Coverage for pygeodesy/heights.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Height interpolations at C{LatLon} points from C{knots}. 

5 

6Classes L{HeightCubic}, L{HeightIDWcosineAndoyerLambert}, 

7L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWcosineLaw}, 

8L{HeightIDWdistanceTo}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, 

9L{HeightIDWflatLocal}, L{HeightIDWflatPolar}, L{HeightIDWhaversine}, 

10L{HeightIDWhubeny}, L{HeightIDWkarney}, L{HeightIDWthomas}, L{HeightIDWvincentys}, 

11L{HeightLinear}, L{HeightLSQBiSpline} and L{HeightSmoothBiSpline} 

12to interpolate the height of C{LatLon} locations or separate 

13lat-/longitudes from a set of C{LatLon} points with I{known heights}. 

14 

15Typical usage 

16============= 

17 

181. Get or create a set of C{LatLon} points with I{known heights}, called 

19C{knots}. The C{knots} do not need to be ordered in any particular way. 

20 

21C{>>> ...} 

22 

232. Select one of the C{Height} classes for height interpolation 

24 

25C{>>> from pygeodesy import HeightCubic # or other Height... as HeightXyz} 

26 

273. Instantiate a height interpolator with the C{knots} and use keyword 

28arguments to select different interpolation options 

29 

30C{>>> hinterpolator = HeightXyz(knots, **options)} 

31 

324. Get the interpolated height of other C{LatLon} location(s) with 

33 

34C{>>> ll = LatLon(1, 2, ...)} 

35 

36C{>>> h = hinterpolator(ll)} 

37 

38or 

39 

40C{>>> h0, h1, h2, ... = hinterpolator(ll0, ll1, ll2, ...)} 

41 

42or a list, tuple, generator, etc. of C{LatLon}s 

43 

44C{>>> hs = hinterpolator(lls)} 

45 

465. For separate lat- and longitudes invoke the C{.height} method 

47 

48C{>>> h = hinterpolator.height(lat, lon)} 

49 

50or as 2 lists, 2 tuples, etc. 

51 

52C{>>> hs = hinterpolator.height(lats, lons)} 

53 

54@note: Classes L{HeightCubic} and L{HeightLinear} require package U{numpy 

55 <https://PyPI.org/project/numpy>}, classes L{HeightLSQBiSpline} and 

56 L{HeightSmoothBiSpline} require package U{scipy<https://SciPy.org>}. 

57 Classes L{HeightIDWkarney} and L{HeightIDWdistanceTo} -if used with 

58 L{ellipsoidalKarney.LatLon} points- require I{Karney}'s U{geographiclib 

59 <https://PyPI.org/project/geographiclib>} to be installed. 

60 

61@note: Errors from C{scipy} are raised as L{SciPyError}s. Warnings issued 

62 by C{scipy} can be thrown as L{SciPyWarning} exceptions, provided 

63 Python C{warnings} are filtered accordingly, see L{SciPyWarning}. 

64 

65@see: U{SciPy<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} 

66 Interpolation. 

67''' 

68# make sure int/int division yields float quotient, see .basics 

69from __future__ import division as _; del _ # PYCHOK semicolon 

70 

71from pygeodesy.basics import isscalar, len2, map1, map2, _xnumpy, _xscipy 

72from pygeodesy.constants import EPS, PI, PI2, _0_0, _90_0, _180_0 

73from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

74from pygeodesy.errors import _AssertionError, LenError, PointsError, \ 

75 _SciPyIssue, _xattr, _xkwds, _xkwds_get 

76# from pygeodesy.fmath import fidw # _MODS 

77# from pygeodesy.formy import cosineAndoyerLambert, cosineForsytheAndoyerLambert, \ 

78# cosineLaw, equirectangular_, euclidean, flatLocal, \ 

79# flatPolar, haversine, thomas, vincentys # _MODS 

80from pygeodesy.interns import NN, _COMMASPACE_, _cubic_, _insufficient_, _knots_, \ 

81 _linear_, _NOTEQUAL_, _PLUS_, _scipy_, _SPACE_, \ 

82 _STAR_, _version2 

83from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS 

84from pygeodesy.named import _Named 

85from pygeodesy.points import _distanceTo, LatLon_, Fmt, radians, _Wrap 

86from pygeodesy.props import Property_RO, property_RO 

87# from pygeodesy.streprs import Fmt # from .points 

88from pygeodesy.units import _isDegrees, Float_, Int_ 

89# from pygeodesy.utily import _Wrap # from .points 

90 

91# from math import radians # from .points 

92 

93__all__ = _ALL_LAZY.heights 

94__version__ = '24.04.07' 

95 

96_error_ = 'error' 

97_llis_ = 'llis' 

98_smoothing_ = 'smoothing' 

99 

100 

101class HeightError(PointsError): 

102 '''Height interpolator C{Height...} or interpolation issue. 

103 ''' 

104 pass 

105 

106 

107def _alist(ais): 

108 # return list of floats, not numpy.float64s 

109 return list(map(float, ais)) 

110 

111 

112def _ascalar(ais): # in .geoids 

113 # return single float, not numpy.float64 

114 ais = list(ais) # np.array, etc. to list 

115 if len(ais) != 1: 

116 n = Fmt.PAREN(len=repr(ais)) 

117 t = _SPACE_(len(ais), _NOTEQUAL_, 1) 

118 raise _AssertionError(n, txt=t) 

119 return float(ais[0]) # remove np.<type> 

120 

121 

122def _atuple(ais): 

123 # return tuple of floats, not numpy.float64s 

124 return tuple(map(float, ais)) 

125 

126 

127def _as_llis2(llis, m=1, Error=HeightError): # in .geoids 

128 # determine return type and convert lli C{LatLon}s to list 

129 if not isinstance(llis, tuple): # llis are *args 

130 n = Fmt.PAREN(type_=_STAR_(NN, _llis_)) 

131 raise _AssertionError(n, txt=repr(llis)) 

132 

133 n = len(llis) 

134 if n == 1: # convert single lli to 1-item list 

135 llis = llis[0] 

136 try: 

137 n, llis = len2(llis) 

138 _as = _alist # return list of interpolated heights 

139 except TypeError: # single lli 

140 n, llis = 1, [llis] 

141 _as = _ascalar # return single interpolated heights 

142 else: # of 0, 2 or more llis 

143 _as = _atuple # return tuple of interpolated heights 

144 

145 if n < m: 

146 raise _insufficientError(m, Error=Error, llis=n) 

147 return _as, llis 

148 

149 

150def _height_called(inst, lats, lons, Error=HeightError, **wrap): # in .geoids 

151 LLis, d = inst._LLis, inst.datum 

152 if _isDegrees(lats) and _isDegrees(lons): 

153 llis = LLis(lats, lons, datum=d) 

154 else: 

155 n, lats = len2(lats) 

156 m, lons = len2(lons) 

157 if n != m: 

158 # format a LenError, but raise an Error 

159 e = LenError(inst.__class__, lats=n, lons=m, txt=None) 

160 raise e if Error is LenError else Error(str(e)) 

161 llis = [LLis(*t, datum=d) for t in zip(lats, lons)] 

162 return inst(llis, **wrap) # __call__(lli) or __call__(llis) 

163 

164 

165def _insufficientError(need, Error=HeightError, **name_value): # PYCHOK no cover 

166 # create an insufficient Error instance 

167 t = _COMMASPACE_(_insufficient_, str(need) + _PLUS_) 

168 return Error(txt=t, **name_value) 

169 

170 

171def _ordedup(ts, lo=EPS, hi=PI2-EPS): 

172 # clip, order and remove duplicates 

173 # p, ks = 0, [] 

174 # for k in sorted(max(lo, min(hi, t)) for t in ts): 

175 # if k > p: 

176 # ks.append(k) 

177 # p = k 

178 # return ks 

179 return sorted(set(max(lo, min(hi, t)) for t in ts)) # list 

180 

181 

182def _xyhs(lls, wrap=False, name=_llis_): 

183 # map (lat, lon, h) to (x, y, h) in radians, offset 

184 # x as 0 <= lon <= PI2 and y as 0 <= lat <= PI 

185 _0, _90, _180 = _0_0, _90_0, _180_0 

186 _m, _r, _w = max, radians, _Wrap._latlonop(wrap) 

187 try: 

188 for i, ll in enumerate(lls): 

189 y, x = _w(ll.lat, ll.lon) 

190 yield _m(_0, _r(x + _180)), \ 

191 _m(_0, _r(y + _90)), ll.height 

192 except Exception as e: 

193 i = Fmt.INDEX(name, i) 

194 raise HeightError(i, ll, cause=e) 

195 

196 

197class _HeightBase(_Named): # in .geoids 

198 '''(INTERNAL) Interpolator base class. 

199 ''' 

200 _datum = _WGS84 # default 

201 _kmin = 2 # min number of knots 

202 _LLis = LatLon_ # ._height class 

203 _np_sp = None # (numpy, scipy) 

204 _wrap = None # wrap knots and llis 

205 

206 @property_RO 

207 def datum(self): 

208 '''Get the C{datum} setting or the default (L{Datum}). 

209 ''' 

210 return self._datum 

211 

212 @property_RO 

213 def kmin(self): 

214 '''Get the minimum number of knots (C{int}). 

215 ''' 

216 return self._kmin 

217 

218 @property_RO 

219 def wrap(self): 

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

221 ''' 

222 return self._wrap 

223 

224 

225class _HeightsBase(_HeightBase): # in .geoids 

226 '''(INTERNAL) Interpolator base class. 

227 ''' 

228 _np_sp = None # (numpy, scipy) 

229 

230 def __call__(self, *llis, **wrap): # PYCHOK no cover 

231 '''Interpolate the height for one or several locations. I{Must be overloaded}. 

232 

233 @arg llis: One or more locations (C{LatLon}s), all positional. 

234 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{llis}} 

235 locations (C{bool}), overriding the B{C{knots}} 

236 setting. 

237 

238 @return: A single interpolated height (C{float}) or a list 

239 or tuple of interpolated heights (C{float}s). 

240 

241 @raise HeightError: Insufficient number of B{C{llis}} or 

242 an invalid B{C{lli}}. 

243 

244 @raise SciPyError: A C{scipy} issue. 

245 

246 @raise SciPyWarning: A C{scipy} warning as exception. 

247 ''' 

248 self._notOverloaded(callername='__call__', *llis, **wrap) 

249 

250 def _as_xyllis4(self, llis, **wrap): 

251 # convert lli C{LatLon}s to tuples or C{NumPy} arrays of 

252 # C{SciPy} sphericals and determine the return type 

253 atype = self.numpy.array 

254 wrap = _xkwds(wrap, wrap=self._wrap) 

255 _as, llis = _as_llis2(llis) 

256 xis, yis, _ = zip(*_xyhs(llis, **wrap)) # PYCHOK yield 

257 return _as, atype(xis), atype(yis), llis 

258 

259 def _ev(self, *args): # PYCHOK no cover 

260 '''(INTERNAL) I{Must be overloaded}.''' 

261 self._notOverloaded(*args) 

262 

263 def _eval(self, llis, **wrap): # XXX single arg, not *args 

264 _as, xis, yis, _ = self._as_xyllis4(llis, **wrap) 

265 try: # SciPy .ev signature: y first, then x! 

266 return _as(self._ev(yis, xis)) 

267 except Exception as x: 

268 raise _SciPyIssue(x) 

269 

270 def height(self, lats, lons, **wrap): # PYCHOK no cover 

271 '''Interpolate the height for one or several lat-/longitudes. I{Must be overloaded}. 

272 

273 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). 

274 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). 

275 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}} 

276 and B{C{lons}} locationts (C{bool}), overriding 

277 the B{C{knots}} setting. 

278 

279 @return: A single interpolated height (C{float}) or a list of 

280 interpolated heights (C{float}s). 

281 

282 @raise HeightError: Insufficient or non-matching number of 

283 B{C{lats}} and B{C{lons}}. 

284 

285 @raise SciPyError: A C{scipy} issue. 

286 

287 @raise SciPyWarning: A C{scipy} warning as exception. 

288 ''' 

289 self._notOverloaded(lats, lons, **wrap) 

290 

291 def _np_sp2(self, throwarnings=False): 

292 '''(INTERNAL) Import C{numpy} and C{scipy}, once. 

293 ''' 

294 t = _HeightsBase._np_sp 

295 if not t: 

296 # raise SciPyWarnings, but not if 

297 # scipy has already been imported 

298 if throwarnings: # PYCHOK no cover 

299 import sys 

300 if _scipy_ not in sys.modules: 

301 import warnings 

302 warnings.filterwarnings(_error_) 

303 

304 sp = _xscipy(self.__class__, 1, 2) 

305 np = _xnumpy(self.__class__, 1, 9) 

306 

307 _HeightsBase._np_sp = t = np, sp 

308 return t 

309 

310 @Property_RO 

311 def numpy(self): 

312 '''Get the C{numpy} module or C{None}. 

313 ''' 

314 np, _ = self._np_sp2() 

315 return np 

316 

317 @Property_RO 

318 def scipy(self): 

319 '''Get the C{scipy} module or C{None}. 

320 ''' 

321 _, sp = self._np_sp2() 

322 return sp 

323 

324 @Property_RO 

325 def scipy_interpolate(self): 

326 '''Get the C{scipy.interpolate} module or C{None}. 

327 ''' 

328 _ = self.scipy 

329 import scipy.interpolate as spi # scipy 1.2.2 

330 return spi 

331 

332 def _scipy_version(self, **n): 

333 '''Get the C{scipy} version as 2- or 3-tuple C{(major, minor, micro)}. 

334 ''' 

335 return _version2(self.scipy.version.version, **n) 

336 

337 def _xyhs3(self, knots, **wrap): 

338 # convert knot C{LatLon}s to tuples or C{NumPy} arrays and C{SciPy} sphericals 

339 xs, ys, hs = zip(*_xyhs(knots, name=_knots_, **wrap)) # PYCHOK yield 

340 n = len(hs) 

341 if n < self.kmin: 

342 raise _insufficientError(self.kmin, knots=n) 

343 return map1(self.numpy.array, xs, ys, hs) 

344 

345 

346class HeightCubic(_HeightsBase): 

347 '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ 

348 doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} 

349 C{kind='cubic'}. 

350 ''' 

351 _interp2d = None 

352 _kind = _cubic_ 

353 _kmin = 16 

354 

355 def __init__(self, knots, name=NN, **wrap): 

356 '''New L{HeightCubic} interpolator. 

357 

358 @arg knots: The points with known height (C{LatLon}s). 

359 @kwarg name: Optional name for this height interpolator (C{str}). 

360 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{knots}} 

361 and B{C{llis}} locations (C{bool}). 

362 

363 @raise HeightError: Insufficient number of B{C{knots}} or 

364 invalid B{C{knot}}. 

365 

366 @raise ImportError: Package C{numpy} or C{scipy} not found 

367 or not installed. 

368 

369 @raise SciPyError: A C{scipy.interpolate.interp2d} issue. 

370 

371 @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning 

372 as exception. 

373 ''' 

374 spi = self.scipy_interpolate 

375 

376 xs, ys, hs = self._xyhs3(knots, **wrap) 

377 try: # SciPy.interpolate.interp2d kind 'linear' or 'cubic' 

378 self._interp2d = spi.interp2d(xs, ys, hs, kind=self._kind) 

379 except Exception as x: 

380 raise _SciPyIssue(x) 

381 

382 if name: 

383 self.name = name 

384 

385 def __call__(self, *llis, **wrap): 

386 '''Interpolate the height for one or several locations. 

387 

388 @raise SciPyError: A C{scipy.interpolate.interp2d} issue. 

389 

390 @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning 

391 as exception. 

392 

393 @see: L{Here<_HeightsBase.__call__>} for other details. 

394 ''' 

395 return _HeightsBase._eval(self, llis, **wrap) 

396 

397 def _ev(self, yis, xis): # PYCHOK expected 

398 # to make SciPy .interp2d signature(x, y), single (x, y) 

399 # match SciPy .ev signature(ys, xs), flipped multiples 

400 return map(self._interp2d, xis, yis) 

401 

402 def height(self, lats, lons, **wrap): 

403 '''Interpolate the height for one or several lat-/longitudes. 

404 

405 @raise SciPyError: A C{scipy.interpolate.interp2d} issue. 

406 

407 @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning 

408 as exception. 

409 

410 @see: L{Here<_HeightsBase.height>} for other details. 

411 ''' 

412 return _height_called(self, lats, lons, **wrap) 

413 

414 

415class HeightLinear(HeightCubic): 

416 '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ 

417 doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} 

418 C{kind='linear'}. 

419 ''' 

420 _kind = _linear_ 

421 _kmin = 2 

422 

423 def __init__(self, knots, name=NN, **wrap): 

424 '''New L{HeightLinear} interpolator. 

425 

426 @see: L{Here<HeightCubic.__init__>} for details. 

427 ''' 

428 HeightCubic.__init__(self, knots, name=name, **wrap) 

429 

430 if _FOR_DOCS: 

431 __call__ = HeightCubic.__call__ 

432 height = HeightCubic.height 

433 

434 

435class HeightLSQBiSpline(_HeightsBase): 

436 '''Height interpolator using C{SciPy} U{LSQSphereBivariateSpline 

437 <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. 

438 interpolate.LSQSphereBivariateSpline.html>}. 

439 ''' 

440 _kmin = 16 # k = 3, always 

441 

442 def __init__(self, knots, weight=None, name=NN, **wrap): 

443 '''New L{HeightLSQBiSpline} interpolator. 

444 

445 @arg knots: The points with known height (C{LatLon}s). 

446 @kwarg weight: Optional weight or weights for each B{C{knot}} 

447 (C{scalar} or C{scalar}s). 

448 @kwarg name: Optional name for this height interpolator (C{str}). 

449 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{knots}} 

450 and B{C{llis}} locations (C{bool}). 

451 

452 @raise HeightError: Insufficient number of B{C{knots}} or 

453 an invalid B{C{knot}} or B{C{weight}}. 

454 

455 @raise LenError: Unequal number of B{C{knots}} and B{C{weight}}s. 

456 

457 @raise ImportError: Package C{numpy} or C{scipy} not found 

458 or not installed. 

459 

460 @raise SciPyError: A C{scipy} C{LSQSphereBivariateSpline} issue. 

461 

462 @raise SciPyWarning: A C{scipy} C{LSQSphereBivariateSpline} 

463 warning as exception. 

464 ''' 

465 np = self.numpy 

466 spi = self.scipy_interpolate 

467 

468 xs, ys, hs = self._xyhs3(knots, **wrap) 

469 n = len(hs) 

470 

471 w = weight 

472 if isscalar(w): 

473 w = float(w) 

474 if w <= 0: 

475 raise HeightError(weight=w) 

476 w = [w] * n 

477 elif w is not None: 

478 m, w = len2(w) 

479 if m != n: 

480 raise LenError(HeightLSQBiSpline, weight=m, knots=n) 

481 w = map2(float, w) 

482 m = min(w) 

483 if m <= 0: # PYCHOK no cover 

484 w = Fmt.INDEX(weight=w.index(m)) 

485 raise HeightError(w, m) 

486 try: 

487 T = 1.0e-4 # like SciPy example 

488 ps = np.array(_ordedup(xs, T, PI2 - T)) 

489 ts = np.array(_ordedup(ys, T, PI - T)) 

490 self._ev = spi.LSQSphereBivariateSpline(ys, xs, hs, 

491 ts, ps, eps=EPS, w=w).ev 

492 except Exception as x: 

493 raise _SciPyIssue(x) 

494 

495 if name: 

496 self.name = name 

497 

498 def __call__(self, *llis, **wrap): 

499 '''Interpolate the height for one or several locations. 

500 

501 @raise SciPyError: A C{scipy} C{LSQSphereBivariateSpline} issue. 

502 

503 @raise SciPyWarning: A C{scipy} C{LSQSphereBivariateSpline} 

504 warning as exception. 

505 

506 @see: L{Here<_HeightsBase.__call__>} for other details. 

507 ''' 

508 return _HeightsBase._eval(self, llis, **wrap) 

509 

510 def height(self, lats, lons, **wrap): 

511 '''Interpolate the height for one or several lat-/longitudes. 

512 

513 @raise SciPyError: A C{scipy} C{LSQSphereBivariateSpline} issue. 

514 

515 @raise SciPyWarning: A C{scipy} C{LSQSphereBivariateSpline} 

516 warning as exception. 

517 

518 @see: L{Here<_HeightsBase.height>} for other details. 

519 ''' 

520 return _height_called(self, lats, lons, **wrap) 

521 

522 

523class HeightSmoothBiSpline(_HeightsBase): 

524 '''Height interpolator using C{SciPy} U{SmoothSphereBivariateSpline 

525 <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. 

526 interpolate.SmoothSphereBivariateSpline.html>}. 

527 ''' 

528 _kmin = 16 # k = 3, always 

529 

530 def __init__(self, knots, s=4, name=NN, **wrap): 

531 '''New L{HeightSmoothBiSpline} interpolator. 

532 

533 @arg knots: The points with known height (C{LatLon}s). 

534 @kwarg s: The spline smoothing factor (C{scalar}), default C{4}. 

535 @kwarg name: Optional name for this height interpolator (C{str}). 

536 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{knots}} 

537 and any called B{C{llis}} and height B{C{lats}} 

538 and B{C{lons}} locations (C{bool}). 

539 

540 @raise HeightError: Insufficient number of B{C{knots}} or 

541 an invalid B{C{knot}} or B{C{s}}. 

542 

543 @raise ImportError: Package C{numpy} or C{scipy} not found 

544 or not installed. 

545 

546 @raise SciPyError: A C{scipy} C{SmoothSphereBivariateSpline} issue. 

547 

548 @raise SciPyWarning: A C{scipy} C{SmoothSphereBivariateSpline} 

549 warning as exception. 

550 ''' 

551 spi = self.scipy_interpolate 

552 

553 s = Float_(s, name=_smoothing_, Error=HeightError, low=4) 

554 

555 xs, ys, hs = self._xyhs3(knots, **wrap) 

556 try: 

557 self._ev = spi.SmoothSphereBivariateSpline(ys, xs, hs, 

558 eps=EPS, s=s).ev 

559 except Exception as x: 

560 raise _SciPyIssue(x) 

561 

562 if name: 

563 self.name = name 

564 

565 def __call__(self, *llis, **wrap): 

566 '''Interpolate the height for one or several locations. 

567 

568 @raise SciPyError: A C{scipy} C{SmoothSphereBivariateSpline} issue. 

569 

570 @raise SciPyWarning: A C{scipy} C{SmoothSphereBivariateSpline} 

571 warning as exception. 

572 

573 @see: L{Here<_HeightsBase.__call__>} for other details. 

574 ''' 

575 return _HeightsBase._eval(self, llis, **wrap) 

576 

577 def height(self, lats, lons, **wrap): 

578 '''Interpolate the height for one or several lat-/longitudes. 

579 

580 @raise SciPyError: A C{scipy} C{SmoothSphereBivariateSpline} issue. 

581 

582 @raise SciPyWarning: A C{scipy} C{SmoothSphereBivariateSpline} 

583 warning as exception. 

584 

585 @see: L{Here<_HeightsBase.height>} for other details. 

586 ''' 

587 return _height_called(self, lats, lons, **wrap) 

588 

589 

590class _HeightIDW(_HeightBase): 

591 '''(INTERNAL) Base class for U{Inverse Distance Weighting 

592 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) height 

593 interpolators. 

594 

595 @see: U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ 

596 geostatistics/Inverse-Distance-Weighting/index.html>}, 

597 U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ 

598 shepard_interp_2d/shepard_interp_2d.html>} and other C{_HeightIDW*} 

599 classes. 

600 ''' 

601 _beta = 0 # fidw inverse power 

602 _func = None # formy function 

603 _knots = () # knots list or tuple 

604 _kwds = {} # func_ options 

605 

606 def __init__(self, knots, beta=2, name=NN, **kwds): 

607 '''New C{_HeightIDW*} interpolator. 

608 

609 @arg knots: The points with known height (C{LatLon}s). 

610 @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). 

611 @kwarg name: Optional name for this height interpolator (C{str}). 

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

613 retrievable with property C{kwds}. 

614 

615 @raise HeightError: Insufficient number of B{C{knots}} or 

616 an invalid B{C{knot}} or B{C{beta}}. 

617 ''' 

618 if name: 

619 self.name = name 

620 n, self._knots = len2(knots) 

621 if n < self.kmin: 

622 raise _insufficientError(self.kmin, knots=n) 

623 self.beta = beta 

624 self._kwds = kwds or {} 

625 

626 def __call__(self, *llis, **wrap): 

627 '''Interpolate the height for one or several locations. 

628 

629 @arg llis: One or more locations (C{LatLon}s), all positional. 

630 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{llis}} 

631 locations (C{bool}). 

632 

633 @return: A single interpolated height (C{float}) or a list 

634 or tuple of interpolated heights (C{float}s). 

635 

636 @raise HeightError: Insufficient number of B{C{llis}}, an 

637 invalid B{C{lli}} or L{pygeodesy.fidw} 

638 issue. 

639 ''' 

640 def _xy2(lls, wrap=False): 

641 _w = _Wrap._latlonop(wrap) 

642 try: # like _xyhs above, but degrees 

643 for i, ll in enumerate(lls): 

644 yield _w(ll.lon, ll.lat) 

645 except Exception as e: 

646 i = Fmt.INDEX(llis=i) 

647 raise HeightError(i, ll, cause=e) 

648 

649 _as, llis = _as_llis2(llis) 

650 return _as(map(self._hIDW, *zip(*_xy2(llis, **wrap)))) 

651 

652 @property_RO 

653 def adjust(self): 

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

655 ''' 

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

657 

658 @property 

659 def beta(self): 

660 '''Get the inverse distance power (C{int}). 

661 ''' 

662 return self._beta 

663 

664 @beta.setter # PYCHOK setter! 

665 def beta(self, beta): 

666 '''Set the inverse distance power (C{int} 1, 2, or 3). 

667 

668 @raise HeightError: Invalid B{C{beta}}. 

669 ''' 

670 self._beta = Int_(beta=beta, Error=HeightError, low=1, high=3) 

671 

672 @property_RO 

673 def datum(self): 

674 '''Get the C{datum} setting or the default (L{Datum}). 

675 ''' 

676 return _xkwds_get(self._kwds, datum=self._datum) 

677 

678 def _datum_setter(self, datum): 

679 '''(INTERNAL) Set the default C{datum}. 

680 ''' 

681 d = datum or _xattr(self._knots[0], datum=None) 

682 if d and d is not self._datum: 

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

684 

685 def _distances(self, x, y): 

686 '''(INTERNAL) Yield distances to C{(x, y)}. 

687 ''' 

688 _f, kwds = self._func, self._kwds 

689 if not callable(_f): # PYCHOK no cover 

690 self._notOverloaded(distance_function=_f) 

691 try: 

692 for i, k in enumerate(self._knots): 

693 yield _f(y, x, k.lat, k.lon, **kwds) 

694 except Exception as e: 

695 i = Fmt.INDEX(knots=i) 

696 raise HeightError(i, k, cause=e) 

697 

698 @property_RO 

699 def _fmath(self): 

700 '''(INTERNAL) Get module C{fmath}, I{once}. 

701 ''' 

702 _HeightIDW._fmath = f = _MODS.fmath # overwrite property_RO 

703 return f 

704 

705 @property_RO 

706 def _formy(self): 

707 '''(INTERNAL) Get module C{formy}, I{once}. 

708 ''' 

709 _HeightIDW._formy = f = _MODS.formy # overwrite property_RO 

710 return f 

711 

712 def height(self, lats, lons, **wrap): 

713 '''Interpolate the height for one or several lat-/longitudes. 

714 

715 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). 

716 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). 

717 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}} 

718 and B{C{lons}} (C{bool}). 

719 

720 @return: A single interpolated height (C{float}) or a list of 

721 interpolated heights (C{float}s). 

722 

723 @raise HeightError: Insufficient or non-matching number of B{C{lats}} 

724 and B{C{lons}} or a L{pygeodesy.fidw} issue. 

725 ''' 

726 return _height_called(self, lats, lons, **wrap) 

727 

728 @Property_RO 

729 def _heights(self): 

730 '''(INTERNAL) Get the knots' heights. 

731 ''' 

732 return tuple(_xattr(k, height=0) for k in self.knots) 

733 

734 def _hIDW(self, x, y): 

735 '''(INTERNAL) Return the IDW-interpolated height at 

736 location (x, y), both C{degrees} or C{radians}. 

737 ''' 

738 ds, hs = self._distances(x, y), self._heights 

739 try: 

740 return self._fmath.fidw(hs, ds, beta=self.beta) 

741 except (TypeError, ValueError) as e: 

742 raise HeightError(x=x, y=y, cause=e) 

743 

744 @property_RO 

745 def hypot(self): 

746 '''Get the C{hypot} setting (C{callable}) or C{None}. 

747 ''' 

748 return _xkwds_get(self._kwds, hypot=None) 

749 

750 @property_RO 

751 def knots(self): 

752 '''Get the B{C{knots}} (C{list} or C{tuple}). 

753 ''' 

754 return self._knots 

755 

756 @property_RO 

757 def kwds(self): 

758 '''Get the optional keyword arguments (C{dict}). 

759 ''' 

760 return self._kwds 

761 

762 @property_RO 

763 def limit(self): 

764 '''Get the C{limit} setting (C{degrees}) or C{None}. 

765 ''' 

766 return _xkwds_get(self._kwds, limit=None) 

767 

768 @property_RO 

769 def radius(self): 

770 '''Get the C{radius} setting (C{bool}) or C{None}. 

771 ''' 

772 return _xkwds_get(self._kwds, radius=None) 

773 

774 @property_RO 

775 def scaled(self): 

776 '''Get the C{scaled} setting (C{bool}) or C{None}. 

777 ''' 

778 return _xkwds_get(self._kwds, scaled=None) 

779 

780 @property_RO 

781 def wrap(self): 

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

783 ''' 

784 return _xkwds_get(self._kwds, wrap=self._wrap) 

785 

786 

787class HeightIDWcosineAndoyerLambert(_HeightIDW): 

788 '''Height interpolator using U{Inverse Distance Weighting 

789 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

790 and the I{angular} distance in C{radians} from function 

791 L{pygeodesy.cosineAndoyerLambert_}. 

792 ''' 

793 def __init__(self, knots, beta=2, name=NN, **datum_wrap): 

794 '''New L{HeightIDWcosineAndoyerLambert} interpolator. 

795 

796 @kwarg datum_wrap: Optional keyword arguments for function 

797 L{pygeodesy.cosineAndoyerLambert}. 

798 

799 @see: L{Here<_HeightIDW.__init__>} for other details. 

800 ''' 

801 _HeightIDW.__init__(self, knots, beta=beta, name=name, **datum_wrap) 

802 self._func = self._formy.cosineAndoyerLambert 

803 

804 if _FOR_DOCS: 

805 __call__ = _HeightIDW.__call__ 

806 height = _HeightIDW.height 

807 

808 

809class HeightIDWcosineForsytheAndoyerLambert(_HeightIDW): 

810 '''Height interpolator using U{Inverse Distance Weighting 

811 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

812 and the I{angular} distance in C{radians} from function 

813 L{pygeodesy.cosineForsytheAndoyerLambert_}. 

814 ''' 

815 def __init__(self, knots, beta=2, name=NN, **datum_wrap): 

816 '''New L{HeightIDWcosineForsytheAndoyerLambert} interpolator. 

817 

818 @kwarg datum_wrap: Optional keyword arguments for function 

819 L{pygeodesy.cosineForsytheAndoyerLambert}. 

820 

821 @see: L{Here<_HeightIDW.__init__>} for other details. 

822 ''' 

823 _HeightIDW.__init__(self, knots, beta=beta, name=name, **datum_wrap) 

824 self._func = self._formy.cosineForsytheAndoyerLambert 

825 

826 if _FOR_DOCS: 

827 __call__ = _HeightIDW.__call__ 

828 height = _HeightIDW.height 

829 

830 

831class HeightIDWcosineLaw(_HeightIDW): 

832 '''Height interpolator using U{Inverse Distance Weighting 

833 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

834 I{angular} distance in C{radians} from function L{pygeodesy.cosineLaw_}. 

835 

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

837 ''' 

838 def __init__(self, knots, beta=2, name=NN, **radius_wrap): 

839 '''New L{HeightIDWcosineLaw} interpolator. 

840 

841 @kwarg radius_wrap: Optional keyword arguments for function 

842 L{pygeodesy.cosineLaw}. 

843 

844 @see: L{Here<_HeightIDW.__init__>} for other details. 

845 ''' 

846 _HeightIDW.__init__(self, knots, beta=beta, name=name, **radius_wrap) 

847 self._func = self._formy.cosineLaw 

848 

849 if _FOR_DOCS: 

850 __call__ = _HeightIDW.__call__ 

851 height = _HeightIDW.height 

852 

853 

854class HeightIDWdistanceTo(_HeightIDW): 

855 '''Height interpolator using U{Inverse Distance Weighting 

856 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

857 and the distance from the points' C{LatLon.distanceTo} method, 

858 conventionally in C{meter}. 

859 ''' 

860 def __init__(self, knots, beta=2, name=NN, **distanceTo_kwds): 

861 '''New L{HeightIDWdistanceTo} interpolator. 

862 

863 @kwarg distanceTo_kwds: Optional keyword arguments for the 

864 B{C{knots}}' C{LatLon.distanceTo} 

865 method. 

866 

867 @see: L{Here<_HeightIDW.__init__>} for other details. 

868 

869 @note: All B{C{points}} I{must} be instances of the same 

870 ellipsoidal or spherical C{LatLon} class, I{not 

871 checked}. 

872 ''' 

873 _HeightIDW.__init__(self, knots, beta=beta, name=name, 

874 **distanceTo_kwds) 

875 ks0 = _distanceTo(HeightError, knots=self._knots)[0] 

876 # use knots[0] class and datum to create compatible points 

877 # in _height_called instead of class LatLon_ and datum None 

878 self._datum = ks0.datum 

879 self._LLis = ks0.classof # type(ks0) 

880 

881 def _distances(self, x, y): 

882 '''(INTERNAL) Yield distances to C{(x, y)}. 

883 ''' 

884 kwds, ll = self._kwds, self._LLis(y, x) 

885 try: 

886 for i, k in enumerate(self._knots): 

887 yield k.distanceTo(ll, **kwds) 

888 except Exception as e: 

889 i = Fmt.INDEX(knots=i) 

890 raise HeightError(i, k, cause=e) 

891 

892 if _FOR_DOCS: 

893 __call__ = _HeightIDW.__call__ 

894 height = _HeightIDW.height 

895 

896 

897class HeightIDWequirectangular(_HeightIDW): 

898 '''Height interpolator using U{Inverse Distance Weighting 

899 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and 

900 the I{angular} distance in C{radians squared} like function 

901 L{pygeodesy.equirectangular_}. 

902 ''' 

903 def __init__(self, knots, beta=2, name=NN, **adjust_limit_wrap): # XXX beta=1 

904 '''New L{HeightIDWequirectangular} interpolator. 

905 

906 @kwarg adjust_limit_wrap: Optional keyword arguments for 

907 function L{pygeodesy.equirectangular_}. 

908 

909 @see: L{Here<_HeightIDW.__init__>} for other details. 

910 ''' 

911 _HeightIDW.__init__(self, knots, beta=beta, name=name, 

912 **adjust_limit_wrap) 

913 

914 def _distances(self, x, y): 

915 '''(INTERNAL) Yield distances to C{(x, y)}. 

916 ''' 

917 _f, kwds = self._formy.equirectangular_, self._kwds 

918 try: 

919 for i, k in enumerate(self._knots): 

920 yield _f(y, x, k.lat, k.lon, **kwds).distance2 

921 except Exception as e: 

922 i = Fmt.INDEX(knots=i) 

923 raise HeightError(i, k, cause=e) 

924 

925 if _FOR_DOCS: 

926 __call__ = _HeightIDW.__call__ 

927 height = _HeightIDW.height 

928 

929 

930class HeightIDWeuclidean(_HeightIDW): 

931 '''Height interpolator using U{Inverse Distance Weighting 

932 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

933 I{angular} distance in C{radians} from function L{pygeodesy.euclidean_}. 

934 ''' 

935 def __init__(self, knots, beta=2, name=NN, **adjust_radius_wrap): 

936 '''New L{HeightIDWeuclidean} interpolator. 

937 

938 @kwarg adjust_radius_wrap: Optional keyword arguments for 

939 function L{pygeodesy.euclidean}. 

940 

941 @see: L{Here<_HeightIDW.__init__>} for other details. 

942 ''' 

943 _HeightIDW.__init__(self, knots, beta=beta, name=name, 

944 **adjust_radius_wrap) 

945 self._func = self._formy.euclidean 

946 

947 if _FOR_DOCS: 

948 __call__ = _HeightIDW.__call__ 

949 height = _HeightIDW.height 

950 

951 

952class HeightIDWexact(_HeightIDW): 

953 '''Height interpolator using U{Inverse Distance Weighting 

954 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

955 and the I{angular} distance in C{degrees} from method 

956 L{GeodesicExact.Inverse}. 

957 ''' 

958 def __init__(self, knots, beta=2, name=NN, datum=None, **wrap): 

959 '''New L{HeightIDWexact} interpolator. 

960 

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

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

963 L{Ellipsoid2} or L{a_f2Tuple}). 

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

965 of class L{geodesicx.GeodesicExact}. 

966 

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

968 

969 @see: L{Here<_HeightIDW.__init__>} for other details. 

970 ''' 

971 _HeightIDW.__init__(self, knots, beta=beta, name=name, **wrap) 

972 self._datum_setter(datum) 

973 self._func = self.datum.ellipsoid.geodesicx.Inverse1 

974 

975 if _FOR_DOCS: 

976 __call__ = _HeightIDW.__call__ 

977 height = _HeightIDW.height 

978 

979 

980class HeightIDWflatLocal(_HeightIDW): 

981 '''Height interpolator using U{Inverse Distance Weighting 

982 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

983 and the I{angular} distance in C{radians squared} like function 

984 L{pygeodesy.flatLocal_}/L{pygeodesy.hubeny_}. 

985 ''' 

986 def __init__(self, knots, beta=2, name=NN, **datum_hypot_scaled_wrap): 

987 '''New L{HeightIDWflatLocal}/L{HeightIDWhubeny} interpolator. 

988 

989 @kwarg datum_hypot_scaled_wrap: Optional keyword arguments for 

990 function L{pygeodesy.flatLocal}. 

991 

992 @see: L{HeightIDW<_HeightIDW.__init__>} for other details. 

993 ''' 

994 _HeightIDW.__init__(self, knots, beta=beta, name=name, 

995 **datum_hypot_scaled_wrap) 

996 self._func = self._formy.flatLocal 

997 

998 if _FOR_DOCS: 

999 __call__ = _HeightIDW.__call__ 

1000 height = _HeightIDW.height 

1001 

1002 

1003class HeightIDWflatPolar(_HeightIDW): 

1004 '''Height interpolator using U{Inverse Distance Weighting 

1005 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) 

1006 and the I{angular} distance in C{radians} from function 

1007 L{pygeodesy.flatPolar_}. 

1008 ''' 

1009 def __init__(self, knots, beta=2, name=NN, **radius_wrap): 

1010 '''New L{HeightIDWflatPolar} interpolator. 

1011 

1012 @kwarg radius_wrap: Optional keyword arguments for function 

1013 L{pygeodesy.flatPolar}. 

1014 

1015 @see: L{Here<_HeightIDW.__init__>} for other details. 

1016 ''' 

1017 _HeightIDW.__init__(self, knots, beta=beta, name=name, **radius_wrap) 

1018 self._func = self._formy.flatPolar 

1019 

1020 if _FOR_DOCS: 

1021 __call__ = _HeightIDW.__call__ 

1022 height = _HeightIDW.height 

1023 

1024 

1025class HeightIDWhaversine(_HeightIDW): 

1026 '''Height interpolator using U{Inverse Distance Weighting 

1027 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

1028 I{angular} distance in C{radians} from function L{pygeodesy.haversine_}. 

1029 

1030 @note: See note at function L{pygeodesy.vincentys_}. 

1031 ''' 

1032 def __init__(self, knots, beta=2, name=NN, **radius_wrap): 

1033 '''New L{HeightIDWhaversine} interpolator. 

1034 

1035 @kwarg radius_wrap: Optional keyword arguments for function 

1036 L{pygeodesy.haversine}. 

1037 

1038 @see: L{Here<_HeightIDW.__init__>} for other details. 

1039 ''' 

1040 _HeightIDW.__init__(self, knots, beta=beta, name=name, **radius_wrap) 

1041 self._func = self._formy.haversine 

1042 

1043 if _FOR_DOCS: 

1044 __call__ = _HeightIDW.__call__ 

1045 height = _HeightIDW.height 

1046 

1047 

1048class HeightIDWhubeny(HeightIDWflatLocal): # for Karl Hubeny 

1049 if _FOR_DOCS: 

1050 __doc__ = HeightIDWflatLocal.__doc__ 

1051 __init__ = HeightIDWflatLocal.__init__ 

1052 __call__ = HeightIDWflatLocal.__call__ 

1053 height = HeightIDWflatLocal.height 

1054 

1055 

1056class HeightIDWkarney(_HeightIDW): 

1057 '''Height interpolator using U{Inverse Distance Weighting 

1058 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

1059 I{angular} distance in C{degrees} from I{Karney}'s U{geographiclib 

1060 <https://PyPI.org/project/geographiclib>} method U{Geodesic.Inverse 

1061 <https://geographiclib.sourceforge.io/Python/doc/code.html# 

1062 geographiclib.geodesic.Geodesic.Inverse>}. 

1063 ''' 

1064 def __init__(self, knots, beta=2, name=NN, datum=None, **wrap): 

1065 '''New L{HeightIDWkarney} interpolator. 

1066 

1067 @kwarg datum: Datum to override the default C{Datums.WGS84} and 

1068 first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, 

1069 L{Ellipsoid2} or L{a_f2Tuple}). 

1070 @kwarg wrap: Optional keyword argument for method C{Inverse1} 

1071 of class L{geodesicw.Geodesic}. 

1072 

1073 @raise ImportError: Package U{geographiclib 

1074 <https://PyPI.org/project/geographiclib>} missing. 

1075 

1076 @raise TypeError: Invalid B{C{datum}}. 

1077 

1078 @see: L{Here<_HeightIDW.__init__>} for other details. 

1079 ''' 

1080 _HeightIDW.__init__(self, knots, beta=beta, name=name, **wrap) 

1081 self._datum_setter(datum) 

1082 self._func = self.datum.ellipsoid.geodesic.Inverse1 

1083 

1084 if _FOR_DOCS: 

1085 __call__ = _HeightIDW.__call__ 

1086 height = _HeightIDW.height 

1087 

1088 

1089class HeightIDWthomas(_HeightIDW): 

1090 '''Height interpolator using U{Inverse Distance Weighting 

1091 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

1092 I{angular} distance in C{radians} from function L{pygeodesy.thomas_}. 

1093 ''' 

1094 def __init__(self, knots, beta=2, name=NN, **datum_wrap): 

1095 '''New L{HeightIDWthomas} interpolator. 

1096 

1097 @kwarg datum_wrap: Optional keyword argument for function 

1098 L{pygeodesy.thomas}. 

1099 

1100 @see: L{Here<_HeightIDW.__init__>} for other details. 

1101 ''' 

1102 _HeightIDW.__init__(self, knots, beta=beta, name=name, **datum_wrap) 

1103 self._func = self._formy.thomas 

1104 

1105 if _FOR_DOCS: 

1106 __call__ = _HeightIDW.__call__ 

1107 height = _HeightIDW.height 

1108 

1109 

1110class HeightIDWvincentys(_HeightIDW): 

1111 '''Height interpolator using U{Inverse Distance Weighting 

1112 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the 

1113 I{angular} distance in C{radians} from function L{pygeodesy.vincentys_}. 

1114 

1115 @note: See note at function L{pygeodesy.vincentys_}. 

1116 ''' 

1117 def __init__(self, knots, beta=2, name=NN, **radius_wrap): 

1118 '''New L{HeightIDWvincentys} interpolator. 

1119 

1120 @kwarg radius_wrap: Optional keyword arguments for function 

1121 L{pygeodesy.vincentys}. 

1122 

1123 @see: L{Here<_HeightIDW.__init__>} for other details. 

1124 ''' 

1125 _HeightIDW.__init__(self, knots, beta=beta, name=name, **radius_wrap) 

1126 self._func = self._formy.vincentys 

1127 

1128 if _FOR_DOCS: 

1129 __call__ = _HeightIDW.__call__ 

1130 height = _HeightIDW.height 

1131 

1132 

1133__all__ += _ALL_DOCS(_HeightBase, _HeightIDW, _HeightsBase) 

1134 

1135# **) MIT License 

1136# 

1137# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1138# 

1139# Permission is hereby granted, free of charge, to any person obtaining a 

1140# copy of this software and associated documentation files (the "Software"), 

1141# to deal in the Software without restriction, including without limitation 

1142# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1143# and/or sell copies of the Software, and to permit persons to whom the 

1144# Software is furnished to do so, subject to the following conditions: 

1145# 

1146# The above copyright notice and this permission notice shall be included 

1147# in all copies or substantial portions of the Software. 

1148# 

1149# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1150# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1151# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1152# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1153# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1154# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1155# OTHER DEALINGS IN THE SOFTWARE.