 0; // to suppress warning about uninitialized variable
280 bool exitflag = false, leaf = current.index < 0;
281 for (int i = 0; i < (leaf ? _bucket : 1); ++i) {
282 int index = leaf ? current.leaves[i] : current.index;
283 if (index < 0) break;
284 dst = dist(pts[index], query);
285 ++c;
286
287 if (dst > mindist && dst <= tau) {
288 if (int(results.size()) == k) results.pop();
289 results.push(std::make_pair(dst, index));
290 if (int(results.size()) == k) {
291 if (exhaustive)
292 tau = results.top().first;
293 else {
294 exitflag = true;
295 break;
296 }
297 if (tau <= tol) {
298 exitflag = true;
299 break;
300 }
301 }
302 }
303 }
304 if (exitflag) break;
305
306 if (current.index < 0) continue;
307 tau1 = tau - tol;
308 for (int l = 0; l < 2; ++l) {
309 if (current.data.child[l] >= 0 &&
310 dst + current.data.upper[l] >= mindist) {
311 if (dst < current.data.lower[l]) {
312 d = current.data.lower[l] - dst;
313 if (tau1 >= d)
314 todo.push(std::make_pair(-d, current.data.child[l]));
315 } else if (dst > current.data.upper[l]) {
316 d = dst - current.data.upper[l];
317 if (tau1 >= d)
318 todo.push(std::make_pair(-d, current.data.child[l]));
319 } else
320 todo.push(std::make_pair(dist_t(1), current.data.child[l]));
321 }
322 }
323 }
324 ++_k;
325 _c1 += c;
326 double omc = _mc;
327 _mc += (c - omc) / _k;
328 _sc += (c - omc) * (c - _mc);
329 if (c > _cmax) _cmax = c;
330 if (c < _cmin) _cmin = c;
331 }
332
333 dist_t d = -1;
334 ind.resize(results.size());
335
336 for (int i = int(ind.size()); i--;) {
337 ind[i] = int(results.top().second);
338 if (i == 0) d = results.top().first;
339 results.pop();
340 }
341 return d;
342
343 }
344
345 /**
346 * @return the total number of points in the set.
347 **********************************************************************/
348 int NumPoints() const { return _numpoints; }
349
350 /**
351 * Write the object to an I/O stream.
352 *
353 * @param[in,out] os the stream to write to.
354 * @param[in] bin if true (the default) save in binary mode.
355 * @exception std::bad_alloc if memory for the string representation of the
356 * object can't be allocated.
357 *
358 * The counters tracking the statistics of searches are not saved; however
359 * the initializtion cost is saved. The format of the binary saves is \e
360 * not portable.
361 *
362 * \note <a href="https://www.boost.org/libs/serialization/doc">
363 * Boost serialization</a> can also be used to save and restore a
364 * NearestNeighbor object. This requires that the
365 * GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION macro be defined.
366 **********************************************************************/
367 void Save(std::ostream& os, bool bin = true) const {
368 int realspec = std::numeric_limits<dist_t>::digits *
369 (std::numeric_limits<dist_t>::is_integer ? -1 : 1);
370 if (bin) {
371 char id[] = "NearestNeighbor_";
372 os.write(id, 16);
373 int buf[6];
374 buf[0] = version;
375 buf[1] = realspec;
376 buf[2] = _bucket;
377 buf[3] = _numpoints;
378 buf[4] = int(_tree.size());
379 buf[5] = _cost;
380 os.write(reinterpret_cast<const char *>(buf), 6 * sizeof(int));
381 for (int i = 0; i < int(_tree.size()); ++i) {
382 const Node& node = _tree[i];
383 os.write(reinterpret_cast<const char *>(&node.index), sizeof(int));
384 if (node.index >= 0) {
385 os.write(reinterpret_cast<const char *>(node.data.lower),
386 2 * sizeof(dist_t));
387 os.write(reinterpret_cast<const char *>(node.data.upper),
388 2 * sizeof(dist_t));
389 os.write(reinterpret_cast<const char *>(node.data.child),
390 2 * sizeof(int));
391 } else {
392 os.write(reinterpret_cast<const char *>(node.leaves),
393 _bucket * sizeof(int));
394 }
395 }
396 } else {
397 std::stringstream ostring;
398 // Ensure enough precision for type dist_t. With C++11, max_digits10
399 // can be used instead.
400 if (!std::numeric_limits<dist_t>::is_integer) {
401 static const int prec
402 = int(std::ceil(std::numeric_limits<dist_t>::digits *
403 std::log10(2.0) + 1));
404 ostring.precision(prec);
405 }
406 ostring << version << " " << realspec << " " << _bucket << " "
407 << _numpoints << " " << _tree.size() << " " << _cost;
408 for (int i = 0; i < int(_tree.size()); ++i) {
409 const Node& node = _tree[i];
410 ostring << "\n" << node.index;
411 if (node.index >= 0) {
412 for (int l = 0; l < 2; ++l)
413 ostring << " " << node.data.lower[l] << " " << node.data.upper[l]
414 << " " << node.data.child[l];
415 } else {
416 for (int l = 0; l < _bucket; ++l)
417 ostring << " " << node.leaves[l];
418 }
419 }
420 os << ostring.str();
421 }
422 }
423
424 /**
425 * Read the object from an I/O stream.
426 *
427 * @param[in,out] is the stream to read from
428 * @param[in] bin if true (the default) load in binary mode.
429 * @exception GeographicErr if the state read from \e is is illegal.
430 * @exception std::bad_alloc if memory for the tree can't be allocated.
431 *
432 * The counters tracking the statistics of searches are reset by this
433 * operation. Binary data must have been saved on a machine with the same
434 * architecture. If an exception is thrown, the state of the
435 * NearestNeighbor is unchanged.
436 *
437 * \note <a href="https://www.boost.org/libs/serialization/doc">
438 * Boost serialization</a> can also be used to save and restore a
439 * NearestNeighbor object. This requires that the
440 * GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION macro be defined.
441 *
442 * \warning The same arguments \e pts and \e dist used for
443 * initialization must be provided to the Search() function.
444 **********************************************************************/
445 void Load(std::istream& is, bool bin = true) {
446 int version1, realspec, bucket, numpoints, treesize, cost;
447 if (bin) {
448 char id[17];
449 is.read(id, 16);
450 id[16] = '\0';
451 if (!(std::strcmp(id, "NearestNeighbor_") == 0))
452 throw GeographicLib::GeographicErr("Bad ID");
453 is.read(reinterpret_cast<char *>(&version1), sizeof(int));
454 is.read(reinterpret_cast<char *>(&realspec), sizeof(int));
455 is.read(reinterpret_cast<char *>(&bucket), sizeof(int));
456 is.read(reinterpret_cast<char *>(&numpoints), sizeof(int));
457 is.read(reinterpret_cast<char *>(&treesize), sizeof(int));
458 is.read(reinterpret_cast<char *>(&cost), sizeof(int));
459 } else {
460 if (!( is >> version1 >> realspec >> bucket >> numpoints >> treesize
461 >> cost ))
462 throw GeographicLib::GeographicErr("Bad header");
463 }
464 if (!( version1 == version ))
465 throw GeographicLib::GeographicErr("Incompatible version");
466 if (!( realspec == std::numeric_limits<dist_t>::digits *
467 (std::numeric_limits<dist_t>::is_integer ? -1 : 1) ))
468 throw GeographicLib::GeographicErr("Different dist_t types");
469 if (!( 0 <= bucket && bucket <= maxbucket ))
470 throw GeographicLib::GeographicErr("Bad bucket size");
471 if (!( 0 <= treesize && treesize <= numpoints ))
472 throw
473 GeographicLib::GeographicErr("Bad number of points or tree size");
474 if (!( 0 <= cost ))
475 throw GeographicLib::GeographicErr("Bad value for cost");
476 std::vector<Node> tree;
477 tree.reserve(treesize);
478 for (int i = 0; i < treesize; ++i) {
479 Node node;
480 if (bin) {
481 is.read(reinterpret_cast<char *>(&node.index), sizeof(int));
482 if (node.index >= 0) {
483 is.read(reinterpret_cast<char *>(node.data.lower),
484 2 * sizeof(dist_t));
485 is.read(reinterpret_cast<char *>(node.data.upper),
486 2 * sizeof(dist_t));
487 is.read(reinterpret_cast<char *>(node.data.child),
488 2 * sizeof(int));
489 } else {
490 is.read(reinterpret_cast<char *>(node.leaves),
491 bucket * sizeof(int));
492 for (int l = bucket; l < maxbucket; ++l)
493 node.leaves[l] = 0;
494 }
495 } else {
496 if (!( is >> node.index ))
497 throw GeographicLib::GeographicErr("Bad index");
498 if (node.index >= 0) {
499 for (int l = 0; l < 2; ++l) {
500 if (!( is >> node.data.lower[l] >> node.data.upper[l]
501 >> node.data.child[l] ))
502 throw GeographicLib::GeographicErr("Bad node data");
503 }
504 } else {
505 // Must be at least one valid leaf followed by a sequence end
506 // markers (-1).
507 for (int l = 0; l < bucket; ++l) {
508 if (!( is >> node.leaves[l] ))
509 throw GeographicLib::GeographicErr("Bad leaf data");
510 }
511 for (int l = bucket; l < maxbucket; ++l)
512 node.leaves[l] = 0;
513 }
514 }
515 node.Check(numpoints, treesize, bucket);
516 tree.push_back(node);
517 }
518 _tree.swap(tree);
519 _numpoints = numpoints;
520 _bucket = bucket;
521 _mc = _sc = 0;
522 _cost = cost; _c1 = _k = _cmax = 0;
523 _cmin = std::numeric_limits<int>::max();
524 }
525
526 /**
527 * Write the object to stream \e os as text.
528 *
529 * @param[in,out] os the output stream.
530 * @param[in] t the NearestNeighbor object to be saved.
531 * @exception std::bad_alloc if memory for the string representation of the
532 * object can't be allocated.
533 **********************************************************************/
534 friend std::ostream& operator<<(std::ostream& os, const NearestNeighbor& t)
535 { t.Save(os, false); return os; }
536
537 /**
538 * Read the object from stream \e is as text.
539 *
540 * @param[in,out] is the input stream.
541 * @param[out] t the NearestNeighbor object to be loaded.
542 * @exception GeographicErr if the state read from \e is is illegal.
543 * @exception std::bad_alloc if memory for the tree can't be allocated.
544 **********************************************************************/
545 friend std::istream& operator>>(std::istream& is, NearestNeighbor& t)
546 { t.Load(is, false); return is; }
547
548 /**
549 * Swap with another NearestNeighbor object.
550 *
551 * @param[in,out] t the NearestNeighbor object to swap with.
552 **********************************************************************/
553 void swap(NearestNeighbor& t) {
554 std::swap(_numpoints, t._numpoints);
555 std::swap(_bucket, t._bucket);
556 std::swap(_cost, t._cost);
557 _tree.swap(t._tree);
558 std::swap(_mc, t._mc);
559 std::swap(_sc, t._sc);
560 std::swap(_c1, t._c1);
561 std::swap(_k, t._k);
562 std::swap(_cmin, t._cmin);
563 std::swap(_cmax, t._cmax);
564 }
565
566 /**
567 * The accumulated statistics on the searches so far.
568 *
569 * @param[out] setupcost the cost of initializing the NearestNeighbor.
570 * @param[out] numsearches the number of calls to Search().
571 * @param[out] searchcost the total cost of the calls to Search().
572 * @param[out] mincost the minimum cost of a Search().
573 * @param[out] maxcost the maximum cost of a Search().
574 * @param[out] mean the mean cost of a Search().
575 * @param[out] sd the standard deviation in the cost of a Search().
576 *
577 * Here "cost" measures the number of distance calculations needed. Note
578 * that the accumulation of statistics is \e not thread safe.
579 **********************************************************************/
580 void Statistics(int& setupcost, int& numsearches, int& searchcost,
581 int& mincost, int& maxcost,
582 double& mean, double& sd) const {
583 setupcost = _cost; numsearches = _k; searchcost = _c1;
584 mincost = _cmin; maxcost = _cmax;
585 mean = _mc; sd = std::sqrt(_sc / (_k - 1));
586 }
587
588 /**
589 * Reset the counters for the accumulated statistics on the searches so
590 * far.
591 **********************************************************************/
592 void ResetStatistics() const {
593 _mc = _sc = 0;
594 _c1 = _k = _cmax = 0;
595 _cmin = std::numeric_limits<int>::max();
596 }
597
598 private:
599 // Package up a dist_t and an int. We will want to sort on the dist_t so
600 // put it first.
601 typedef std::pair<dist_t, int> item;
602 // \cond SKIP
603 class Node {
604 public:
605 struct bounds {
606 dist_t lower[2], upper[2]; // bounds on inner/outer distances
607 int child[2];
608 };
609 union {
610 bounds data;
611 int leaves[maxbucket];
612 };
613 int index;
614
615 Node()
616 : index(-1)
617 {
618 for (int i = 0; i < 2; ++i) {
619 data.lower[i] = data.upper[i] = 0;
620 data.child[i] = -1;
621 }
622 }
623
624 // Sanity check on a Node
625 void Check(int numpoints, int treesize, int bucket) const {
626 if (!( -1 <= index && index < numpoints ))
627 throw GeographicLib::GeographicErr("Bad index");
628 if (index >= 0) {
629 if (!( -1 <= data.child[0] && data.child[0] < treesize &&
630 -1 <= data.child[1] && data.child[1] < treesize ))
631 throw GeographicLib::GeographicErr("Bad child pointers");
632 if (!( 0 <= data.lower[0] && data.lower[0] <= data.upper[0] &&
633 data.upper[0] <= data.lower[1] &&
634 data.lower[1] <= data.upper[1] ))
635 throw GeographicLib::GeographicErr("Bad bounds");
636 } else {
637 // Must be at least one valid leaf followed by a sequence end markers
638 // (-1).
639 bool start = true;
640 for (int l = 0; l < bucket; ++l) {
641 if (!( (start ?
642 ((l == 0 ? 0 : -1) <= leaves[l] && leaves[l] < numpoints) :
643 leaves[l] == -1) ))
644 throw GeographicLib::GeographicErr("Bad leaf data");
645 start = leaves[l] >= 0;
646 }
647 for (int l = bucket; l < maxbucket; ++l) {
648 if (leaves[l] != 0)
649 throw GeographicLib::GeographicErr("Bad leaf data");
650 }
651 }
652 }
653
654#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
655 GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
656 friend class boost::serialization::access;
657 template<class Archive>
658 void save(Archive& ar, const unsigned int) const {
659 ar & boost::serialization::make_nvp("index", index);
660 if (index < 0)
661 ar & boost::serialization::make_nvp("leaves", leaves);
662 else
663 ar & boost::serialization::make_nvp("lower", data.lower)
664 & boost::serialization::make_nvp("upper", data.upper)
665 & boost::serialization::make_nvp("child", data.child);
666 }
667 template<class Archive>
668 void load(Archive& ar, const unsigned int) {
669 ar & boost::serialization::make_nvp("index", index);
670 if (index < 0)
671 ar & boost::serialization::make_nvp("leaves", leaves);
672 else
673 ar & boost::serialization::make_nvp("lower", data.lower)
674 & boost::serialization::make_nvp("upper", data.upper)
675 & boost::serialization::make_nvp("child", data.child);
676 }
677 template<class Archive>
678 void serialize(Archive& ar, const unsigned int file_version)
679 { boost::serialization::split_member(ar, *this, file_version); }
680#endif
681 };
682 // \endcond
683#if defined(GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION) && \
684 GEOGRAPHICLIB_HAVE_BOOST_SERIALIZATION
685 friend class boost::serialization::access;
686 template<class Archive> void save(Archive& ar, const unsigned) const {
687 int realspec = std::numeric_limits<dist_t>::digits *
688 (std::numeric_limits<dist_t>::is_integer ? -1 : 1);
689 // Need to use version1, otherwise load error in debug mode on Linux:
690 // undefined reference to GeographicLib::NearestNeighbor<...>::version.
691 int version1 = version;
692 ar & boost::serialization::make_nvp("version", version1)
693 & boost::serialization::make_nvp("realspec", realspec)
694 & boost::serialization::make_nvp("bucket", _bucket)
695 & boost::serialization::make_nvp("numpoints", _numpoints)
696 & boost::serialization::make_nvp("cost", _cost)
697 & boost::serialization::make_nvp("tree", _tree);
698 }
699 template<class Archive> void load(Archive& ar, const unsigned) {
700 int version1, realspec, bucket, numpoints, cost;
701 ar & boost::serialization::make_nvp("version", version1);
702 if (version1 != version)
703 throw GeographicLib::GeographicErr("Incompatible version");
704 std::vector<Node> tree;
705 ar & boost::serialization::make_nvp("realspec", realspec);
706 if (!( realspec == std::numeric_limits<dist_t>::digits *
707 (std::numeric_limits<dist_t>::is_integer ? -1 : 1) ))
708 throw GeographicLib::GeographicErr("Different dist_t types");
709 ar & boost::serialization::make_nvp("bucket", bucket);
710 if (!( 0 <= bucket && bucket <= maxbucket ))
711 throw GeographicLib::GeographicErr("Bad bucket size");
712 ar & boost::serialization::make_nvp("numpoints", numpoints)
713 & boost::serialization::make_nvp("cost", cost)
714 & boost::serialization::make_nvp("tree", tree);
715 if (!( 0 <= int(tree.size()) && int(tree.size()) <= numpoints ))
716 throw
717 GeographicLib::GeographicErr("Bad number of points or tree size");
718 for (int i = 0; i < int(tree.size()); ++i)
719 tree[i].Check(numpoints, int(tree.size()), bucket);
720 _tree.swap(tree);
721 _numpoints = numpoints;
722 _bucket = bucket;
723 _mc = _sc = 0;
724 _cost = cost; _c1 = _k = _cmax = 0;
725 _cmin = std::numeric_limits<int>::max();
726 }
727 template<class Archive>
728 void serialize(Archive& ar, const unsigned int file_version)
729 { boost::serialization::split_member(ar, *this, file_version); }
730#endif
731
732 int _numpoints, _bucket, _cost;
733 std::vector<Node> _tree;
734 // Counters to track stastistics on the cost of searches
735 mutable double _mc, _sc;
736 mutable int _c1, _k, _cmin, _cmax;
737
738 int init(const std::vector<pos_t>& pts, const distfun_t& dist, int bucket,
739 std::vector<Node>& tree, std::vector<item>& ids, int& cost,
740 int l, int u, int vp) {
741
742 if (u == l)
743 return -1;
744 Node node;
745
746 if (u - l > (bucket == 0 ? 1 : bucket)) {
747
748 // choose a vantage point and move it to the start
749 int i = vp;
750 std::swap(ids[l], ids[i]);
751
752 int m = (u + l + 1) / 2;
753
754 for (int k = l + 1; k < u; ++k) {
755 ids[k].first = dist(pts[ids[l].second], pts[ids[k].second]);
756 ++cost;
757 }
758 // partition around the median distance
759 std::nth_element(ids.begin() + l + 1,
760 ids.begin() + m,
761 ids.begin() + u);
762 node.index = ids[l].second;
763 if (m > l + 1) { // node.child[0] is possibly empty
764 typename std::vector<item>::iterator
765 t = std::min_element(ids.begin() + l + 1, ids.begin() + m);
766 node.data.lower[0] = t->first;
767 t = std::max_element(ids.begin() + l + 1, ids.begin() + m);
768 node.data.upper[0] = t->first;
769 // Use point with max distance as vantage point; this point act as a
770 // "corner" point and leads to a good partition.
771 node.data.child[0] = init(pts, dist, bucket, tree, ids, cost,
772 l + 1, m, int(t - ids.begin()));
773 }
774 typename std::vector<item>::iterator
775 t = std::max_element(ids.begin() + m, ids.begin() + u);
776 node.data.lower[1] = ids[m].first;
777 node.data.upper[1] = t->first;
778 // Use point with max distance as vantage point here too
779 node.data.child[1] = init(pts, dist, bucket, tree, ids, cost,
780 m, u, int(t - ids.begin()));
781 } else {
782 if (bucket == 0)
783 node.index = ids[l].second;
784 else {
785 node.index = -1;
786 // Sort the bucket entries so that the tree is independent of the
787 // implementation of nth_element.
788 std::sort(ids.begin() + l, ids.begin() + u);
789 for (int i = l; i < u; ++i)
790 node.leaves[i-l] = ids[i].second;
791 for (int i = u - l; i < bucket; ++i)
792 node.leaves[i] = -1;
793 for (int i = bucket; i < maxbucket; ++i)
794 node.leaves[i] = 0;
795 }
796 }
797
798 tree.push_back(node);
799 return int(tree.size()) - 1;
800 }
801
802 };
803
804} // namespace GeographicLib
805
806 namespace std {
807
808 /**
809 * Swap two GeographicLib::NearestNeighbor objects.
810 *
811 * @tparam dist_t the type used for measuring distances.
812 * @tparam pos_t the type for specifying the positions of points.
813 * @tparam distfun_t the type for a function object which calculates
814 * distances between points.
815 * @param[in,out] a the first GeographicLib::NearestNeighbor to swap.
816 * @param[in,out] b the second GeographicLib::NearestNeighbor to swap.
817 **********************************************************************/
818 template<typename dist_t, typename pos_t, class distfun_t>
819 void swap(GeographicLib::NearestNeighbor<dist_t, pos_t, distfun_t>& a,
820 GeographicLib::NearestNeighbor<dist_t, pos_t, distfun_t>& b) {
821 a.swap(b);
822 }
823
824} // namespace std
825
826#endif // GEOGRAPHICLIB_NEARESTNEIGHBOR_HPP
Constants.hpp
Header for GeographicLib::Constants class.
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:316
GeographicLib::NearestNeighbor
Nearest-neighbor calculations.
Definition NearestNeighbor.hpp:96
GeographicLib::NearestNeighbor::NumPoints
int NumPoints() const
Definition NearestNeighbor.hpp:348
GeographicLib::NearestNeighbor::Statistics
void Statistics(int &setupcost, int &numsearches, int &searchcost, int &mincost, int &maxcost, double &mean, double &sd) const
Definition NearestNeighbor.hpp:580
GeographicLib::NearestNeighbor::operator>>
friend std::istream & operator>>(std::istream &is, NearestNeighbor &t)
Definition NearestNeighbor.hpp:545
GeographicLib::NearestNeighbor::Search
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
Definition NearestNeighbor.hpp:251
GeographicLib::NearestNeighbor::Initialize
void Initialize(const std::vector< pos_t > &pts, const distfun_t &dist, int bucket=4)
Definition NearestNeighbor.hpp:163
GeographicLib::NearestNeighbor::Load
void Load(std::istream &is, bool bin=true)
Definition NearestNeighbor.hpp:445
GeographicLib::NearestNeighbor::Save
void Save(std::ostream &os, bool bin=true) const
Definition NearestNeighbor.hpp:367
GeographicLib::NearestNeighbor::ResetStatistics
void ResetStatistics() const
Definition NearestNeighbor.hpp:592
GeographicLib::NearestNeighbor::NearestNeighbor
NearestNeighbor()
Definition NearestNeighbor.hpp:111
GeographicLib::NearestNeighbor::NearestNeighbor
NearestNeighbor(const std::vector< pos_t > &pts, const distfun_t &dist, int bucket=4)
Definition NearestNeighbor.hpp:142
GeographicLib::NearestNeighbor::swap
void swap(NearestNeighbor &t)
Definition NearestNeighbor.hpp:553
GeographicLib::NearestNeighbor::operator<<
friend std::ostream & operator<<(std::ostream &os, const NearestNeighbor &t)
Definition NearestNeighbor.hpp:534
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806
std::swap
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)
Definition NearestNeighbor.hpp:819