1

2# -*- coding: utf-8 -*-

3

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

5

6 Classes L{HeightCubic}, L{HeightIDWcosineLaw}, L{HeightIDWdistanceTo},

7 L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWflatLocal},

8 L{HeightIDWflatPolar}, L{HeightIDWhaversine}, L{HeightIDWhubeny},

9 L{HeightIDWkarney}, L{HeightIDWthomas}, L{HeightIDWvincentys}, L{HeightLinear},

10 L{HeightLSQBiSpline} and L{HeightSmoothBiSpline} to interpolate the height of

11 C{LatLon} locations or separate lat-/longitudes from a set of C{LatLon} points

12 with I{known heights}.

13

14 Typical usage

15=============

16

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

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

19

20 C{>>> ...}

21

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

23

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

25

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

27 arguments to select different interpolation options

28

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

30

31 4. Get the interpolated height of C{LatLon} location(s) with

32

33 C{>>> ll = LatLon(1, 2, ...)}

34

35 C{>>> h = hinterpolator(ll)}

36

37 or

38

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

40

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

42

43 C{>>> hs = hinterpolator(lls)}

44

45 5. For separate lat- and longitudes invoke the C{height} method as

46

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

48

49 or as 2 lists, 2 tuples, etc.

50

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

52

53 or for several positionals use the C{height_} method

54

55 C{>>> h1, h2, ... = hinterpolator.height_(lat1, lon1, lat2, lon2, ...)}

56

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

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

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

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

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

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

63

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

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

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

67

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

69 Interpolation.

70'''

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

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

73

74 from pygeodesy.basics import isscalar, len2, map1, min2, _xnumpy, _xscipy

75 from pygeodesy.constants import EPS, PI, PI_2, PI2, _0_0, _90_0, _180_0

76 from pygeodesy.datums import _ellipsoidal_datum, _WGS84

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

78 _SciPyIssue, _xattr, _xkwds, _xkwds_get, _xkwds_item2

79# from pygeodesy.fmath import fidw # _MODS

80# from pygeodesy import formy as _formy # _MODS.into

81# from pygeodesy.internals import _version2 # _MODS

82 from pygeodesy.interns import NN, _COMMASPACE_, _insufficient_, _NOTEQUAL_, \

83 _PLUS_, _scipy_, _SPACE_, _STAR_

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

85 from pygeodesy.named import _name2__, _Named

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

87 from pygeodesy.props import Property_RO, property_RO, property_ROver

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

89 from pygeodesy.units import _isDegrees, Float_, Int_

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

91

92# from math import radians # from .points

93

94__all__ = _ALL_LAZY.heights

95__version__ = '25.04.21'

96

97_error_ = 'error'

98_formy = _MODS.into(formy=__name__)

99_linear_ = 'linear'

100_llis_ = 'llis'

101

102

103 class HeightError(PointsError):

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

105 '''

106 pass

107

108

109 def _alist(ais):

110 # return list of floats, not numpy.float64s

111 return list(map(float, ais))

112

113

114 def _ascalar(ais): # in .geoids

115 # return single float, not numpy.float64

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

117 if len(ais) != 1:

118 n = Fmt.PAREN(len=repr(ais))

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

120 raise _AssertionError(n, txt=t)

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

122

123

124 def _atuple(ais):

125 # return tuple of floats, not numpy.float64s

126 return tuple(map(float, ais))

127

128

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

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

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

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

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

134

135 n = len(llis)

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

137 llis = llis[0]

138 try:

139 n, llis = len2(llis)

140 _as = _alist # return list of interpolated heights

141 except TypeError: # single lli

142 n, llis = 1, [llis]

143 _as = _ascalar # return single interpolated heights

144 else: # of 0, 2 or more llis

145 _as = _atuple # return tuple of interpolated heights

146

147 if n < m:

148 raise _InsufficientError(m, Error=Error, llis=n)

149 return _as, llis

150

151

152 def _InsufficientError(need, Error=HeightError, **name_value): # PYCHOK no cover

153 # create an insufficient Error instance

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

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

156

157

158 def _orderedup(ts, lo=EPS, hi=PI2-EPS):

159 # clip, order and remove duplicates

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

161

162

163 def _xyhs(wrap=False, _lat=_90_0, _lon=_180_0, **name_lls):

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

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

166 name, lls = _xkwds_item2(name_lls)

167 _w, _r = _Wrap._latlonop(wrap), radians

168 try:

169 for i, ll in enumerate(lls):

170 y, x = _w(ll.lat, ll.lon)

171 yield max(_0_0, _r(x + _lon)), \

172 max(_0_0, _r(y + _lat)), ll.height

173 except Exception as x:

174 i = Fmt.INDEX(name, i)

175 raise HeightError(i, ll, cause=x)

176

177

178 class _HeightNamed(_Named): # in .geoids

179 '''(INTERNAL) Interpolator base class.

180 '''

181 _datum = _WGS84 # default

182 _Error = HeightError

183 _kmin = 2 # min number of knots

184

185 _LLiC = LatLon_ # ._height class

186 _np_sp = None # (numpy, scipy)

187 _wrap = None # wrap knots and llis

188

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

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

191

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

193 @kwarg wrap: If C{B{wrap}=True} to wrap or I{normalize} all B{C{llis}}

194 locations (C{bool}), overriding the B{C{knots}}' setting.

195

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

197 interpolated heights (each C{float}).

198

199 @raise HeightError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}.

200

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

202

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

204 '''

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

206

207 def _as_lls(self, lats, lons): # in .geoids

208 LLiC, d = self._LLiC, self.datum

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

210 llis = LLiC(lats, lons, datum=d)

211 else:

212 n, lats = len2(lats)

213 m, lons = len2(lons)

214 if n != m: # format a LenError, but raise self._Error

215 e = LenError(self.__class__, lats=n, lons=m, txt=None)

216 raise self._Error(str(e))

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

218 return llis

219

220 @property_RO

221 def datum(self):

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

223 '''

224 return self._datum

225

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

227 '''I{Must be overloaded}.'''

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

229

230 def height_(self, *latlons, **wrap):

231 '''Interpolate the height for each M{(latlons[i], latlons[i+1]) pair

232 for i in range(0, len(latlons), B{2})}.

233

234 @arg latlons: Alternating lat-/longitude pairs (each C{degrees}),

235 all positional.

236

237 @see: Method C{height} for further details.

238

239 @return: A tuple of interpolated heights (each C{float}).

240 '''

241 lls = self._as_lls(latlons[0::2], latlons[1::2])

242 return tuple(self(lls, **wrap))

243

244 @property_RO

245 def kmin(self):

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

247 '''

248 return self._kmin

249

250 @property_RO

251 def wrap(self):

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

253 '''

254 return self._wrap

255

256

257 class _HeightBase(_HeightNamed): # in .geoids

258 '''(INTERNAL) Interpolator base class.

259 '''

260 _k2interp2d = {-1: _linear_, # in .geoids._GeoidBase.__init__

261 -2: _linear_, # for backward compatibility

262 -3: 'cubic',

263 -5: 'quintic'}

264

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

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

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

268 atype = self.numpy.array

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

270 _as, llis = _as_llis2(llis)

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

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

273

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

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

276 self._notOverloaded(*args)

277

278 def _evalls(self, llis, **wrap): # XXX single arg, not *args

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

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

281 return _as(self._ev(yis, xis))

282 except Exception as x:

283 raise _SciPyIssue(x, self._ev_name)

284

285 def _ev2d(self, x, y): # PYCHOK no cover

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

287 self._notOverloaded(x, y)

288

289 @property_RO

290 def _ev_name(self):

291 '''(INTERNAL) Get the name of the C{.ev} method.

292 '''

293 _ev = str(self._ev)

294 if _scipy_ not in _ev:

295 _ev = str(self._ev2d)

296 # '<scipy.interpolate._interpolate.interp2d object at ...>

297 # '<function _HeightBase._interp2d.<locals>._bisplev at ...>

298 # '<bound method BivariateSpline.ev of ... object at ...>

299 _ev = _ev[1:].split(None, 4)

300 return Fmt.PAREN(_ev['sfb'.index(_ev[0][0])])

301

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

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

304

305 @arg lats: Latitude or latitudes (each C{degrees}).

306 @arg lons: Longitude or longitudes (each C{degrees}).

307 @kwarg wrap: Kewyord argument C{B{wrap}=False} (C{bool}). Use C{True} to

308 wrap or I{normalize} all B{C{lats}} and B{C{lons}} locationts,

309 overriding the B{C{knots}}' setting.

310

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

312 heights (each C{float}).

313

314 @raise HeightError: Insufficient or unequal number of B{C{lats}} and B{C{lons}}.

315

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

317

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

319 '''

320 lls = self._as_lls(lats, lons) # dup of _HeightIDW.height

321 return self(lls, **wrap) # __call__(ll) or __call__(lls)

322

323 def _interp2d(self, xs, ys, hs, kind=-3):

324 '''Create a C{scipy.interpolate.interp2d} or C{-.bisplrep/-ev}

325 interpolator before, respectively since C{SciPy} version 1.14.

326 '''

327 try:

328 spi = self.scipy_interpolate

329 if self._scipy_version() < (1, 14) and kind in self._k2interp2d:

330 # SciPy.interpolate.interp2d kind 'linear', 'cubic' or 'quintic'

331 # DEPRECATED since scipy 1.10, removed altogether in 1.14

332 self._ev2d = spi.interp2d(xs, ys, hs, kind=self._k2interp2d[kind])

333

334 else: # <https://scipy.GitHub.io/devdocs/tutorial/interpolate/interp_transition_guide.html>

335 k = self._kxky(abs(kind))

336 # spi.RectBivariateSpline needs strictly ordered xs and ys

337 r = spi.bisplrep(xs, ys, hs.T, kx=k, ky=k)

338

339 def _bisplev(x, y):

340 return spi.bisplev(x, y, r) # .T

341

342 self._ev2d = _bisplev

343

344 except Exception as x:

345 raise _SciPyIssue(x, self._ev_name)

346

347 def _kxky(self, kind):

348 return Int_(kind=kind, low=1, high=5, Error=self._Error)

349

350 def _np_sp2(self, throwarnings=False): # PYCHOK no cover

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

352 '''

353 # raise SciPyWarnings, but not if

354 # scipy has already been imported

355 if throwarnings: # PYCHOK no cover

356 import sys

357 if _scipy_ not in sys.modules:

358 import warnings

359 warnings.filterwarnings(_error_)

360 return self.numpy, self.scipy

361

362 @property_ROver

363 def numpy(self):

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

365 '''

366 return _xnumpy(self.__class__, 1, 9) # overwrite property_ROver

367

368 @property_ROver

369 def scipy(self):

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

371 '''

372 return _xscipy(self.__class__, 1, 2) # overwrite property_ROver

373

374 @property_ROver

375 def scipy_interpolate(self):

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

377 '''

378 _ = self.scipy

379 import scipy.interpolate as spi # scipy 1.2.2

380 return spi # overwrite property_ROver

381

382 def _scipy_version(self, **n):

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

384 '''

385 return _MODS.internals._version2(self.scipy.version.version, **n)

386

387 def _xyhs3(self, knots, wrap=False, **name):

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

389 xs, ys, hs = zip(*_xyhs(knots=knots, wrap=wrap)) # PYCHOK yield

390 n = len(hs)

391 if n < self.kmin:

392 raise _InsufficientError(self.kmin, knots=n)

393 if name:

394 self.name = name

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

396

397

398 class HeightCubic(_HeightBase):

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

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

401 C{kind='cubic'} or U{bisplrep/-ev<https://docs.SciPy.org/doc/scipy/

402 reference/generated/scipy.interpolate.interp2d.html>} C{kx=ky=3}.

403 '''

404 _kind = -3

405 _kmin = 16

406

407 def __init__(self, knots, **name_wrap):

408 '''New L{HeightCubic} interpolator.

409

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

411 @kwarg name_wrap: Optional C{B{name}=NN} for this height interpolator (C{str})

412 and keyword argument C{b{wrap}=False} to wrap or I{normalize} all

413 B{C{knots}} and B{C{llis}} locations iff C{True} (C{bool}).

414

415 @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}.

416

417 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

418

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

420

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

422 '''

423 xs_yx_hs = self._xyhs3(knots, **name_wrap)

424 self._interp2d(*xs_yx_hs, kind=self._kind)

425

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

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

428

429 @see: L{Here<_HeightBase.__call__>} for further details.

430 '''

431 return self._evalls(llis, **wrap)

432

433 def _ev(self, yis, xis): # PYCHOK overwritten with .RectBivariateSpline.ev

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

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

436 return map(self._ev2d, xis, yis)

437

438

439 class HeightLinear(HeightCubic):

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

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

442 C{kind='linear'} or U{bisplrep/-ev<https://docs.SciPy.org/doc/scipy/

443 reference/generated/scipy.interpolate.interp2d.html>} C{kx=ky=1}.

444 '''

445 _kind = -1

446 _kmin = 2

447

448 def __init__(self, knots, **name_wrap):

449 '''New L{HeightLinear} interpolator.

450

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

452 '''

453 HeightCubic.__init__(self, knots, **name_wrap)

454

455 if _FOR_DOCS:

456 __call__ = HeightCubic.__call__

457 height = HeightCubic.height

458

459

460 class HeightLSQBiSpline(_HeightBase):

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

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

463 interpolate.LSQSphereBivariateSpline.html>}.

464 '''

465 _kmin = 16 # k = 3, always

466

467 def __init__(self, knots, weight=None, low=1e-4, **name_wrap):

468 '''New L{HeightLSQBiSpline} interpolator.

469

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

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

472 (C{scalar} or C{scalar}s).

473 @kwarg low: Optional lower bound for I{ordered knots} (C{radians}).

474 @kwarg name_wrap: Optional C{B{name}=NN} for this height interpolator

475 (C{str}) and keyword argument C{b{wrap}=False} to wrap or

476 I{normalize} all B{C{knots}} and B{C{llis}} locations iff

477 C{True} (C{bool}).

478

479 @raise HeightError: Insufficient number of B{C{knots}} or an invalid

480 B{C{knot}}, B{C{weight}} or B{C{eps}}.

481

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

483

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

485 installed.

486

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

488

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

490 '''

491 np = self.numpy

492 spi = self.scipy_interpolate

493

494 xs, ys, hs = self._xyhs3(knots, **name_wrap)

495 n = len(hs)

496

497 w = weight

498 if isscalar(w):

499 w = float(w)

500 if w <= 0:

501 raise HeightError(weight=w)

502 w = (w,) * n

503 elif w is not None:

504 m, w = len2(w)

505 if m != n:

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

507 m, i = min2(*map(float, w))

508 if m <= 0: # PYCHOK no cover

509 raise HeightError(Fmt.INDEX(weight=i), m)

510 try:

511 if not EPS < low < (PI_2 - EPS): # 1e-4 like SciPy example

512 raise HeightError(low=low)

513 ps = np.array(_orderedup(xs, low, PI2 - low))

514 ts = np.array(_orderedup(ys, low, PI - low))

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

516 ts, ps, eps=EPS, w=w).ev

517 except Exception as x:

518 raise _SciPyIssue(x, self._ev_name)

519

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

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

522

523 @see: L{Here<_HeightBase.__call__>} for further details.

524 '''

525 return self._evalls(llis, **wrap)

526

527

528 class HeightSmoothBiSpline(_HeightBase):

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

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

531 interpolate.SmoothSphereBivariateSpline.html>}.

532 '''

533 _kmin = 16 # k = 3, always

534

535 def __init__(self, knots, s=4, **name_wrap):

536 '''New L{HeightSmoothBiSpline} interpolator.

537

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

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

540 @kwarg name_wrap: Optional C{B{name}=NN} for this height interpolator

541 (C{str}) and keyword argument C{b{wrap}=False} to wrap or

542 I{normalize} all B{C{knots}} and B{C{llis}} locations iff

543 C{True} (C{bool}).

544

545 @raise HeightError: Insufficient number of B{C{knots}} or an invalid

546 B{C{knot}} or B{C{s}}.

547

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

549 installed.

550

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

552

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

554 '''

555 spi = self.scipy_interpolate

556

557 s = Float_(smoothing=s, Error=HeightError, low=4)

558

559 xs, ys, hs = self._xyhs3(knots, **name_wrap)

560 try:

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

562 eps=EPS, s=s).ev

563 except Exception as x:

564 raise _SciPyIssue(x, self._ev_name)

565

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

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

568

569 @see: L{Here<_HeightBase.__call__>} for further details.

570 '''

571 return self._evalls(llis, **wrap)

572

573

574 class _HeightIDW(_HeightNamed):

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

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

577 interpolators.

578

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

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

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

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

583 classes.

584 '''

585 _beta = 0 # fidw inverse power

586 _func = None # formy function

587 _knots = () # knots list or tuple

588 _kwds = {} # func_ options

589

590 def __init__(self, knots, beta=2, **name__kwds):

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

592

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

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

595 @kwarg name__kwds: Optional C{B{name}=NN} for this height interpolator

596 (C{str}) and any keyword arguments for the distance function,

597 retrievable with property C{kwds}.

598

599 @raise HeightError: Insufficient number of B{C{knots}} or an invalid

600 B{C{knot}} or B{C{beta}}.

601 '''

602 name, kwds = _name2__(**name__kwds)

603 if name:

604 self.name = name

605

606 n, self._knots = len2(knots)

607 if n < self.kmin:

608 raise _InsufficientError(self.kmin, knots=n)

609 self.beta = beta

610 self._kwds = kwds or {}

611

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

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

614

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

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

617 locations (C{bool}).

618

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

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

621

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

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

624 issue.

625 '''

626 def _xy2(wrap=False):

627 _w = _Wrap._latlonop(wrap)

628 try: # like _xyhs above, but degrees

629 for i, ll in enumerate(llis):

630 yield _w(ll.lon, ll.lat)

631 except Exception as x:

632 i = Fmt.INDEX(llis=i)

633 raise HeightError(i, ll, cause=x)

634

635 _as, llis = _as_llis2(llis)

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

637

638 @property_RO

639 def adjust(self):

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

641 '''

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

643

644 @property

645 def beta(self):

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

647 '''

648 return self._beta

649

650 @beta.setter # PYCHOK setter!

651 def beta(self, beta):

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

653

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

655 '''

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

657

658 @property_RO

659 def datum(self):

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

661 '''

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

663

664 def _datum_setter(self, datum):

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

666 '''

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

668 if d and d is not self._datum:

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

670

671 def _distances(self, x, y):

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

673 '''

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

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

676 self._notOverloaded(distance_function=_f)

677 try:

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

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

680 except Exception as x:

681 i = Fmt.INDEX(knots=i)

682 raise HeightError(i, k, cause=x)

683

684 def _distancesTo(self, _To):

685 '''(INTERNAL) Yield distances C{_To}.

686 '''

687 try:

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

689 yield _To(k)

690 except Exception as x:

691 i = Fmt.INDEX(knots=i)

692 raise HeightError(i, k, cause=x)

693

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

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

696

697 @arg lats: Latitude or latitudes (each C{degrees}).

698 @arg lons: Longitude or longitudes (each C{degrees}).

699 @kwarg wrap: Keyword argument C{B{wrap}=False} (C{bool}). Use

700 C{B{wrap}=True} to wrap or I{normalize} all B{C{lats}}

701 and B{C{lons}}.

702

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

704 interpolated heights (each C{float}).

705

706 @raise HeightError: Insufficient or unequal number of B{C{lats}}

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

708 '''

709 lls = self._as_lls(lats, lons) # dup of _HeightBase.height

710 return self(lls, **wrap) # __call__(ll) or __call__(lls)

711

712 @Property_RO

713 def _heights(self):

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

715 '''

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

717

718 def _hIDW(self, x, y):

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

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

721 '''

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

723 try:

724 return _MODS.fmath.fidw(hs, ds, beta=self.beta)

725 except (TypeError, ValueError) as e:

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

727

728 @property_RO

729 def hypot(self):

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

731 '''

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

733

734 @property_RO

735 def knots(self):

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

737 '''

738 return self._knots

739

740 @property_RO

741 def kwds(self):

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

743 '''

744 return self._kwds

745

746 @property_RO

747 def limit(self):

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

749 '''

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

751

752 @property_RO

753 def radius(self):

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

755 '''

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

757

758 @property_RO

759 def scaled(self):

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

761 '''

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

763

764 @property_RO

765 def wrap(self):

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

767 '''

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

769

770

771 class HeightIDWcosineLaw(_HeightIDW):

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

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

774 and function L{pygeodesy.cosineLaw}.

775

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

777 '''

778 def __init__(self, knots, beta=2, **name__corr_earth_datum_radius_wrap):

779 '''New L{HeightIDWcosineLaw} interpolator.

780

781 @kwarg name__corr_earth_datum_radius_wrap: Optional C{B{name}=NN}

782 for this height interpolator (C{str}) and any keyword

783 arguments for function L{pygeodesy.cosineLaw}.

784

785 @see: L{Here<_HeightIDW.__init__>} for further details.

786 '''

787 _HeightIDW.__init__(self, knots, beta=beta, **name__corr_earth_datum_radius_wrap)

788 self._func = _formy.cosineLaw

789

790 if _FOR_DOCS:

791 __call__ = _HeightIDW.__call__

792 height = _HeightIDW.height

793

794

795 class HeightIDWdistanceTo(_HeightIDW):

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

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

798 and the points' C{LatLon.distanceTo} method.

799 '''

800 def __init__(self, knots, beta=2, **name__distanceTo_kwds):

801 '''New L{HeightIDWdistanceTo} interpolator.

802

803 @kwarg name__distanceTo_kwds: Optional C{B{name}=NN} for this

804 height interpolator (C{str}) and keyword arguments

805 for B{C{knots}}' method C{LatLon.distanceTo}.

806

807 @see: L{Here<_HeightIDW.__init__>} for further details.

808

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

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

811 checked}.

812 '''

813 _HeightIDW.__init__(self, knots, beta=beta, **name__distanceTo_kwds)

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

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

816 # in ._as_lls instead of class LatLon_ and datum None

817 self._datum = ks0.datum

818 self._LLiC = ks0.classof # type(ks0)

819

820 def _distances(self, x, y):

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

822 '''

823 kwds, ll = self._kwds, self._LLiC(y, x)

824

825 def _To(k):

826 return k.distanceTo(ll, **kwds)

827

828 return self._distancesTo(_To)

829

830 if _FOR_DOCS:

831 __call__ = _HeightIDW.__call__

832 height = _HeightIDW.height

833

834

835 class HeightIDWequirectangular(_HeightIDW):

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

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

838 and function L{pygeodesy.equirectangular4}.

839 '''

840 def __init__(self, knots, beta=2, **name__adjust_limit_wrap): # XXX beta=1

841 '''New L{HeightIDWequirectangular} interpolator.

842

843 @kwarg name__adjust_limit_wrap: Optional C{B{name}=NN} for this

844 height interpolator (C{str}) and keyword arguments

845 for function L{pygeodesy.equirectangular4}.

846

847 @see: L{Here<_HeightIDW.__init__>} for further details.

848 '''

849 _HeightIDW.__init__(self, knots, beta=beta, **name__adjust_limit_wrap)

850

851 def _distances(self, x, y):

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

853 '''

854 _f, kwds = _formy.equirectangular4, self._kwds

855

856 def _To(k):

857 return _f(y, x, k.lat, k.lon, **kwds).distance2

858

859 return self._distancesTo(_To)

860

861 if _FOR_DOCS:

862 __call__ = _HeightIDW.__call__

863 height = _HeightIDW.height

864

865

866 class HeightIDWeuclidean(_HeightIDW):

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

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

869 and function L{pygeodesy.euclidean_}.

870 '''

871 def __init__(self, knots, beta=2, **name__adjust_radius_wrap):

872 '''New L{HeightIDWeuclidean} interpolator.

873

874 @kwarg name__adjust_radius_wrap: Optional C{B{name}=NN} for this

875 height interpolator (C{str}) and keyword arguments

876 for function function L{pygeodesy.euclidean}.

877

878 @see: L{Here<_HeightIDW.__init__>} for further details.

879 '''

880 _HeightIDW.__init__(self, knots, beta=beta, **name__adjust_radius_wrap)

881 self._func = _formy.euclidean

882

883 if _FOR_DOCS:

884 __call__ = _HeightIDW.__call__

885 height = _HeightIDW.height

886

887

888 class HeightIDWexact(_HeightIDW):

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

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

891 and method L{GeodesicExact.Inverse}.

892 '''

893 def __init__(self, knots, beta=2, datum=None, **name__wrap):

894 '''New L{HeightIDWexact} interpolator.

895

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

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

898 L{Ellipsoid2} or L{a_f2Tuple}).

899 @kwarg name__wrap: Optional C{B{name}=NN} for this height interpolator

900 (C{str}) and a keyword argument for method C{Inverse1} of

901 class L{geodesicx.GeodesicExact}.

902

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

904

905 @see: L{Here<_HeightIDW.__init__>} for further details.

906 '''

907 _HeightIDW.__init__(self, knots, beta=beta, **name__wrap)

908 self._datum_setter(datum)

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

910

911 if _FOR_DOCS:

912 __call__ = _HeightIDW.__call__

913 height = _HeightIDW.height

914

915

916 class HeightIDWflatLocal(_HeightIDW):

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

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

919 the function L{pygeodesy.flatLocal_}/L{pygeodesy.hubeny_}.

920 '''

921 def __init__(self, knots, beta=2, **name__datum_hypot_scaled_wrap):

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

923

924 @kwarg name__datum_hypot_scaled_wrap: Optional C{B{name}=NN}

925 for this height interpolator (C{str}) and any

926 keyword arguments for L{pygeodesy.flatLocal}.

927

928 @see: L{HeightIDW<_HeightIDW.__init__>} for further details.

929 '''

930 _HeightIDW.__init__(self, knots, beta=beta,

931 **name__datum_hypot_scaled_wrap)

932 self._func = _formy.flatLocal

933

934 if _FOR_DOCS:

935 __call__ = _HeightIDW.__call__

936 height = _HeightIDW.height

937

938

939 class HeightIDWflatPolar(_HeightIDW):

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

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

942 and function L{pygeodesy.flatPolar_}.

943 '''

944 def __init__(self, knots, beta=2, **name__radius_wrap):

945 '''New L{HeightIDWflatPolar} interpolator.

946

947 @kwarg name__radius_wrap: Optional C{B{name}=NN} for this

948 height interpolator (C{str}) and any keyword

949 arguments for function L{pygeodesy.flatPolar}.

950

951 @see: L{Here<_HeightIDW.__init__>} for further details.

952 '''

953 _HeightIDW.__init__(self, knots, beta=beta, **name__radius_wrap)

954 self._func = _formy.flatPolar

955

956 if _FOR_DOCS:

957 __call__ = _HeightIDW.__call__

958 height = _HeightIDW.height

959

960

961 class HeightIDWhaversine(_HeightIDW):

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

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

964 and function L{pygeodesy.haversine_}.

965

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

967 '''

968 def __init__(self, knots, beta=2, **name__radius_wrap):

969 '''New L{HeightIDWhaversine} interpolator.

970

971 @kwarg name__radius_wrap: Optional C{B{name}=NN} for this

972 height interpolator (C{str}) and any keyword

973 arguments for function L{pygeodesy.haversine}.

974

975 @see: L{Here<_HeightIDW.__init__>} for further details.

976 '''

977 _HeightIDW.__init__(self, knots, beta=beta, **name__radius_wrap)

978 self._func = _formy.haversine

979

980 if _FOR_DOCS:

981 __call__ = _HeightIDW.__call__

982 height = _HeightIDW.height

983

984

985 class HeightIDWhubeny(HeightIDWflatLocal): # for Karl Hubeny

986 if _FOR_DOCS:

987 __doc__ = HeightIDWflatLocal.__doc__

988 __init__ = HeightIDWflatLocal.__init__

989 __call__ = HeightIDWflatLocal.__call__

990 height = HeightIDWflatLocal.height

991

992

993 class HeightIDWkarney(_HeightIDW):

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

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

996 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}

997 method U{geodesic.Geodesic.Inverse<https://GeographicLib.SourceForge.io/

998 Python/doc/code.html#geographiclib.geodesic.Geodesic.Inverse>}.

999 '''

1000 def __init__(self, knots, beta=2, datum=None, **name__wrap):

1001 '''New L{HeightIDWkarney} interpolator.

1002

1003 @kwarg datum: Datum to override the default C{Datums.WGS84} and

1004 first B{C{knots}}' datum (L{Datum}, L{Ellipsoid},

1005 L{Ellipsoid2} or L{a_f2Tuple}).

1006 @kwarg name__wrap: Optional C{B{name}=NN} for this height interpolator

1007 (C{str}) and a keyword argument for method C{Inverse1} of

1008 class L{geodesicw.Geodesic}.

1009

1010 @raise ImportError: Package U{geographiclib

1011 <https://PyPI.org/project/geographiclib>} missing.

1012

1013 @raise TypeError: Invalid B{C{datum}}.

1014

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

1016 '''

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

1018 self._datum_setter(datum)

1019 self._func = self.datum.ellipsoid.geodesic.Inverse1

1020

1021 if _FOR_DOCS:

1022 __call__ = _HeightIDW.__call__

1023 height = _HeightIDW.height

1024

1025

1026 class HeightIDWthomas(_HeightIDW):

1027 '''Height interpolator using U{Inverse Distance Weighting

1028 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW)

1029 and function L{pygeodesy.thomas_}.

1030 '''

1031 def __init__(self, knots, beta=2, **name__datum_wrap):

1032 '''New L{HeightIDWthomas} interpolator.

1033

1034 @kwarg name__datum_wrap: Optional C{B{name}=NN} for this

1035 height interpolator (C{str}) and any keyword

1036 arguments for function L{pygeodesy.thomas}.

1037

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

1039 '''

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

1041 self._func = _formy.thomas

1042

1043 if _FOR_DOCS:

1044 __call__ = _HeightIDW.__call__

1045 height = _HeightIDW.height

1046

1047

1048 class HeightIDWvincentys(_HeightIDW):

1049 '''Height interpolator using U{Inverse Distance Weighting

1050 <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW)

1051 and function L{pygeodesy.vincentys_}.

1052

1053 @note: See note at function L{pygeodesy.vincentys_}.

1054 '''

1055 def __init__(self, knots, beta=2, **name__radius_wrap):

1056 '''New L{HeightIDWvincentys} interpolator.

1057

1058 @kwarg name__radius_wrap: Optional C{B{name}=NN} for this

1059 height interpolator (C{str}) and any keyword

1060 arguments for function L{pygeodesy.vincentys}.

1061

1062 @see: L{Here<_HeightIDW.__init__>} for further details.

1063 '''

1064 _HeightIDW.__init__(self, knots, beta=beta, **name__radius_wrap)

1065 self._func = _formy.vincentys

1066

1067 if _FOR_DOCS:

1068 __call__ = _HeightIDW.__call__

1069 height = _HeightIDW.height

1070

1071

1072__all__ += _ALL_DOCS(_HeightBase, _HeightIDW, _HeightNamed)

1073

1074# **) MIT License

1075#

1076# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1077#

1078# Permission is hereby granted, free of charge, to any person obtaining a

1079# copy of this software and associated documentation files (the "Software"),

1080# to deal in the Software without restriction, including without limitation

1081# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1082# and/or sell copies of the Software, and to permit persons to whom the

1083# Software is furnished to do so, subject to the following conditions:

1084#

1085# The above copyright notice and this permission notice shall be included

1086# in all copies or substantial portions of the Software.

1087#

1088# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1089# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1090# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1091# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1092# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1093# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1094# OTHER DEALINGS IN THE SOFTWARE.