Coverage for pygeodesy/frechet.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Fréchet distances. 

5 

6Classes L{Frechet}, L{FrechetDegrees}, L{FrechetRadians}, 

7L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, 

8L{FrechetCosineLaw}, L{FrechetDistanceTo}< L{FrechetEquirectangular}, 

9L{FrechetEuclidean}, L{FrechetExact}, L{FrechetFlatLocal}, L{FrechetFlatPolar}, 

10L{FrechetHaversine}, L{FrechetHubeny}, L{FrechetKarney}, L{FrechetThomas} 

11and L{FrechetVincentys} to compute I{discrete} U{Fréchet 

12<https://WikiPedia.org/wiki/Frechet_distance>} distances between two sets 

13of C{LatLon}, C{NumPy}, C{tuples} or other types of points. 

14 

15Only L{FrechetDistanceTo} -iff used with L{ellipsoidalKarney.LatLon} 

16points- and L{FrechetKarney} requires installation of I{Charles Karney}'s 

17U{geographiclib<https://PyPI.org/project/geographiclib>}. 

18 

19Typical usage is as follows. First, create a C{Frechet} calculator 

20from one set of C{LatLon} points. 

21 

22C{f = FrechetXyz(point1s, ...)} 

23 

24Get the I{discrete} Fréchet distance to another set of C{LatLon} points 

25by 

26 

27C{t6 = f.discrete(point2s)} 

28 

29Or, use function C{frechet_} with a proper C{distance} function passed 

30as keyword arguments as follows 

31 

32C{t6 = frechet_(point1s, point2s, ..., distance=...)}. 

33 

34In both cases, the returned result C{t6} is a L{Frechet6Tuple}. 

35 

36For C{(lat, lon, ...)} points in a C{NumPy} array or plain C{tuples}, 

37wrap the points in a L{Numpy2LatLon} respectively L{Tuple2LatLon} 

38instance, more details in the documentation thereof. 

39 

40For other points, create a L{Frechet} sub-class with the appropriate 

41C{distance} method overloading L{Frechet.distance} as in this example. 

42 

43 >>> from pygeodesy import Frechet, hypot_ 

44 >>> 

45 >>> class F3D(Frechet): 

46 >>> """Custom Frechet example. 

47 >>> """ 

48 >>> def distance(self, p1, p2): 

49 >>> return hypot_(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z) 

50 >>> 

51 >>> f3D = F3D(xyz1, ..., units="...") 

52 >>> t6 = f3D.discrete(xyz2) 

53 

54Transcribed from the original U{Computing Discrete Fréchet Distance 

55<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>} by 

56Eiter, T. and Mannila, H., 1994, April 25, Technical Report CD-TR 94/64, 

57Information Systems Department/Christian Doppler Laboratory for Expert 

58Systems, Technical University Vienna, Austria. 

59 

60This L{Frechet.discrete} implementation optionally generates intermediate 

61points for each point set separately. For example, using keyword argument 

62C{fraction=0.5} adds one additional point halfway between each pair of 

63points. Or using C{fraction=0.1} interpolates nine additional points 

64between each points pair. 

65 

66The L{Frechet6Tuple} attributes C{fi1} and/or C{fi2} will be I{fractional} 

67indices of type C{float} if keyword argument C{fraction} is used. Otherwise, 

68C{fi1} and/or C{fi2} are simply type C{int} indices into the respective 

69points set. 

70 

71For example, C{fractional} index value 2.5 means an intermediate point 

72halfway between points[2] and points[3]. Use function L{fractional} 

73to obtain the intermediate point for a I{fractional} index in the 

74corresponding set of points. 

75 

76The C{Fréchet} distance was introduced in 1906 by U{Maurice Fréchet 

77<https://WikiPedia.org/wiki/Maurice_Rene_Frechet>}, see U{reference 

78[6]<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>}. 

79It is a measure of similarity between curves that takes into account the 

80location and ordering of the points. Therefore, it is often a better metric 

81than the well-known C{Hausdorff} distance, see the L{hausdorff} module. 

82''' 

83 

84# from pygeodesy.basics import isscalar # from .points 

85from pygeodesy.constants import EPS, EPS1, INF, NINF 

86from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

87from pygeodesy.errors import _IsnotError, PointsError, _xattr, \ 

88 _xkwds, _xkwds_get 

89import pygeodesy.formy as _formy 

90from pygeodesy.interns import NN, _DOT_, _n_, _units_ 

91# from pygeodesy.iters import points2 as _points2 # from .points 

92from pygeodesy.lazily import _ALL_LAZY, _FOR_DOCS 

93from pygeodesy.named import _Named, _NamedTuple, notOverloaded, _Pass 

94# from pygeodesy.namedTuples import PhiLam2Tuple # from .points 

95from pygeodesy.points import _distanceTo, _fractional, isscalar, \ 

96 PhiLam2Tuple, points2 as _points2, radians 

97from pygeodesy.props import property_doc_, property_RO 

98from pygeodesy.units import FIx, Float, Number_, _xUnit, _xUnits 

99from pygeodesy.unitsBase import _Str_degrees, _Str_meter, _Str_NN, \ 

100 _Str_radians, _Str_radians2 

101 

102from collections import defaultdict as _defaultdict 

103# from math import radians # from .points 

104 

105__all__ = _ALL_LAZY.frechet 

106__version__ = '23.08.06' 

107 

108 

109def _fraction(fraction, n): 

110 f = 1 # int, no fractional indices 

111 if fraction in (None, 1): 

112 pass 

113 elif not (isscalar(fraction) and EPS < fraction < EPS1 

114 and (float(n) - fraction) < n): 

115 raise FrechetError(fraction=fraction) 

116 elif fraction < EPS1: 

117 f = float(fraction) 

118 return f 

119 

120 

121class FrechetError(PointsError): 

122 '''Fréchet issue. 

123 ''' 

124 pass 

125 

126 

127class Frechet(_Named): 

128 '''Frechet base class, requires method L{Frechet.distance} to 

129 be overloaded. 

130 ''' 

131 _datum = _WGS84 

132 _func = None # formy function 

133 _f1 = 1 

134 _kwds = {} # func_ options 

135 _n1 = 0 

136 _ps1 = None 

137 _units = _Str_NN # XXX Str to _Pass and for backward compatibility 

138 

139 def __init__(self, point1s, fraction=None, name=NN, units=NN, **kwds): 

140 '''New C{Frechet...} calculator/interpolator. 

141 

142 @arg point1s: First set of points (C{LatLon}[], L{Numpy2LatLon}[], 

143 L{Tuple2LatLon}[] or C{other}[]). 

144 @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to 

145 interpolate intermediate B{C{point1s}} or use 

146 C{None}, C{0} or C{1} for no intermediate 

147 B{C{point1s}} and no I{fractional} indices. 

148 @kwarg name: Optional calculator/interpolator name (C{str}). 

149 @kwarg units: Optional distance units (C{Unit} or C{str}). 

150 @kwarg kwds: Optional keyword argument for distance function, 

151 retrievable with property C{kwds}. 

152 

153 @raise FrechetError: Insufficient number of B{C{point1s}} or 

154 an invalid B{C{point1}}, B{C{fraction}} 

155 or B{C{units}}. 

156 ''' 

157 self._n1, self._ps1 = self._points2(point1s) 

158 if fraction: 

159 self.fraction = fraction 

160 if name: 

161 self.name = name 

162 if units: # and not self.units: 

163 self.units = units 

164 if kwds: 

165 self._kwds = kwds 

166 

167 @property_RO 

168 def adjust(self): 

169 '''Get the C{adjust} setting (C{bool} or C{None}). 

170 ''' 

171 return _xkwds_get(self._kwds, adjust=None) 

172 

173 @property_RO 

174 def datum(self): 

175 '''Get the datum (L{Datum} or C{None} if not applicable). 

176 ''' 

177 return self._datum 

178 

179 def _datum_setter(self, datum): 

180 '''(INTERNAL) Set the datum. 

181 ''' 

182 d = datum or _xattr(self._ps1[0], datum=None) 

183 if d and d is not self._datum: # PYCHOK no cover 

184 self._datum = _ellipsoidal_datum(d, name=self.name) 

185 

186 def discrete(self, point2s, fraction=None): 

187 '''Compute the C{forward, discrete Fréchet} distance. 

188 

189 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], 

190 L{Tuple2LatLon}[] or C{other}[]). 

191 @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to 

192 interpolate intermediate B{C{point2s}} or use 

193 C{None}, C{0} or C{1} for no intermediate 

194 B{C{point2s}} and no I{fractional} indices. 

195 

196 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}. 

197 

198 @raise FrechetError: Insufficient number of B{C{point2s}} or 

199 an invalid B{C{point2}} or B{C{fraction}}. 

200 

201 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit 

202 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. 

203 ''' 

204 return self._discrete(point2s, fraction, self.distance) 

205 

206 def _discrete(self, point2s, fraction, distance): 

207 '''(INTERNAL) Detailed C{discrete} with C{disance}. 

208 ''' 

209 n2, ps2 = self._points2(point2s) 

210 

211 f2 = _fraction(fraction, n2) 

212 p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected 

213 

214 f1 = self.fraction 

215 p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected 

216 

217 def _dF(fi1, fi2): 

218 return distance(p1(self._ps1, fi1), p2(ps2, fi2)) 

219 

220 try: 

221 return _frechet_(self._n1, f1, n2, f2, _dF, self.units) 

222 except TypeError as x: 

223 t = _DOT_(self.classname, self.discrete.__name__) 

224 raise FrechetError(t, cause=x) 

225 

226 def distance(self, point1, point2): 

227 '''Return the distance between B{C{point1}} and B{C{point2s}}, 

228 subject to the supplied optional keyword arguments, see 

229 property C{kwds}. 

230 ''' 

231 return self._func(point1.lat, point1.lon, 

232 point2.lat, point2.lon, **self._kwds) 

233 

234 @property_doc_(''' the index fraction (C{float}).''') 

235 def fraction(self): 

236 '''Get the index fraction (C{float} or C{1}). 

237 ''' 

238 return self._f1 

239 

240 @fraction.setter # PYCHOK setter! 

241 def fraction(self, fraction): 

242 '''Set the index fraction (C{float} in C{EPS}..L{EPS1}) to interpolate 

243 intermediate B{C{point1s}} or use C{None}, C{0} or C{1} for no 

244 intermediate B{C{point1s}} and no I{fractional} indices. 

245 

246 @raise FrechetError: Invalid B{C{fraction}}. 

247 ''' 

248 self._f1 = _fraction(fraction, self._n1) 

249 

250 def _func(self, *args, **kwds): # PYCHOK no cover 

251 notOverloaded(self, *args, **kwds) 

252 

253 @property_RO 

254 def kwds(self): 

255 '''Get the supplied, optional keyword arguments (C{dict}). 

256 ''' 

257 return self._kwds 

258 

259 def point(self, point): 

260 '''Convert a point for the C{.distance} method. 

261 

262 @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon}, 

263 L{Tuple2LatLon} or C{other}). 

264 

265 @return: The converted B{C{point}}. 

266 ''' 

267 return point # pass thru 

268 

269 def points_(self, points, i): 

270 '''Get and convert a point for the C{.distance} method. 

271 

272 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], 

273 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). 

274 @arg i: The B{C{points}} index (C{int}). 

275 

276 @return: The converted B{C{points[i]}}. 

277 ''' 

278 return self.point(points[i]) 

279 

280 def points_fraction(self, points, fi): 

281 '''Get and convert a I{fractional} point for the C{.distance} method. 

282 

283 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], 

284 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). 

285 @arg fi: The I{fractional} index in B{C{points}} (C{float} or C{int}). 

286 

287 @return: The interpolated, converted, intermediate B{C{points[fi]}}. 

288 ''' 

289 return self.point(_fractional(points, fi, None, wrap=None)) # was=self.wrap 

290 

291 def _points2(self, points): 

292 '''(INTERNAL) Check a set of points, overloaded in L{FrechetDistanceTo}. 

293 ''' 

294 return _points2(points, closed=False, Error=FrechetError) 

295 

296 @property_doc_(''' the distance units (C{Unit} or C{str}).''') 

297 def units(self): 

298 '''Get the distance units (C{Unit} or C{str}). 

299 ''' 

300 return self._units 

301 

302 @units.setter # PYCHOK setter! 

303 def units(self, units): 

304 '''Set the distance units (C{Unit} or C{str}). 

305 

306 @raise TypeError: Invalid B{C{units}}. 

307 ''' 

308 self._units = _xUnits(units, Base=Float) 

309 

310 @property_RO 

311 def wrap(self): 

312 '''Get the C{wrap} setting (C{bool} or C{None}). 

313 ''' 

314 return _xkwds_get(self._kwds, wrap=None) 

315 

316 

317class FrechetDegrees(Frechet): 

318 '''DEPRECATED, use an other C{Frechet*} class. 

319 ''' 

320 _units = _Str_degrees 

321 

322 if _FOR_DOCS: 

323 __init__ = Frechet.__init__ 

324 discrete = Frechet.discrete 

325 

326 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover 

327 '''I{Must be overloaded} to return the distance between 

328 B{C{point1}} and B{C{point2}} in C{degrees}. 

329 ''' 

330 notOverloaded(self, point1, point2, *args, **kwds) 

331 

332 

333class FrechetRadians(Frechet): 

334 '''DEPRECATED, use an other C{Frechet*} class. 

335 ''' 

336 _units = _Str_radians 

337 

338 if _FOR_DOCS: 

339 __init__ = Frechet.__init__ 

340 discrete = Frechet.discrete 

341 

342 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover 

343 '''I{Must be overloaded} to return the distance between 

344 B{C{point1}} and B{C{point2}} in C{radians}. 

345 ''' 

346 notOverloaded(self, point1, point2, *args, **kwds) 

347 

348 def point(self, point): 

349 '''Return B{C{point}} as L{PhiLam2Tuple} to maintain 

350 I{backward compatibility} of L{FrechetRadians}. 

351 

352 @return: A L{PhiLam2Tuple}C{(phi, lam)}. 

353 ''' 

354 try: 

355 return point.philam 

356 except AttributeError: 

357 return PhiLam2Tuple(radians(point.lat), radians(point.lon)) 

358 

359 

360class _FrechetMeterRadians(Frechet): 

361 '''(INTERNAL) Returning C{meter} or C{radians} depending on 

362 the optional keyword arguments supplied at instantiation 

363 of the C{Frechet*} sub-class. 

364 ''' 

365 _units = _Str_meter 

366 _units_ = _Str_radians 

367 

368 def discrete(self, point2s, fraction=None): 

369 '''Overloaded method L{Frechet.discrete} to determine 

370 the distance function and units from the optional 

371 keyword arguments given at this instantiation, see 

372 property C{kwds}. 

373 

374 @see: L{Frechet.discrete} for other details. 

375 ''' 

376 return self._discrete(point2s, fraction, _formy._radistance(self)) 

377 

378 def _func_(self, *args, **kwds): # PYCHOK no cover 

379 notOverloaded(self, *args, **kwds) 

380 

381 

382class FrechetCosineAndoyerLambert(_FrechetMeterRadians): 

383 '''Compute the C{Frechet} distance based on the I{angular} distance 

384 in C{radians} from function L{pygeodesy.cosineAndoyerLambert}. 

385 ''' 

386 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap): 

387 '''New L{FrechetCosineAndoyerLambert} calculator/interpolator. 

388 

389 @kwarg datum_wrap: Optional keyword arguments for function 

390 L{pygeodesy.cosineAndoyerLambert}. 

391 

392 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

393 B{C{fraction}}, B{C{name}} and other exceptions. 

394 ''' 

395 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

396 **datum_wrap) 

397 self._func = _formy.cosineAndoyerLambert 

398 self._func_ = _formy.cosineAndoyerLambert_ 

399 

400 if _FOR_DOCS: 

401 discrete = Frechet.discrete 

402 

403 

404class FrechetCosineForsytheAndoyerLambert(_FrechetMeterRadians): 

405 '''Compute the C{Frechet} distance based on the I{angular} distance 

406 in C{radians} from function L{pygeodesy.cosineForsytheAndoyerLambert}. 

407 ''' 

408 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap): 

409 '''New L{FrechetCosineForsytheAndoyerLambert} calculator/interpolator. 

410 

411 @kwarg datum_wrap: Optional keyword arguments for function 

412 L{pygeodesy.cosineAndoyerLambert}. 

413 

414 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

415 B{C{fraction}}, B{C{name}} and other exceptions. 

416 ''' 

417 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

418 **datum_wrap) 

419 self._func = _formy.cosineForsytheAndoyerLambert 

420 self._func_ = _formy.cosineForsytheAndoyerLambert_ 

421 

422 if _FOR_DOCS: 

423 discrete = Frechet.discrete 

424 

425 

426class FrechetCosineLaw(_FrechetMeterRadians): 

427 '''Compute the C{Frechet} distance based on the I{angular} distance 

428 in C{radians} from function L{pygeodesy.cosineLaw}. 

429 

430 @note: See note at function L{pygeodesy.vincentys_}. 

431 ''' 

432 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap): 

433 '''New L{FrechetCosineLaw} calculator/interpolator. 

434 

435 @kwarg radius_wrap: Optional keyword arguments for function 

436 L{pygeodesy.cosineLaw}. 

437 

438 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

439 B{C{fraction}}, B{C{name}} and other exceptions. 

440 ''' 

441 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

442 **radius_wrap) 

443 self._func = _formy.cosineLaw 

444 self._func_ = _formy.cosineLaw_ 

445 

446 if _FOR_DOCS: 

447 discrete = Frechet.discrete 

448 

449 

450class FrechetDistanceTo(Frechet): # FrechetMeter 

451 '''Compute the C{Frechet} distance based on the distance from the 

452 point1s' C{LatLon.distanceTo} method, conventionally in C{meter}. 

453 ''' 

454 _units = _Str_meter 

455 

456 def __init__(self, point1s, fraction=None, name=NN, **distanceTo_kwds): 

457 '''New L{FrechetDistanceTo} calculator/interpolator. 

458 

459 @kwarg distanceTo_kwds: Optional keyword arguments for each 

460 B{C{point1s}}' C{LatLon.distanceTo} 

461 method. 

462 

463 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

464 B{C{fraction}}, B{C{name}} and other exceptions. 

465 

466 @note: All B{C{point1s}} I{must} be instances of the same 

467 ellipsoidal or spherical C{LatLon} class. 

468 ''' 

469 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

470 **distanceTo_kwds) 

471 

472 if _FOR_DOCS: 

473 discrete = Frechet.discrete 

474 

475 def distance(self, p1, p2): 

476 '''Return the distance in C{meter}. 

477 ''' 

478 return p1.distanceTo(p2, **self._kwds) 

479 

480 def _points2(self, points): 

481 '''(INTERNAL) Check a set of points. 

482 ''' 

483 np, ps = Frechet._points2(self, points) 

484 return np, _distanceTo(FrechetError, points=ps) 

485 

486 

487class FrechetEquirectangular(Frechet): 

488 '''Compute the C{Frechet} distance based on the I{equirectangular} 

489 distance in C{radians squared} like function L{pygeodesy.equirectangular}. 

490 ''' 

491 _units = _Str_radians2 

492 

493 def __init__(self, point1s, fraction=None, name=NN, **adjust_limit_wrap): 

494 '''New L{FrechetEquirectangular} calculator/interpolator. 

495 

496 @kwarg adjust_limit_wrap: Optional keyword arguments for function 

497 L{pygeodesy.equirectangular_} I{with default} 

498 C{B{limit}=0} for I{backward compatibility}. 

499 

500 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

501 B{C{fraction}}, B{C{name}} and other exceptions. 

502 ''' 

503 adjust_limit_wrap = _xkwds(adjust_limit_wrap, limit=0) 

504 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

505 **adjust_limit_wrap) 

506 self._func = _formy._equirectangular # helper 

507 

508 if _FOR_DOCS: 

509 discrete = Frechet.discrete 

510 

511 

512class FrechetEuclidean(_FrechetMeterRadians): 

513 '''Compute the C{Frechet} distance based on the I{Euclidean} 

514 distance in C{radians} from function L{pygeodesy.euclidean}. 

515 ''' 

516 def __init__(self, point1s, fraction=None, name=NN, **adjust_radius_wrap): # was=True 

517 '''New L{FrechetEuclidean} calculator/interpolator. 

518 

519 @kwarg adjust_radius_wrap: Optional keyword arguments for 

520 function L{pygeodesy.euclidean}. 

521 

522 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

523 B{C{fraction}}, B{C{name}} and other exceptions. 

524 ''' 

525 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

526 **adjust_radius_wrap) 

527 self._func = _formy.euclidean 

528 self._func_ = _formy.euclidean_ 

529 

530 if _FOR_DOCS: 

531 discrete = Frechet.discrete 

532 

533 

534class FrechetExact(Frechet): 

535 '''Compute the C{Frechet} distance based on the I{angular} distance 

536 in C{degrees} from method L{GeodesicExact}C{.Inverse}. 

537 ''' 

538 _units = _Str_degrees 

539 

540 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap): 

541 '''New L{FrechetExact} calculator/interpolator. 

542 

543 @kwarg datum: Datum to override the default C{Datums.WGS84} and 

544 first B{C{point1s}}' datum (L{Datum}, L{Ellipsoid}, 

545 L{Ellipsoid2} or L{a_f2Tuple}). 

546 @kwarg wrap: Optional keyword argument for method C{Inverse1} 

547 of class L{geodesicx.GeodesicExact}. 

548 

549 @raise TypeError: Invalid B{C{datum}}. 

550 

551 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

552 B{C{fraction}}, B{C{name}} and other exceptions. 

553 ''' 

554 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

555 **wrap) 

556 self._datum_setter(datum) 

557 self._func = self.datum.ellipsoid.geodesicx.Inverse1 # note -x 

558 

559 if _FOR_DOCS: 

560 discrete = Frechet.discrete 

561 

562 

563class FrechetFlatLocal(_FrechetMeterRadians): 

564 '''Compute the C{Frechet} distance based on the I{angular} distance in 

565 C{radians squared} like function L{pygeodesy.flatLocal_}/L{pygeodesy.hubeny}. 

566 ''' 

567 _units_ = _Str_radians2 # see L{flatLocal_} 

568 

569 def __init__(self, point1s, fraction=None, name=NN, **datum_scaled_wrap): 

570 '''New L{FrechetFlatLocal}/L{FrechetHubeny} calculator/interpolator. 

571 

572 @kwarg datum_scaled_wrap: Optional keyword arguments for 

573 function L{pygeodesy.flatLocal}. 

574 

575 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

576 B{C{fraction}}, B{C{name}} and other exceptions. 

577 

578 @note: The distance C{units} are C{radians squared}, not C{radians}. 

579 ''' 

580 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

581 **datum_scaled_wrap) 

582 self._func = _formy.flatLocal 

583 self._func_ = self.datum.ellipsoid._hubeny_2 

584 

585 if _FOR_DOCS: 

586 discrete = Frechet.discrete 

587 

588 

589class FrechetFlatPolar(_FrechetMeterRadians): 

590 '''Compute the C{Frechet} distance based on the I{angular} distance 

591 in C{radians} from function L{flatPolar_}. 

592 ''' 

593 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap): 

594 '''New L{FrechetFlatPolar} calculator/interpolator. 

595 

596 @kwarg radius_wrap: Optional keyword arguments for function 

597 L{pygeodesy.flatPolar}. 

598 

599 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

600 B{C{fraction}}, B{C{name}} and other exceptions. 

601 ''' 

602 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

603 **radius_wrap) 

604 self._func = _formy.flatPolar 

605 self._func_ = _formy.flatPolar_ 

606 

607 if _FOR_DOCS: 

608 discrete = Frechet.discrete 

609 

610 

611class FrechetHaversine(_FrechetMeterRadians): 

612 '''Compute the C{Frechet} distance based on the I{angular} 

613 distance in C{radians} from function L{pygeodesy.haversine_}. 

614 

615 @note: See note at function L{pygeodesy.vincentys_}. 

616 ''' 

617 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap): 

618 '''New L{FrechetHaversine} calculator/interpolator. 

619 

620 @kwarg radius_wrap: Optional keyword arguments for function 

621 L{pygeodesy.haversine}. 

622 

623 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

624 B{C{fraction}}, B{C{name}} and other exceptions. 

625 ''' 

626 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

627 **radius_wrap) 

628 self._func = _formy.haversine 

629 self._func_ = _formy.haversine_ 

630 

631 if _FOR_DOCS: 

632 discrete = Frechet.discrete 

633 

634 

635class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny 

636 if _FOR_DOCS: 

637 __doc__ = FrechetFlatLocal.__doc__ 

638 __init__ = FrechetFlatLocal.__init__ 

639 discrete = FrechetFlatLocal.discrete 

640 distance = FrechetFlatLocal.discrete 

641 

642 

643class FrechetKarney(Frechet): 

644 '''Compute the C{Frechet} distance based on the I{angular} 

645 distance in C{degrees} from I{Karney}'s U{geographiclib 

646 <https://PyPI.org/project/geographiclib>} U{geodesic.Geodesic 

647 <https://GeographicLib.SourceForge.io/Python/doc/code.html>} 

648 C{Inverse} method. 

649 ''' 

650 _units = _Str_degrees 

651 

652 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap): 

653 '''New L{FrechetKarney} calculator/interpolator. 

654 

655 @kwarg datum: Datum to override the default C{Datums.WGS84} and 

656 first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, 

657 L{Ellipsoid2} or L{a_f2Tuple}). 

658 @kwarg wrap: Optional keyword argument for method C{Inverse1} 

659 of class L{geodesicw.Geodesic}. 

660 

661 @raise ImportError: Package U{geographiclib 

662 <https://PyPI.org/project/geographiclib>} missing. 

663 

664 @raise TypeError: Invalid B{C{datum}}. 

665 

666 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

667 B{C{fraction}}, B{C{name}} and other exceptions. 

668 ''' 

669 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

670 **wrap) 

671 self._datum_setter(datum) 

672 self._func = self.datum.ellipsoid.geodesic.Inverse1 

673 

674 if _FOR_DOCS: 

675 discrete = Frechet.discrete 

676 

677 

678class FrechetThomas(_FrechetMeterRadians): 

679 '''Compute the C{Frechet} distance based on the I{angular} distance 

680 in C{radians} from function L{pygeodesy.thomas_}. 

681 ''' 

682 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap): 

683 '''New L{FrechetThomas} calculator/interpolator. 

684 

685 @kwarg datum_wrap: Optional keyword argument for function 

686 L{pygeodesy.thomas}. 

687 

688 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

689 B{C{fraction}}, B{C{name}} and other exceptions. 

690 ''' 

691 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

692 **datum_wrap) 

693 self._func = _formy.thomas 

694 self._func_ = _formy.thomas_ 

695 

696 if _FOR_DOCS: 

697 discrete = Frechet.discrete 

698 

699 

700class FrechetVincentys(_FrechetMeterRadians): 

701 '''Compute the C{Frechet} distance based on the I{angular} 

702 distance in C{radians} from function L{pygeodesy.vincentys_}. 

703 

704 @note: See note at function L{pygeodesy.vincentys_}. 

705 ''' 

706 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap): 

707 '''New L{FrechetVincentys} calculator/interpolator. 

708 

709 @kwarg radius_wrap: Optional keyword arguments for function 

710 L{pygeodesy.vincentys}. 

711 

712 @see: L{Frechet.__init__} for details about B{C{point1s}}, 

713 B{C{fraction}}, B{C{name}} and other exceptions. 

714 ''' 

715 Frechet.__init__(self, point1s, fraction=fraction, name=name, 

716 **radius_wrap) 

717 self._func = _formy.vincentys 

718 self._func_ = _formy.vincentys_ 

719 

720 if _FOR_DOCS: 

721 discrete = Frechet.discrete 

722 

723 

724def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14 

725 '''(INTERNAL) Recursive core of function L{frechet_} 

726 and method C{discrete} of C{Frechet...} classes. 

727 ''' 

728 iFs = {} 

729 

730 def iF(i): # cache index, depth ints and floats 

731 return iFs.setdefault(i, i) 

732 

733 cF = _defaultdict(dict) 

734 

735 def _rF(i, j, r): # recursive Fréchet 

736 i = iF(i) 

737 j = iF(j) 

738 try: 

739 t = cF[i][j] 

740 except KeyError: 

741 r = iF(r + 1) 

742 try: 

743 if i > 0: 

744 if j > 0: 

745 t = min(_rF(i - fi, j, r), 

746 _rF(i - fi, j - fj, r), 

747 _rF(i, j - fj, r)) 

748 elif j < 0: 

749 raise IndexError 

750 else: # j == 0 

751 t = _rF(i - fi, 0, r) 

752 elif i < 0: 

753 raise IndexError 

754 

755 elif j > 0: # i == 0 

756 t = _rF(0, j - fj, r) 

757 elif j < 0: # i == 0 

758 raise IndexError 

759 else: # i == j == 0 

760 t = (NINF, i, j, r) 

761 

762 d = dF(i, j) 

763 if d > t[0]: 

764 t = (d, i, j, r) 

765 except IndexError: 

766 t = (INF, i, j, r) 

767 cF[i][j] = t 

768 return t 

769 

770 t = _rF(ni - 1, nj - 1, 0) 

771 t += (sum(map(len, cF.values())), units) 

772# del cF, iFs 

773 return Frechet6Tuple(t) # *t 

774 

775 

776def frechet_(point1s, point2s, distance=None, units=NN): 

777 '''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} 

778 distance between two paths, each given as a set of points. 

779 

780 @arg point1s: First set of points (C{LatLon}[], L{Numpy2LatLon}[], 

781 L{Tuple2LatLon}[] or C{other}[]). 

782 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], 

783 L{Tuple2LatLon}[] or C{other}[]). 

784 @kwarg distance: Callable returning the distance between a B{C{point1s}} 

785 and a B{C{point2s}} point (signature C{(point1, point2)}). 

786 @kwarg units: Optional, the distance units (C{Unit} or C{str}). 

787 

788 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1} 

789 and C{fi2} are type C{int} indices into B{C{point1s}} respectively 

790 B{C{point2s}}. 

791 

792 @raise FrechetError: Insufficient number of B{C{point1s}} or B{C{point2s}}. 

793 

794 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit() 

795 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. 

796 

797 @raise TypeError: If B{C{distance}} is not a callable. 

798 

799 @note: Function L{frechet_} does I{not} support I{fractional} indices 

800 for intermediate B{C{point1s}} and B{C{point2s}}. 

801 ''' 

802 if not callable(distance): 

803 raise _IsnotError(callable.__name__, distance=distance) 

804 

805 n1, ps1 = _points2(point1s, closed=False, Error=FrechetError) 

806 n2, ps2 = _points2(point2s, closed=False, Error=FrechetError) 

807 

808 def _dF(i1, i2): 

809 return distance(ps1[i1], ps2[i2]) 

810 

811 return _frechet_(n1, 1, n2, 1, _dF, units) 

812 

813 

814class Frechet6Tuple(_NamedTuple): 

815 '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete} 

816 U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance 

817 C{fd}, I{fractional} indices C{fi1} and C{fi2} as C{FIx}, the 

818 recursion depth C{r}, the number of distances computed C{n} and 

819 the L{units} class or class or name of the distance C{units}. 

820 

821 If I{fractional} indices C{fi1} and C{fi2} are C{int}, the 

822 returned C{fd} is the distance between C{point1s[fi1]} and 

823 C{point2s[fi2]}. For C{float} indices, the distance is 

824 between an intermediate point along C{point1s[int(fi1)]} and 

825 C{point1s[int(fi1) + 1]} respectively an intermediate point 

826 along C{point2s[int(fi2)]} and C{point2s[int(fi2) + 1]}. 

827 

828 Use function L{fractional} to compute the point at a 

829 I{fractional} index. 

830 ''' 

831 _Names_ = ('fd', 'fi1', 'fi2', 'r', _n_, _units_) 

832 _Units_ = (_Pass, FIx, FIx, Number_, Number_, _Pass) 

833 

834 def toUnits(self, **Error): # PYCHOK expected 

835 '''Overloaded C{_NamedTuple.toUnits} for C{fd} units. 

836 ''' 

837 U = _xUnit(self.units, Float) # PYCHOK expected 

838 self._Units_ = (U,) + Frechet6Tuple._Units_[1:] 

839 return _NamedTuple.toUnits(self, **Error) 

840 

841# def __gt__(self, other): 

842# _xinstanceof(Frechet6Tuple, other=other) 

843# return self if self.fd > other.fd else other # PYCHOK .fd=[0] 

844# 

845# def __lt__(self, other): 

846# _xinstanceof(Frechet6Tuple, other=other) 

847# return self if self.fd < other.fd else other # PYCHOK .fd=[0] 

848 

849# **) MIT License 

850# 

851# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

852# 

853# Permission is hereby granted, free of charge, to any person obtaining a 

854# copy of this software and associated documentation files (the "Software"), 

855# to deal in the Software without restriction, including without limitation 

856# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

857# and/or sell copies of the Software, and to permit persons to whom the 

858# Software is furnished to do so, subject to the following conditions: 

859# 

860# The above copyright notice and this permission notice shall be included 

861# in all copies or substantial portions of the Software. 

862# 

863# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

864# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

865# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

866# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

867# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

868# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

869# OTHER DEALINGS IN THE SOFTWARE.