Coverage for pygeodesy/geoids.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Geoid models and geoid height interpolations. 

5 

6Classes L{GeoidG2012B}, L{GeoidKarney} and L{GeoidPGM} to interpolate the 

7height of various U{geoid<https://WikiPedia.org/wiki/Geoid>}s at C{LatLon} 

8locations or separate lat-/longitudes using different interpolation methods 

9and C{geoid} model files. 

10 

11L{GeoidKarney} is a transcoding of I{Charles Karney}'s C++ class U{Geoid 

12<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} to pure Python. 

13The L{GeoidG2012B} and L{GeoidPGM} interpolators both depend on U{scipy 

14<https://SciPy.org>} and U{numpy<https://PyPI.org/project/numpy>} and 

15require those packages to be installed. 

16 

17In addition, each geoid interpolator needs C{grid knots} (down)loaded from 

18a C{geoid} model file, I{specific to the interpolator}, more details below 

19and in the documentation of the interpolator class. For each interpolator, 

20there are several interpolation choices, like I{linear}, I{cubic}, etc. 

21 

22Typical usage 

23============= 

24 

251. Choose one of the interpolator classes L{GeoidG2012B}, L{GeoidKarney} 

26or L{GeoidPGM} and download a C{geoid} model file, containing locations with 

27known heights also referred to as the C{grid knots}. See the documentation 

28of the interpolator class for references to available C{grid} models. 

29 

30C{>>> from pygeodesy import GeoidG2012B # or -Karney or -PGM as GeoidXyz} 

31 

322. Instantiate an interpolator with the C{geoid} model file and use keyword 

33arguments to select different interpolation options 

34 

35C{>>> ginterpolator = GeoidXyz(geoid_model_file, **options)} 

36 

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

38 

39C{>>> ll = LatLon(1, 2, ...)} 

40 

41C{>>> h = ginterpolator(ll)} 

42 

43or 

44 

45C{>>> h0, h1, h2, ... = ginterpolator(ll0, ll1, ll2, ...)} 

46 

47or a list, tuple, generator, etc. of C{LatLon}s 

48 

49C{>>> hs = ginterpolator(lls)} 

50 

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

52 

53C{>>> h = ginterpolator.height(lat, lon)} 

54 

55or as 2 lists, 2 tuples, etc. 

56 

57C{>>> hs = ginterpolator.height(lats, lons)} 

58 

595. An example is in U{issue #64<https://GitHub.com/mrJean1/PyGeodesy/issues/64>}, 

60courtesy of SBFRF. 

61 

62@note: Classes L{GeoidG2012B} and L{GeoidPGM} require both U{numpy 

63 <https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} 

64 to be installed. 

65 

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

67 C{scipy} can be thrown as L{SciPyWarning} exceptions, provided Python 

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

69 

70@see: I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}, 

71 U{Geoid height<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} and U{Installing 

72 the Geoid datasets<https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}, 

73 U{SciPy<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} interpolation 

74 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/generated/scipy. 

75 interpolate.RectBivariateSpline.html>} and U{interp2d<https://docs.SciPy.org/doc/scipy/ 

76 reference/generated/scipy.interpolate.interp2d.html>}, functions L{elevations.elevation2} 

77 and L{elevations.geoidHeight2}, U{I{Ellispoid vs Orthometric Elevations}<https:// 

78 www.YouTube.com/watch?v=dX6a6kCk3Po>} and U{I{Pitfalls Related to Ellipsoid Height 

79 and Height Above Mean Sea Level (AMSL)}<https://Wiki.ROS.org/mavros#mavros.2FPlugins. 

80 Avoiding_Pitfalls_Related_to_Ellipsoid_Height_and_Height_Above_Mean_Sea_Level>}. 

81''' 

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

83from __future__ import division as _; del _ # PYCHOK semicolon 

84 

85from pygeodesy.basics import len2, map1, isodd, ub2str as _ub2str 

86from pygeodesy.constants import EPS, _float as _F, _0_0, _1_0, _180_0, _360_0 

87# from pygeodesy.datums import _ellipsoidal_datum # from .heights 

88# from pygeodesy.dms import parseDMS2 # _MODS 

89from pygeodesy.errors import _incompatible, LenError, RangeError, SciPyError, \ 

90 _SciPyIssue, _xkwds_pop2 

91from pygeodesy.fmath import favg, Fdot, fdot, Fhorner, frange 

92# from pygoedesy.formy import heightOrthometric # _MODS 

93from pygeodesy.heights import _as_llis2, _ascalar, _height_called, HeightError, \ 

94 _HeightsBase, _ellipsoidal_datum, _Wrap 

95# from pygeodesy.internals import _version2 # _MODS 

96from pygeodesy.interns import MISSING, NN, _4_, _COLONSPACE_, _COMMASPACE_, _cubic_, \ 

97 _E_, _height_, _in_, _kind_, _lat_, _linear_, _lon_, \ 

98 _mean_, _N_, _n_a_, _numpy_, _on_, _outside_, _S_, _s_, \ 

99 _scipy_, _SPACE_, _stdev_, _tbd_, _W_, _width_ 

100from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS 

101from pygeodesy.named import _name__, _Named, _NamedTuple 

102# from pygeodesy.namedTuples import LatLon3Tuple # _MODS 

103from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_ROver 

104from pygeodesy.streprs import attrs, Fmt, fstr, pairs 

105from pygeodesy.units import Height, Int_, Lat, Lon 

106# from pygeodesy.utily import _Wrap # from .heights 

107 

108from math import floor 

109import os.path as _os_path 

110from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET 

111from struct import calcsize as _calcsize, unpack as _unpack 

112try: 

113 from StringIO import StringIO as _BytesIO # reads bytes 

114 _ub2str = str # PYCHOK convert bytes to str for egm*.pgm text 

115 

116except ImportError: # Python 3+ 

117 from io import BytesIO as _BytesIO # PYCHOK expected 

118 

119__all__ = _ALL_LAZY.geoids 

120__version__ = '24.07.12' 

121 

122_assert_ = 'assert' 

123_bHASH_ = b'#' 

124_endian_ = 'endian' 

125_format_ = '%s %r' 

126_header_ = 'header' 

127_intCs = {} # cache int value 

128_interp2d_ks = {-2: _linear_, 

129 -3: _cubic_, 

130 -5: 'quintic'} 

131_lli_ = 'lli' 

132_non_increasing_ = 'non-increasing' 

133_rb_ = 'rb' 

134_supported_ = 'supported' 

135 

136 

137class _GeoidBase(_HeightsBase): 

138 '''(INTERNAL) Base class for C{Geoid...}s. 

139 ''' 

140 _cropped = None 

141# _datum = _WGS84 # from _HeightsBase 

142 _egm = None # open C{egm*.pgm} geoid file 

143 _endian = _tbd_ 

144 _geoid = _n_a_ 

145 _hs_y_x = None # numpy 2darray, row-major order 

146 _interp2d = None # interp2d interpolation 

147 _kind = 3 # order for interp2d, RectBivariateSpline 

148# _kmin = 2 # min number of knots 

149 _knots = 0 # nlat * nlon 

150 _mean = None # fixed in GeoidKarney 

151# _name = NN # _Named 

152 _nBytes = 0 # numpy size in bytes, float64 

153 _pgm = None # PGM attributes, C{_PGM} or C{None} 

154 _sizeB = 0 # geoid file size in bytes 

155 _smooth = 0 # used only for RectBivariateSpline 

156 _stdev = None # fixed in GeoidKarney 

157 _u2B = 0 # np.itemsize or undefined 

158 

159 _lat_d = _0_0 # increment, +tive 

160 _lat_lo = _0_0 # lower lat, south 

161 _lat_hi = _0_0 # upper lat, noth 

162 _lon_d = _0_0 # increment, +tive 

163 _lon_lo = _0_0 # left lon, west 

164 _lon_hi = _0_0 # right lon, east 

165 _lon_of = _0_0 # forward lon offset 

166 _lon_og = _0_0 # reverse lon offset 

167 

168 _center = None # (lat, lon, height) 

169 _yx_hits = None # cache hits, ala Karney 

170 

171 def __init__(self, hs, p): 

172 '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator 

173 and several internal geoid attributes. 

174 

175 @arg hs: Grid knots with known height (C{numpy 2darray}). 

176 @arg p: The C{slat, wlon, nlat, nlon, dlat, dlon} and 

177 other geoid parameters (C{INTERNAL}). 

178 

179 @raise GeoidError: Incompatible grid B{C{hs}} shape or 

180 invalid B{C{kind}}. 

181 

182 @raise LenError: Mismatch grid B{C{hs}} axis. 

183 

184 @raise SciPyError: A C{scipy.interpolate.inter2d} or 

185 C{-.RectBivariateSpline} issue. 

186 

187 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or 

188 C{-.RectBivariateSpline} warning as 

189 exception. 

190 

191 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, 

192 specify keyword argument C{B{kind}=1..5} to use 

193 C{scipy.interpolate.RectBivariateSpline}. 

194 ''' 

195 spi = self.scipy_interpolate 

196 # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and 

197 # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...) 

198 # require the shape of hs to be (len(ys), len(xs)), note 

199 # the different (xs, ys, ...) and (ys, xs, ...) orders 

200 if (p.nlat, p.nlon) != hs.shape: 

201 raise GeoidError(shape=hs.shape, txt=_incompatible((p.nlat, p.nlon))) 

202 

203 # both axes and bounding box 

204 ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, _lat_ + _s_) 

205 xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, _lon_ + _s_) 

206 

207 bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi 

208 # geoid grids are typically stored in row-major order, some 

209 # with rows (90..-90) reversed and columns (0..360) wrapped 

210 # to Easten longitude, 0 <= east < 180 and 180 <= west < 360 

211 k = self.kind 

212 if k in _interp2d_ks: # .interp2d DEPRECATED since scipy 1.10 

213 if self._scipy_version() < (1, 10): 

214 self._interp2d = spi.interp2d(xs, ys, hs, kind=_interp2d_ks[k]) 

215 else: # call and overwrite the DEPRECATED .interp2d 

216 self._interp2d = self._interp2d(xs, ys, hs, k) 

217 elif 1 <= k <= 5: 

218 self._ev = spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k, 

219 s=self._smooth).ev 

220 else: 

221 raise GeoidError(kind=k) 

222 

223 self._hs_y_x = hs # numpy 2darray, row-major 

224 self._nBytes = hs.nbytes # numpy size in bytes 

225 self._knots = p.knots # grid knots 

226 self._lon_of = float(p.flon) # forward offset 

227 self._lon_og = float(p.glon) # reverse offset 

228 # shrink the box by 1 unit on every side 

229 # bb += self._lat_d, -self._lat_d, self._lon_d, -self._lon_d 

230 self._lat_lo = float(bb[0]) 

231 self._lat_hi = float(bb[1]) 

232 self._lon_lo = float(bb[2] - p.glon) 

233 self._lon_hi = float(bb[3] - p.glon) 

234 

235 def __call__(self, *llis, **wrap_H): 

236 '''Interpolate the geoid height for one or several locations. 

237 

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

239 @kwarg wrap_H: Keyword arguments C{B{wrap}=False} (C{bool}) and 

240 C{B{H}=False} (C{bool}). If C{B{wrap} is True}, 

241 wrap or I{normalize} all B{C{llis}} locations. If 

242 C{B{H} is True}, return the I{orthometric} height 

243 instead of the I{geoid} height at each location. 

244 

245 @return: A single interpolated geoid (or orthometric) height 

246 (C{float}) or a list or tuple of interpolated geoid 

247 (or orthometric) heights (C{float}s). 

248 

249 @raise GeoidError: Insufficient number of B{C{llis}}, an 

250 invalid B{C{lli}} or the C{egm*.pgm} 

251 geoid file is closed. 

252 

253 @raise RangeError: An B{C{lli}} is outside this geoid's lat- 

254 or longitude range. 

255 

256 @raise SciPyError: A C{scipy.interpolate.inter2d} or 

257 C{-.RectBivariateSpline} issue. 

258 

259 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or 

260 C{-.RectBivariateSpline} warning as 

261 exception. 

262 

263 @note: To obtain I{orthometric} heights, each B{C{llis}} 

264 location must have an ellipsoid C{height} or C{h} 

265 attribute, otherwise C{height=0} is used. 

266 

267 @see: Function L{pygeodesy.heightOrthometric}. 

268 ''' 

269 return self._called(llis, True, **wrap_H) 

270 

271 def __enter__(self): 

272 '''Open context. 

273 ''' 

274 return self 

275 

276 def __exit__(self, *unused): # PYCHOK exc_type, exc_value, exc_traceback) 

277 '''Close context. 

278 ''' 

279 self.close() 

280 # return None # XXX False 

281 

282 def __repr__(self): 

283 return self.toStr() 

284 

285 def __str__(self): 

286 return Fmt.PAREN(self.classname, repr(self.name)) 

287 

288 def _called(self, llis, scipy, wrap=False, H=False): 

289 # handle __call__ 

290 _H = _MODS.formy.heightOrthometric if H else None 

291 _as, llis = _as_llis2(llis, Error=GeoidError) 

292 hs, _w = [], _Wrap._latlonop(wrap) 

293 _a, _h = hs.append, self._hGeoid 

294 try: 

295 for i, lli in enumerate(llis): 

296 N = _h(*_w(lli.lat, lli.lon)) 

297 # orthometric or geoid height 

298 _a(_H(lli, N) if _H else N) 

299 return _as(hs) 

300 

301 except (GeoidError, RangeError) as x: 

302 # XXX avoid str(LatLon()) degree symbols 

303 t = _lli_ if _as is _ascalar else Fmt.INDEX(llis=i) 

304 lli = fstr((lli.lat, lli.lon), strepr=repr) 

305 raise type(x)(t, lli, wrap=wrap, H=H, cause=x) 

306 except Exception as x: 

307 if scipy and self.scipy: 

308 raise _SciPyIssue(x) 

309 else: 

310 raise 

311 

312 @Property_RO 

313 def _center(self): 

314 ''' Cache for method L{center}. 

315 ''' 

316 return self._llh3(favg(self._lat_lo, self._lat_hi), 

317 favg(self._lon_lo, self._lon_hi)) 

318 

319 def center(self, LatLon=None): 

320 '''Return the center location and height of this geoid. 

321 

322 @kwarg LatLon: Optional class to return the location and height 

323 (C{LatLon}) or C{None}. 

324 

325 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, 

326 height)} otherwise a B{C{LatLon}} instance with the lat-, 

327 longitude and geoid height of the center grid location. 

328 ''' 

329 return self._llh3LL(self._center, LatLon) 

330 

331 def close(self): 

332 '''Close the C{egm*.pgm} geoid file if open (and applicable). 

333 ''' 

334 if not self.closed: 

335 self._egm.close() 

336 self._egm = None 

337 

338 @property_RO 

339 def closed(self): 

340 '''Get the C{egm*.pgm} geoid file status. 

341 ''' 

342 return self._egm is None 

343 

344 @Property_RO 

345 def cropped(self): 

346 '''Is geoid cropped (C{bool} or C{None} if crop not supported). 

347 ''' 

348 return self._cropped 

349 

350 @Property_RO 

351 def dtype(self): 

352 '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/ 

353 reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}). 

354 ''' 

355 return self._hs_y_x.dtype 

356 

357 @Property_RO 

358 def endian(self): 

359 '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/ 

360 doc/numpy/reference/generated/numpy.dtype.html>} (C{str}). 

361 ''' 

362 return self._endian 

363 

364 def _ev(self, y, x): # PYCHOK expected 

365 # only used for .interpolate.interp2d, but 

366 # overwritten for .RectBivariateSpline, 

367 # note (y, x) must be flipped! 

368 return self._interp2d(x, y) 

369 

370 def _gaxis2(self, lo, d, n, name): 

371 # build grid axis, hi = lo + (n - 1) * d 

372 m, a = len2(frange(lo, n, d)) 

373 if m != n: 

374 raise LenError(self.__class__, grid=m, **{name: n}) 

375 if d < 0: 

376 d, a = -d, list(reversed(a)) 

377 for i in range(1, m): 

378 e = a[i] - a[i-1] 

379 if e < EPS: # non-increasing axis 

380 i = Fmt.INDEX(name, i) 

381 raise GeoidError(i, e, txt=_non_increasing_) 

382 return self.numpy.array(a), d 

383 

384 def _g2ll2(self, lat, lon): # PYCHOK no cover 

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

386 self._notOverloaded(lat, lon) 

387 

388 def _gyx2g2(self, y, x): 

389 # convert grid (y, x) indices to grid (lat, lon) 

390 return ((self._lat_lo + self._lat_d * y), 

391 (self._lon_lo + self._lon_of + self._lon_d * x)) 

392 

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

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

395 

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

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

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

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

400 

401 @return: A single interpolated geoid height (C{float}) or a 

402 list of interpolated geoid heights (C{float}s). 

403 

404 @raise GeoidError: Insufficient or non-matching number of 

405 B{C{lats}} and B{C{lons}}. 

406 

407 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this 

408 geoid's lat- or longitude range. 

409 

410 @raise SciPyError: A C{scipy.interpolate.inter2d} or 

411 C{-.RectBivariateSpline} issue. 

412 

413 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or 

414 C{-.RectBivariateSpline} warning as 

415 exception. 

416 ''' 

417 return _height_called(self, lats, lons, Error=GeoidError, **wrap) 

418 

419 def _hGeoid(self, lat, lon): 

420 out = self.outside(lat, lon) 

421 if out: 

422 lli = fstr((lat, lon), strepr=repr) 

423 raise RangeError(lli=lli, txt=_SPACE_(_outside_, _on_, out)) 

424 return float(self._ev(*self._ll2g2(lat, lon))) 

425 

426 @Property_RO 

427 def _highest(self): 

428 '''(INTERNAL) Cache for L{highest} method. 

429 ''' 

430 return self._llh3minmax(True) 

431 

432 def highest(self, LatLon=None, **unused): 

433 '''Return the location and largest height of this geoid. 

434 

435 @kwarg LatLon: Optional class to return the location and height 

436 (C{LatLon}) or C{None}. 

437 

438 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, 

439 height)} otherwise a B{C{LatLon}} instance with the lat-, 

440 longitude and geoid height of the highest grid location. 

441 ''' 

442 return self._llh3LL(self._highest, LatLon) 

443 

444 @Property_RO 

445 def hits(self): 

446 '''Get the number of cache hits (C{int} or C{None}). 

447 ''' 

448 return self._yx_hits 

449 

450 @deprecated_method 

451 def _interp2d(self, xs, ys, hs=(), k=0): # overwritten in .__init__ above 

452 '''DEPRECATED on 23.01.06, use keyword argument C{B{kind}=1..5}.''' 

453 # assert k in _interp2d_ks # and len(hs) == len(xs) == len(ys) 

454 try: 

455 return self.scipy_interpolate.interp2d(xs, ys, hs, kind=_interp2d_ks[k]) 

456 except AttributeError as x: 

457 raise SciPyError(interp2d=MISSING, kind=k, cause=x) 

458 

459 @Property_RO 

460 def kind(self): 

461 '''Get the interpolator kind and order (C{int}). 

462 ''' 

463 return self._kind 

464 

465 @Property_RO 

466 def knots(self): 

467 '''Get the number of grid knots (C{int}). 

468 ''' 

469 return self._knots 

470 

471 def _ll2g2(self, lat, lon): # PYCHOK no cover 

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

473 self._notOverloaded(lat, lon) 

474 

475 @property_ROver 

476 def _LL3T(self): 

477 '''(INTERNAL) Get L{LatLon3Tuple}, I{once}. 

478 ''' 

479 return _MODS.namedTuples.LatLon3Tuple # overwrite property_ROver 

480 

481 def _llh3(self, lat, lon): 

482 return self._LL3T(lat, lon, self._hGeoid(lat, lon), name=self.name) 

483 

484 def _llh3LL(self, llh, LatLon): 

485 return llh if LatLon is None else self._xnamed(LatLon(*llh)) 

486 

487 def _llh3minmax(self, highest=True, *unused): 

488 hs, np = self._hs_y_x, self.numpy 

489 # <https://docs.SciPy.org/doc/numpy/reference/generated/ 

490 # numpy.argmin.html#numpy.argmin> 

491 arg = np.argmax if highest else np.argmin 

492 y, x = np.unravel_index(arg(hs, axis=None), hs.shape) 

493 return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),) 

494 

495 def _load(self, g, dtype, n, offset=0): 

496 # numpy.fromfile, like .frombuffer 

497 g.seek(offset, _SEEK_SET) 

498 return self.numpy.fromfile(g, dtype, n) 

499 

500 @Property_RO 

501 def _lowerleft(self): 

502 '''(INTERNAL) Cache for L{lowerleft}. 

503 ''' 

504 return self._llh3(self._lat_lo, self._lon_lo) 

505 

506 def lowerleft(self, LatLon=None): 

507 '''Return the lower-left location and height of this geoid. 

508 

509 @kwarg LatLon: Optional class to return the location 

510 (C{LatLon}) and height or C{None}. 

511 

512 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)} 

513 otherwise a B{C{LatLon}} instance with the lat-, longitude and 

514 geoid height of the lower-left, SW grid corner. 

515 ''' 

516 return self._llh3LL(self._lowerleft, LatLon) 

517 

518 @Property_RO 

519 def _loweright(self): 

520 '''(INTERNAL) Cache for L{loweright}. 

521 ''' 

522 return self._llh3(self._lat_lo, self._lon_hi) 

523 

524 def loweright(self, LatLon=None): 

525 '''Return the lower-right location and height of this geoid. 

526 

527 @kwarg LatLon: Optional class to return the location and height 

528 (C{LatLon}) or C{None}. 

529 

530 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)} 

531 otherwise a B{C{LatLon}} instance with the lat-, longitude and 

532 geoid height of the lower-right, SE grid corner. 

533 ''' 

534 

535 return self._llh3LL(self._loweright, LatLon) 

536 

537 lowerright = loweright # synonymous 

538 

539 @Property_RO 

540 def _lowest(self): 

541 '''(INTERNAL) Cache for L{lowest}. 

542 ''' 

543 return self._llh3minmax(False) 

544 

545 def lowest(self, LatLon=None, **unused): 

546 '''Return the location and lowest height of this geoid. 

547 

548 @kwarg LatLon: Optional class to return the location and height 

549 (C{LatLon}) or C{None}. 

550 

551 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, 

552 height)} otherwise a B{C{LatLon}} instance with the lat-, 

553 longitude and geoid height of the lowest grid location. 

554 ''' 

555 return self._llh3LL(self._lowest, LatLon) 

556 

557 @Property_RO 

558 def mean(self): 

559 '''Get the mean of this geoid's heights (C{float}). 

560 ''' 

561 if self._mean is None: # see GeoidKarney 

562 self._mean = float(self.numpy.mean(self._hs_y_x)) 

563 return self._mean 

564 

565 @property_RO 

566 def name(self): 

567 '''Get the name of this geoid (C{str}). 

568 ''' 

569 return _HeightsBase.name.fget(self) or self._geoid # recursion 

570 

571 @Property_RO 

572 def nBytes(self): 

573 '''Get the grid in-memory size in bytes (C{int}). 

574 ''' 

575 return self._nBytes 

576 

577 def _open(self, geoid, datum, kind, name, smooth): 

578 # open the geoid file 

579 try: 

580 self._geoid = _os_path.basename(geoid) 

581 self._sizeB = _os_path.getsize(geoid) 

582 g = open(geoid, _rb_) 

583 except (IOError, OSError) as x: 

584 raise GeoidError(geoid=geoid, cause=x) 

585 

586 if datum not in (None, self._datum): 

587 self._datum = _ellipsoidal_datum(datum, name=name) 

588 self._kind = int(kind) 

589 if name: 

590 _HeightsBase.name.fset(self, name) # rename 

591 if smooth: 

592 self._smooth = Int_(smooth=smooth, Error=GeoidError, low=0) 

593 

594 return g 

595 

596 def outside(self, lat, lon): 

597 '''Check whether a location is outside this geoid's 

598 lat-/longitude or crop range. 

599 

600 @arg lat: The latitude (C{degrees}). 

601 @arg lon: The longitude (C{degrees}). 

602 

603 @return: A 1- or 2-character C{str} if outside or an 

604 empty C{str} if inside. 

605 ''' 

606 return (_S_ if lat < self._lat_lo else 

607 (_N_ if lat > self._lat_hi else NN)) + \ 

608 (_W_ if lon < self._lon_lo else 

609 (_E_ if lon > self._lon_hi else NN)) 

610 

611 @Property_RO 

612 def pgm(self): 

613 '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable). 

614 ''' 

615 return self._pgm 

616 

617 @Property_RO 

618 def sizeB(self): 

619 '''Get the geoid grid file size in bytes (C{int}). 

620 ''' 

621 return self._sizeB 

622 

623 @Property_RO 

624 def smooth(self): 

625 '''Get the C{RectBivariateSpline} smoothing (C{int}). 

626 ''' 

627 return self._smooth 

628 

629 @Property_RO 

630 def stdev(self): 

631 '''Get the standard deviation of this geoid's heights (C{float}) or C{None}. 

632 ''' 

633 if self._stdev is None: # see GeoidKarney 

634 self._stdev = float(self.numpy.std(self._hs_y_x)) 

635 return self._stdev 

636 

637 def _swne(self, crop): 

638 # crop box to 4-tuple (s, w, n, e) 

639 try: 

640 if len(crop) == 2: 

641 try: # sw, ne LatLons 

642 swne = (crop[0].lat, crop[0].lon, 

643 crop[1].lat, crop[1].lon) 

644 except AttributeError: # (s, w), (n, e) 

645 swne = tuple(crop[0]) + tuple(crop[1]) 

646 else: # (s, w, n, e) 

647 swne = crop 

648 if len(swne) == 4: 

649 s, w, n, e = map(float, swne) 

650 if -90 <= s <= (n - _1_0) <= 89 and \ 

651 -180 <= w <= (e - _1_0) <= 179: 

652 return s, w, n, e 

653 except (IndexError, TypeError, ValueError): 

654 pass 

655 raise GeoidError(crop=crop) 

656 

657 def toStr(self, prec=3, sep=_COMMASPACE_): # PYCHOK signature 

658 '''This geoid and all geoid attributes as a string. 

659 

660 @kwarg prec: Number of decimal digits (0..9 or C{None} for 

661 default). Trailing zero decimals are stripped 

662 for B{C{prec}} values of 1 and above, but kept 

663 for negative B{C{prec}} values. 

664 @kwarg sep: Separator to join (C{str}). 

665 

666 @return: Geoid name and attributes (C{str}). 

667 ''' 

668 s = 1 if self.kind < 0 else 2 

669 t = tuple(Fmt.PAREN(m.__name__, fstr(m(), prec=prec)) for m in 

670 (self.lowerleft, self.upperright, 

671 self.center, 

672 self.highest, self.lowest)) + \ 

673 attrs( _mean_, _stdev_, prec=prec, Nones=False) + \ 

674 attrs((_kind_, 'smooth')[:s], prec=prec, Nones=False) + \ 

675 attrs( 'cropped', 'dtype', _endian_, 'hits', 'knots', 'nBytes', 

676 'sizeB', _scipy_, _numpy_, prec=prec, Nones=False) 

677 return _COLONSPACE_(self, sep.join(t)) 

678 

679 @Property_RO 

680 def u2B(self): 

681 '''Get the PGM itemsize in bytes (C{int}). 

682 ''' 

683 return self._u2B 

684 

685 @Property_RO 

686 def _upperleft(self): 

687 '''(INTERNAL) Cache for method L{upperleft}. 

688 ''' 

689 return self._llh3(self._lat_hi, self._lon_lo) 

690 

691 def upperleft(self, LatLon=None): 

692 '''Return the upper-left location and height of this geoid. 

693 

694 @kwarg LatLon: Optional class to return the location and height 

695 (C{LatLon}) or C{None}. 

696 

697 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)} 

698 otherwise a B{C{LatLon}} instance with the lat-, longitude and 

699 geoid height of the upper-left, NW grid corner. 

700 ''' 

701 return self._llh3LL(self._upperleft, LatLon) 

702 

703 @Property_RO 

704 def _upperright(self): 

705 '''(INTERNAL) Cache for method L{upperright}. 

706 ''' 

707 return self._llh3(self._lat_hi, self._lon_hi) 

708 

709 def upperright(self, LatLon=None): 

710 '''Return the upper-right location and height of this geoid. 

711 

712 @kwarg LatLon: Optional class to return the location and height 

713 (C{LatLon}) or C{None}. 

714 

715 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)} 

716 otherwise a B{C{LatLon}} instance with the lat-, longitude and 

717 geoid height of the upper-right, NE grid corner. 

718 ''' 

719 return self._llh3LL(self._upperright, LatLon) 

720 

721 

722class GeoidError(HeightError): 

723 '''Geoid interpolator C{Geoid...} or interpolation issue. 

724 ''' 

725 pass 

726 

727 

728class GeoidG2012B(_GeoidBase): 

729 '''Geoid height interpolator for U{GEOID12B Model 

730 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS 

731 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>}, 

732 U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>}, 

733 U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>}, 

734 U{Guam and Northern Mariana Islands 

735 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>}, 

736 U{Puerto Rico and U.S. Virgin Islands 

737 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and 

738 U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>} 

739 based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/ 

740 scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} 

741 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ 

742 scipy.interpolate.interp2d.html>} interpolation. 

743 

744 Use any of the binary C{le} (little endian) or C{be} (big endian) 

745 C{g2012b*.bin} grid files. 

746 ''' 

747 def __init__(self, g2012b_bin, datum=None, # NAD 83 Ellipsoid 

748 kind=3, smooth=0, **name_crop): 

749 '''New L{GeoidG2012B} interpolator. 

750 

751 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}). 

752 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

753 or L{a_f2Tuple}), default C{WGS84}. 

754 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for 

755 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ 

756 reference/generated/scipy.interpolate.RectBivariateSpline.html>}, 

757 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ 

758 reference/generated/scipy.interpolate.interp2d.html>}, -3 

759 for C{interp2d cubic} or -5 for C{interp2d quintic}. 

760 @kwarg smooth: Smoothing factor for U{RectBivariateSpline 

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

762 scipy.interpolate.RectBivariateSpline.html>} 

763 only (C{int}). 

764 @kwarg name_crop: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED 

765 keyword argument C{B{crop}}, use C{B{crop}=None} to ignore. 

766 

767 @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue or invalid 

768 B{C{crop}}, B{C{kind}} or B{C{smooth}}. 

769 

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

771 installed. 

772 

773 @raise LenError: Grid file B{C{g2012b_bin}} axis mismatch. 

774 

775 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. 

776 

777 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} 

778 warning as exception. 

779 

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

781 

782 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify 

783 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}. 

784 ''' 

785 crop, name = _xkwds_pop2(name_crop, crop=None) 

786 if crop is not None: 

787 raise GeoidError(crop=crop, txt_not_=_supported_) 

788 

789 g = self._open(g2012b_bin, datum, kind, _name__(**name), smooth) 

790 _ = self.numpy # import numpy for ._load and 

791 

792 try: 

793 p = _Gpars() 

794 n = (self.sizeB // 4) - 11 # number of f4 heights 

795 # U{numpy dtype formats are different from Python struct formats 

796 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} 

797 for en_ in ('<', '>'): 

798 # skip 4xf8, get 3xi4 

799 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32)) 

800 if ien == 1: # correct endian 

801 p.knots = p.nlat * p.nlon 

802 if p.knots == n and 1 < p.nlat < n \ 

803 and 1 < p.nlon < n: 

804 self._endian = en_+'f4' 

805 break 

806 else: # couldn't validate endian 

807 raise GeoidError(_endian_) 

808 

809 # get the first 4xf8 

810 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4)) 

811 # read all f4 heights, ignoring the first 4xf8 and 3xi4 

812 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon) 

813 p.wlon -= _360_0 # western-most East longitude to earth (..., lon) 

814 _GeoidBase.__init__(self, hs, p) 

815 

816 except Exception as x: 

817 raise _SciPyIssue(x, _in_, repr(g2012b_bin)) 

818 finally: 

819 g.close() 

820 

821 def _g2ll2(self, lat, lon): 

822 # convert grid (lat, lon) to earth (lat, lon) 

823 return lat, lon 

824 

825 def _ll2g2(self, lat, lon): 

826 # convert earth (lat, lon) to grid (lat, lon) 

827 return lat, lon 

828 

829 if _FOR_DOCS: 

830 __call__ = _GeoidBase.__call__ 

831 height = _GeoidBase.height 

832 

833 

834class GeoidHeight5Tuple(_NamedTuple): # .geoids.py 

835 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat 

836 <https://SourceForge.net/projects/geographiclib/files/testdata/>} 

837 tests with the heights for 3 different EGM grids at C{degrees90} 

838 and C{degrees180} degrees (after converting C{lon} from original 

839 C{0 <= EasterLon <= 360}). 

840 ''' 

841 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008') 

842 _Units_ = ( Lat, Lon, Height, Height, Height) 

843 

844 

845def _I(i): 

846 '''(INTERNAL) Cache a single C{int} constant. 

847 ''' 

848 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs 

849 

850 

851def _T(*cs): 

852 '''(INTERNAL) Cache a tuple of single C{int} constants. 

853 ''' 

854 return map1(_I, *cs) 

855 

856_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0) 

857 

858 

859class GeoidKarney(_GeoidBase): 

860 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth 

861 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/ 

862 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ 

863 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic 

864 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching 

865 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>} 

866 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid 

867 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}. 

868 

869 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm 

870 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>} 

871 datasets. 

872 ''' 

873 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators 

874 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp 

875 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0), 

876 _T0s12, 

877 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7), 

878 _T0s12, 

879 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent 

880 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42), 

881 _T0s12, 

882 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0), 

883 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84), 

884 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent 

885 

886 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9), 

887 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18), 

888 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8), 

889 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0), 

890 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent 

891 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30), 

892 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0), 

893 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0), 

894 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60), 

895 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)), 

896 

897 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent 

898 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36), 

899 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2), 

900 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0), 

901 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent 

902 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51), 

903 _T0s12, 

904 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0), 

905 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102), 

906 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31))) 

907 

908 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices 

909 _T(1, 0), 

910 _T(0, 1), 

911 _T(1, 1)) 

912 

913 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices 

914 _T( 1, -1), 

915 _T(-1, 0), 

916 _T( 0, 0), 

917 _T( 1, 0), 

918 _T( 2, 0), 

919 _T(-1, 1), 

920 _T( 0, 1), 

921 _T( 1, 1), 

922 _T( 2, 1), 

923 _T( 0, 2), 

924 _T( 1, 2)) 

925 

926 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short) 

927 _4endian = '>4H' # struct.unpack 4 ushorts 

928 _Rendian = NN # struct.unpack a row of ushorts 

929# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else ( 

930# (-8.167, 147.25, 85.422) if egm96-5.pgm else 

931# (-4.5, 148.75, 81.33)) # egm84-15.pgm 

932# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else ( 

933# (4.667, 78.833, -107.043) if egm96-5.pgm else 

934# (4.75, 79.25, -107.34)) # egm84-15.pgm 

935 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15 

936 _nBytes = None # not applicable 

937 _nterms = len(_C3[0]) # columns length, number of row 

938 _smooth = None # not applicable 

939 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15 

940 _u2B = _calcsize(_endian) # pixelsize_ in bytes 

941 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes 

942 _Ru2B = 0 # row of pixelsize_s in bytes 

943 _yxH = () # cache (y, x) indices 

944 _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H 

945 _yx_hits = 0 # cache hits 

946 

947 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 

948 kind=3, **name_smooth): 

949 '''New L{GeoidKarney} interpolator. 

950 

951 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ 

952 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see 

953 note below. 

954 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south, 

955 west, north, east}), 2-tuple (C{(south, west), (north, 

956 east)}) or 2, in C{degrees90} lat- and C{degrees180} 

957 longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of 

958 C{LatLon} instances. 

959 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

960 or L{a_f2Tuple}), default C{WGS84}. 

961 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3 

962 for C{cubic}. 

963 @kwarg name_smooth: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED 

964 keyword argument C{B{smooth}}, use C{B{smooth}=None} to ignore. 

965 

966 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid 

967 B{C{crop}}, B{C{kind}} or B{C{smooth}}. 

968 

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

970 

971 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}. 

972 

973 @note: Geoid file B{C{egm_pgm}} remains open and must be closed 

974 by calling the C{close} method or by using this instance 

975 in a C{with B{GeoidKarney}(...) as ...} context. 

976 ''' 

977 smooth, name = _xkwds_pop2(name_smooth, smooth=None) 

978 if smooth is not None: 

979 raise GeoidError(smooth=smooth, txt_not_=_supported_) 

980 

981 if kind in (2,): 

982 self._evH = self._ev2H 

983 elif kind not in (3,): 

984 raise GeoidError(kind=kind) 

985 

986 self._egm = g = self._open(egm_pgm, datum, kind, _name__(**name), None) 

987 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) 

988 

989 self._Rendian = self._4endian.replace(_4_, str(p.nlon)) 

990 self._Ru2B = _calcsize(self._Rendian) 

991 

992 self._knots = p.knots # grid knots 

993 self._lon_of = float(p.flon) # forward offset 

994 self._lon_og = float(p.glon) # reverse offset 

995 # set earth (lat, lon) limits (s, w, n, e) 

996 self._lat_lo, self._lon_lo, \ 

997 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4) 

998 self._cropped = True if crop else False 

999 

1000 def __call__(self, *llis, **wrap_H): 

1001 '''Interpolate the geoid height for one or several locations. 

1002 

1003 @arg llis: One or more locations (C{LatLon}s), all positional. 

1004 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}. 

1005 If C{B{wrap} is True}, wrap or I{normalize} all 

1006 B{C{llis}} locations (C{bool}). If C{B{H} is True}, 

1007 return the I{orthometric} height instead of the 

1008 I{geoid} height at each location (C{bool}). 

1009 

1010 @return: A single interpolated geoid (or orthometric) height 

1011 (C{float}) or a list or tuple of interpolated geoid 

1012 (or orthometric) heights (C{float}s). 

1013 

1014 @raise GeoidError: Insufficient number of B{C{llis}}, an 

1015 invalid B{C{lli}} or the C{egm*.pgm} 

1016 geoid file is closed. 

1017 

1018 @raise RangeError: An B{C{lli}} is outside this geoid's lat- 

1019 or longitude range. 

1020 

1021 @note: To obtain I{orthometric} heights, each B{C{llis}} 

1022 location must have an ellipsoid C{height} or C{h} 

1023 attribute, otherwise C{height=0} is used. 

1024 

1025 @see: Function L{pygeodesy.heightOrthometric}. 

1026 ''' 

1027 return self._called(llis, False, **wrap_H) 

1028 

1029 def _c0c3v(self, y, x): 

1030 # get the common denominator, the 10x12 cubic matrix and 

1031 # the 12 cubic v-coefficients around geoid index (y, x) 

1032 p = self._pgm 

1033 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2): 

1034 # read 4x4 ushorts, drop the 4 corners 

1035 g = self._egm 

1036 e = self._4endian 

1037 n = self._4u2B 

1038 R = self._Ru2B 

1039 

1040 b = self._seek(y - 1, x - 1) 

1041 v = _unpack(e, g.read(n))[1:3] 

1042 b += R 

1043 g.seek(b, _SEEK_SET) 

1044 v += _unpack(e, g.read(n)) 

1045 b += R 

1046 g.seek(b, _SEEK_SET) 

1047 v += _unpack(e, g.read(n)) 

1048 b += R 

1049 g.seek(b, _SEEK_SET) 

1050 v += _unpack(e, g.read(n))[1:3] 

1051 j = 1 

1052 

1053 else: # likely some wrapped y and/or x's 

1054 v = self._raws(y, x, GeoidKarney._CM) 

1055 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2) 

1056 

1057 return GeoidKarney._C0[j], GeoidKarney._C3[j], v 

1058 

1059 @Property_RO 

1060 def dtype(self): 

1061 '''Get the geoid's grid data type (C{str}). 

1062 ''' 

1063 return 'ushort' 

1064 

1065 def _ev(self, lat, lon): # PYCHOK expected 

1066 # interpolate the geoid height at grid (lat, lon) 

1067 fy, fx = self._g2yx2(lat, lon) 

1068 y, x = int(floor(fy)), int(floor(fx)) 

1069 fy -= y 

1070 fx -= x 

1071 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H 

1072 H *= self._pgm.Scale # H.fmul(self._pgm.Scale) 

1073 H += self._pgm.Offset # H.fadd(self._pgm.Offset) 

1074 return H.fsum() 

1075 

1076 def _ev2H(self, fy, fx, *yx): 

1077 # compute the bilinear 4-tuple and interpolate raw H 

1078 if self._yxH == yx: 

1079 t = self._yxHt 

1080 self._yx_hits += 1 

1081 else: 

1082 y, x = self._yxH = yx 

1083 self._yxHt = t = self._raws(y, x, GeoidKarney._BT) 

1084 v = _1_0, -fx, fx 

1085 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy) 

1086 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy 

1087 return H 

1088 

1089 def _ev3H(self, fy, fx, *yx): 

1090 # compute the cubic 10-tuple and interpolate raw H 

1091 if self._yxH == yx: 

1092 t = self._yxHt 

1093 self._yx_hits += 1 

1094 else: 

1095 self._yxH = yx 

1096 c0, c3, v = self._c0c3v(*yx) 

1097 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)] 

1098 self._yxHt = t = tuple(t) 

1099 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ... 

1100 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) + 

1101 # fy * (t[2] + fx * (t[4] + fx * t[7]) + 

1102 # fy * (t[5] + fx * t[8] + fy * t[9])); 

1103 v = _1_0, fx, fy 

1104 H = Fdot(v, t[5], t[8], t[9]) 

1105 H *= fy 

1106 H += Fhorner(fx, t[2], t[4], t[7]) 

1107 H *= fy 

1108 H += Fhorner(fx, t[0], t[1], t[3], t[6]) 

1109 return H 

1110 

1111 _evH = _ev3H # overriden for kind == 2 

1112 

1113 def _g2ll2(self, lat, lon): 

1114 # convert grid (lat, lon) to earth (lat, lon), uncropped 

1115 while lon > _180_0: 

1116 lon -= _360_0 

1117 return lat, lon 

1118 

1119 def _g2yx2(self, lat, lon): 

1120 # convert grid (lat, lon) to grid (y, x) indices 

1121 p = self._pgm 

1122 # note, slat = +90, rlat < 0 makes y >=0 

1123 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon) 

1124 

1125 def _gyx2g2(self, y, x): 

1126 # convert grid (y, x) indices to grid (lat, lon) 

1127 p = self._pgm 

1128 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x) 

1129 

1130 def height(self, lats, lons, **wrap): 

1131 '''Interpolate the geoid height for one or several lat-/longitudes. 

1132 

1133 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). 

1134 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). 

1135 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}} 

1136 and B{C{lons}} locations (C{bool}). 

1137 

1138 @return: A single interpolated geoid height (C{float}) or a 

1139 list of interpolated geoid heights (C{float}s). 

1140 

1141 @raise GeoidError: Insufficient or non-matching number of 

1142 B{C{lats}} and B{C{lons}} or the C{egm*.pgm} 

1143 geoid file is closed. 

1144 

1145 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this 

1146 geoid's lat- or longitude range. 

1147 ''' 

1148 return _height_called(self, lats, lons, Error=GeoidError, **wrap) 

1149 

1150 @Property_RO 

1151 def _highest_ltd(self): 

1152 '''(INTERNAL) Cache for L{highest} mesthod. 

1153 ''' 

1154 return self._llh3minmax(True, -12, -4) 

1155 

1156 def highest(self, LatLon=None, full=False): # PYCHOK full 

1157 '''Return the location and largest height of this geoid. 

1158 

1159 @kwarg LatLon: Optional class to return the location and height 

1160 (C{LatLon}) or C{None}. 

1161 @kwarg full: Search the full or limited latitude range (C{bool}). 

1162 

1163 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, 

1164 height)} otherwise a B{C{LatLon}} instance with the lat-, 

1165 longitude and geoid height of the highest grid location. 

1166 ''' 

1167 llh = self._highest if full or self.cropped else self._highest_ltd 

1168 return self._llh3LL(llh, LatLon) 

1169 

1170 def _lat2y2(self, lat2): 

1171 # convert earth lat(s) to min and max grid y indices 

1172 ys, m = [], self._pgm.nlat - 1 

1173 for lat in lat2: 

1174 y, _ = self._g2yx2(*self._ll2g2(lat, 0)) 

1175 ys.append(max(min(int(y), m), 0)) 

1176 return min(ys), max(ys) + 1 

1177 

1178 def _ll2g2(self, lat, lon): 

1179 # convert earth (lat, lon) to grid (lat, lon), uncropped 

1180 while lon < 0: 

1181 lon += _360_0 

1182 return lat, lon 

1183 

1184 def _llh3minmax(self, highest=True, *lat2): 

1185 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid 

1186 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3) 

1187 y = x = 0 

1188 h = self._raw(y, x) 

1189 if highest: 

1190 for j, r in self._raw2(*lat2): 

1191 m = max(r) 

1192 if m > h: 

1193 h, y, x = m, j, r.index(m) 

1194 else: # lowest 

1195 for j, r in self._raw2(*lat2): 

1196 m = min(r) 

1197 if m < h: 

1198 h, y, x = m, j, r.index(m) 

1199 h *= self._pgm.Scale 

1200 h += self._pgm.Offset 

1201 return self._g2ll2(*self._gyx2g2(y, x)) + (h,) 

1202 

1203 @Property_RO 

1204 def _lowest_ltd(self): 

1205 '''(INTERNAL) Cache for L{lowest}. 

1206 ''' 

1207 return self._llh3minmax(False, 0, 8) 

1208 

1209 def lowest(self, LatLon=None, full=False): # PYCHOK full 

1210 '''Return the location and lowest height of this geoid. 

1211 

1212 @kwarg LatLon: Optional class to return the location and height 

1213 (C{LatLon}) or C{None}. 

1214 @kwarg full: Search the full or limited latitude range (C{bool}). 

1215 

1216 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, 

1217 height)} otherwise a B{C{LatLon}} instance with the lat-, 

1218 longitude and geoid height of the lowest grid location. 

1219 ''' 

1220 llh = self._lowest if full or self.cropped else self._lowest_ltd 

1221 return self._llh3LL(llh, LatLon) 

1222 

1223 def _raw(self, y, x): 

1224 # get the ushort geoid height at geoid index (y, x), 

1225 # like GeographicLib/Geoid.hpp real rawval(is, iy) 

1226 p = self._pgm 

1227 if x < 0: 

1228 x += p.nlon 

1229 elif x >= p.nlon: 

1230 x -= p.nlon 

1231 h = p.nlon // 2 

1232 if y < 0: 

1233 y = -y 

1234 elif y >= p.nlat: 

1235 y = (p.nlat - 1) * 2 - y 

1236 else: 

1237 h = 0 

1238 x += h if x < h else -h 

1239 self._seek(y, x) 

1240 h = _unpack(self._endian, self._egm.read(self._u2B)) 

1241 return h[0] 

1242 

1243 def _raws(self, y, x, ijs): 

1244 # get bilinear 4-tuple or 10x12 cubic matrix 

1245 return tuple(self._raw(y + j, x + i) for i, j in ijs) 

1246 

1247 def _raw2(self, *lat2): 

1248 # yield a 2-tuple (y, ushorts) for each row or for 

1249 # the rows between two (or more) earth lat values 

1250 p = self._pgm 

1251 g = self._egm 

1252 e = self._Rendian 

1253 n = self._Ru2B 

1254 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat 

1255 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat) 

1256 self._seek(s, 0) # to start of row s 

1257 for y in range(s, t): 

1258 yield y, _unpack(e, g.read(n)) 

1259 

1260 def _seek(self, y, x): 

1261 # position geoid to grid index (y, x) 

1262 p, g = self._pgm, self._egm 

1263 if g: 

1264 b = p.skip + (y * p.nlon + x) * self._u2B 

1265 g.seek(b, _SEEK_SET) 

1266 return b # position 

1267 raise GeoidError('closed file', txt=repr(p.egm)) # IOError 

1268 

1269 

1270class GeoidPGM(_GeoidBase): 

1271 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth 

1272 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/ 

1273 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ 

1274 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy} 

1275 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/ 

1276 generated/scipy.interpolate.RectBivariateSpline.html>} or 

1277 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ 

1278 scipy.interpolate.interp2d.html>} interpolation. 

1279 

1280 Use any of the U{egm84-, egm96- or egm2008-*.pgm 

1281 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>} 

1282 datasets. However, unless cropped, an entire C{egm*.pgm} dataset 

1283 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/ 

1284 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} 

1285 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ 

1286 scipy.interpolate.interp2d.html>} interpolator and converted from 

1287 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory 

1288 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/ 

1289 geoid.html#geoidinst>} file size and may exceed the available memory, 

1290 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}. 

1291 ''' 

1292 _cropped = False 

1293 _endian = '>u2' 

1294 

1295 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 

1296 kind=3, smooth=0, **name): 

1297 '''New L{GeoidPGM} interpolator. 

1298 

1299 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ 

1300 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}). 

1301 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west, 

1302 north, east}) or 2-tuple (C{(south, west), (north, east)}), 

1303 in C{degrees90} lat- and C{degrees180} longitudes or a 

1304 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances. 

1305 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

1306 or L{a_f2Tuple}), default C{WGS84}. 

1307 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for 

1308 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ 

1309 reference/generated/scipy.interpolate.RectBivariateSpline.html>}, 

1310 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ 

1311 reference/generated/scipy.interpolate.interp2d.html>}, -3 

1312 for C{interp2d cubic} or -5 for C{interp2d quintic}. 

1313 @kwarg smooth: Smoothing factor for U{RectBivariateSpline 

1314 <https://docs.SciPy.org/doc/scipy/reference/generated/ 

1315 scipy.interpolate.RectBivariateSpline.html>} 

1316 only (C{int}). 

1317 @kwarg name: Optional geoid C{B{name}=NN} (C{str}). 

1318 

1319 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, 

1320 B{C{kind}} or B{C{smooth}}. 

1321 

1322 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. 

1323 

1324 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch. 

1325 

1326 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. 

1327 

1328 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} 

1329 warning as exception. 

1330 

1331 @raise TypeError: Invalid B{C{datum}} or unexpected argument. 

1332 

1333 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify 

1334 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}. 

1335 

1336 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/ 

1337 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte 

1338 C{int} height converted to 8-byte C{dtype float64} for C{scipy} 

1339 interpolators. Therefore, internal memory usage is 4 times the 

1340 C{egm*.pgm} file size and may exceed the available memory, 

1341 especially with 32-bit Python. To reduce memory usage, set 

1342 keyword argument B{C{crop}} to the region of interest. For example 

1343 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https:// 

1344 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>} 

1345 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset. 

1346 

1347 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}. 

1348 ''' 

1349 np = self.numpy 

1350 self._u2B = np.dtype(self.endian).itemsize 

1351 

1352 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth) 

1353 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) 

1354 if crop: 

1355 g = p._cropped(g, abs(kind) + 1, *self._swne(crop)) 

1356 if _MODS.internals._version2(np.__version__) < (1, 9): 

1357 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0- 

1358 self._cropped = True 

1359 try: 

1360 # U{numpy dtype formats are different from Python struct formats 

1361 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} 

1362 # read all heights, skipping the PGM header lines, converted to float 

1363 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale 

1364 if p.Offset: # offset 

1365 hs = p.Offset + hs 

1366 if p.dlat < 0: # flip the rows 

1367 hs = np.flipud(hs) 

1368 _GeoidBase.__init__(self, hs, p) 

1369 except Exception as x: 

1370 raise _SciPyIssue(x, _in_, repr(egm_pgm)) 

1371 finally: 

1372 g.close() 

1373 

1374 def _g2ll2(self, lat, lon): 

1375 # convert grid (lat, lon) to earth (lat, lon), un-/cropped 

1376 if self._cropped: 

1377 lon -= self._lon_of 

1378 else: 

1379 while lon > _180_0: 

1380 lon -= _360_0 

1381 return lat, lon 

1382 

1383 def _ll2g2(self, lat, lon): 

1384 # convert earth (lat, lon) to grid (lat, lon), un-/cropped 

1385 if self._cropped: 

1386 lon += self._lon_of 

1387 else: 

1388 while lon < 0: 

1389 lon += _360_0 

1390 return lat, lon 

1391 

1392 if _FOR_DOCS: 

1393 __call__ = _GeoidBase.__call__ 

1394 height = _GeoidBase.height 

1395 

1396 

1397class _Gpars(_Named): 

1398 '''(INTERNAL) Basic geoid parameters. 

1399 ''' 

1400 # interpolator parameters 

1401 dlat = 0 # +/- latitude resolution in C{degrees} 

1402 dlon = 0 # longitude resolution in C{degrees} 

1403 nlat = 1 # number of latitude knots (C{int}) 

1404 nlon = 0 # number of longitude knots (C{int}) 

1405 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat 

1406 rlon = 0 # longitude resolution in C{float}, 1 / .dlon 

1407 slat = 0 # nothern- or southern most latitude (C{degrees90}) 

1408 wlon = 0 # western-most longitude in Eastern lon (C{degrees360}) 

1409 

1410 flon = 0 # forward, earth to grid longitude offset 

1411 glon = 0 # reverse, grid to earth longitude offset 

1412 

1413 knots = 0 # number of knots, nlat * nlon (C{int}) 

1414 skip = 0 # header bytes to skip (C{int}) 

1415 

1416 def __repr__(self): 

1417 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for 

1418 a in dir(self.__class__) 

1419 if a[:1].isupper())) 

1420 return _COLONSPACE_(self, t) 

1421 

1422 def __str__(self): 

1423 return Fmt.PAREN(self.classname, repr(self.name)) 

1424 

1425 

1426class _PGM(_Gpars): 

1427 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file. 

1428 

1429 # Geoid file in PGM format for the GeographicLib::Geoid class 

1430 # Description WGS84 EGM96, 5-minute grid 

1431 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html 

1432 # DateTime 2009-08-29 18:45:03 

1433 # MaxBilinearError 0.140 

1434 # RMSBilinearError 0.005 

1435 # MaxCubicError 0.003 

1436 # RMSCubicError 0.001 

1437 # Offset -108 

1438 # Scale 0.003 

1439 # Origin 90N 0E 

1440 # AREA_OR_POINT Point 

1441 # Vertical_Datum WGS84 

1442 <width> <height> 

1443 <pixel> 

1444 ... 

1445 ''' 

1446 crop4 = () # 4-tuple (C{south, west, north, east}). 

1447 egm = None 

1448 glon = 180 # reverse offset, uncropped 

1449# pgm = NN # name 

1450 sizeB = 0 

1451 u2B = 2 # item size of grid height (C{int}). 

1452 

1453 @staticmethod 

1454 def _llstr2floats(latlon): 

1455 # llstr to (lat, lon) floats 

1456 lat, lon = latlon.split() 

1457 return _MODS.dms.parseDMS2(lat, lon) 

1458 

1459 # PGM file attributes, CamelCase but not .istitle() 

1460 AREA_OR_POINT = str 

1461 DateTime = str 

1462 Description = str # 'WGS84 EGM96, 5-minute grid' 

1463 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class' 

1464 MaxBilinearError = float 

1465 MaxCubicError = float 

1466 Offset = float 

1467 Origin = _llstr2floats 

1468 Pixel = 0 

1469 RMSBilinearError = float 

1470 RMSCubicError = float 

1471 Scale = float 

1472 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...' 

1473 Vertical_Datum = str 

1474 

1475 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22 

1476 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset. 

1477 ''' 

1478 self.name = pgm # geoid file name 

1479 if itemsize: 

1480 self._u2B = itemsize 

1481 if sizeB: 

1482 self.sizeB = sizeB 

1483 

1484 t = g.readline() # make sure newline == '\n' 

1485 if t != b'P5\n' and t.strip() != b'P5': 

1486 raise self._Errorf(_format_, _header_, t) 

1487 

1488 while True: # read all # Attr ... lines, 

1489 try: # ignore empty ones or comments 

1490 t = g.readline().strip() 

1491 if t.startswith(_bHASH_): 

1492 t = t.lstrip(_bHASH_).lstrip() 

1493 a, v = map(_ub2str, t.split(None, 1)) 

1494 f = getattr(_PGM, a, None) 

1495 if callable(f) and a[:1].isupper(): 

1496 setattr(self, a, f(v)) 

1497 elif t: 

1498 break 

1499 except (TypeError, ValueError): 

1500 raise self._Errorf(_format_, 'Attr', t) 

1501 else: # should never get here 

1502 raise self._Errorf(_format_, _header_, g.tell()) 

1503 

1504 try: # must be (even) width and (odd) height 

1505 nlon, nlat = map(int, t.split()) 

1506 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \ 

1507 nlat < 2 or nlat > (181 * 60) or not isodd(nlat): 

1508 raise ValueError 

1509 except (TypeError, ValueError): 

1510 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t) 

1511 

1512 try: # must be 16 bit pixel height 

1513 t = g.readline().strip() 

1514 self.Pixel = int(t) 

1515 if not 255 < self.Pixel < 65536: # >u2 or >H only 

1516 raise ValueError 

1517 except (TypeError, ValueError): 

1518 raise self._Errorf(_format_, 'pixel', t) 

1519 

1520 for a in dir(_PGM): # set undefined # Attr ... to None 

1521 if a[:1].isupper() and callable(getattr(self, a)): 

1522 setattr(self, a, None) 

1523 

1524 if self.Origin is None: 

1525 raise self._Errorf(_format_, 'Origin', self.Origin) 

1526 if self.Offset is None or self.Offset > 0: 

1527 raise self._Errorf(_format_, 'Offset', self.Offset) 

1528 if self.Scale is None or self.Scale < EPS: 

1529 raise self._Errorf(_format_, 'Scale', self.Scale) 

1530 

1531 self.skip = g.tell() 

1532 self.knots = nlat * nlon 

1533 

1534 self.nlat, self.nlon = nlat, nlon 

1535 self.slat, self.wlon = self.Origin 

1536 # note, negative .dlat and .rlat since rows 

1537 # are from .slat 90N down in decreasing lat 

1538 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon 

1539 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0 

1540 

1541 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0 

1542 n = float(self.slat) 

1543 s = n + self.dlat * (nlat - 1) 

1544 w = self.wlon - self.glon 

1545 e = w + self.dlon * nlon 

1546 self.crop4 = s, w, n, e 

1547 

1548 n = self.sizeB - self.skip 

1549 if n > 0 and n != (self.knots * self.u2B): 

1550 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n) 

1551 

1552 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15 

1553 '''Crop the geoid to (south, west, north, east) box. 

1554 ''' 

1555 # flon offset for both west and east 

1556 f = 360 if west < 0 else 0 

1557 # earth (lat, lon) to grid indices (y, x), 

1558 # note y is decreasing, i.e. n < s 

1559 s, w = self._lle2yx2(south, west, f) 

1560 n, e = self._lle2yx2(north, east, f) 

1561 s += 1 # s > n 

1562 e += 1 # e > w 

1563 

1564 hi, wi = self.nlat, self.nlon 

1565 # handle special cases 

1566 if (s - n) > hi: 

1567 n, s = 0, hi # entire lat range 

1568 if (e - w) > wi: 

1569 w, e, f = 0, wi, 180 # entire lon range 

1570 if s == hi and w == n == 0 and e == wi: 

1571 return g # use entire geoid as-is 

1572 

1573 if (e - w) < k1 or (s - n) < (k1 + 1): 

1574 raise self._Errorf(_format_, 'swne', (north - south, east - west)) 

1575 

1576 if e > wi > w: # wrap around 

1577 # read w..wi and 0..e 

1578 r, p = (wi - w), (e - wi) 

1579 elif e > w: 

1580 r, p = (e - w), 0 

1581 else: 

1582 raise self._Errorf('%s(%s < %s)', _assert_, w, e) 

1583 

1584 # convert to bytes 

1585 r *= self.u2B 

1586 p *= self.u2B 

1587 q = wi * self.u2B # stride 

1588 # number of rows and cols to skip from 

1589 # the original (.slat, .wlon) origin 

1590 z = self.skip + (n * wi + w) * self.u2B 

1591 # sanity check 

1592 if r < 2 or p < 0 or q < 2 or z < self.skip \ 

1593 or z > self.sizeB: 

1594 raise self._Errorf(_format_, _assert_, (r, p, q, z)) 

1595 

1596 # can't use _BytesIO since numpy 

1597 # needs .fileno attr in .fromfile 

1598 t, c = 0, self._tmpfile() 

1599 # reading (s - n) rows, forward 

1600 for y in range(n, s): # PYCHOK y unused 

1601 g.seek(z, _SEEK_SET) 

1602 # Python 2 tmpfile.write returns None 

1603 t += c.write(g.read(r)) or r 

1604 if p: # wrap around to start of row 

1605 g.seek(-q, _SEEK_CUR) 

1606 # assert(g.tell() == (z - w * self.u2B)) 

1607 # Python 2 tmpfile.write returns None 

1608 t += c.write(g.read(p)) or p 

1609 z += q 

1610 c.flush() 

1611 g.close() 

1612 

1613 s -= n # nlat 

1614 e -= w # nlon 

1615 k = s * e # knots 

1616 z = k * self.u2B 

1617 if t != z: 

1618 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self) 

1619 

1620 # update the _Gpars accordingly, note attributes 

1621 # .dlat, .dlon, .rlat and .rlon remain unchanged 

1622 self.slat += n * self.dlat 

1623 self.wlon += w * self.dlon 

1624 self.nlat = s 

1625 self.nlon = e 

1626 self.flon = self.glon = f 

1627 

1628 self.crop4 = south, west, north, east 

1629 self.knots = k 

1630 self.skip = 0 # no header lines in c 

1631 

1632 c.seek(0, _SEEK_SET) 

1633 # c = open(c.name, _rb_) # reopen for numpy 1.8.0- 

1634 return c 

1635 

1636 def _Errorf(self, fmt, *args): # PYCHOK no cover 

1637 t = fmt % args 

1638 e = self.pgm or NN 

1639 if e: 

1640 t = _SPACE_(t, _in_, repr(e)) 

1641 return PGMError(t) 

1642 

1643 def _lle2yx2(self, lat, lon, flon): 

1644 # earth (lat, lon) to grid indices (y, x) 

1645 # with .dlat decreasing from 90N .slat 

1646 lat -= self.slat 

1647 lon += flon - self.wlon 

1648 return (min(self.nlat - 1, max(0, int(lat * self.rlat))), 

1649 max(0, int(lon * self.rlon))) 

1650 

1651 def _tmpfile(self): 

1652 # create a tmpfile to hold the cropped geoid grid 

1653 try: 

1654 from tempfile import NamedTemporaryFile as tmpfile 

1655 except ImportError: # Python 2.7.16- 

1656 from os import tmpfile 

1657 t = _os_path.splitext(_os_path.basename(self.pgm))[0] 

1658 f = tmpfile(mode='w+b', prefix=t or 'egm') 

1659 f.seek(0, _SEEK_SET) # force overwrite 

1660 return f 

1661 

1662 @Property_RO 

1663 def pgm(self): 

1664 '''Get the geoid file name (C{str}). 

1665 ''' 

1666 return self.name 

1667 

1668 

1669class PGMError(GeoidError): 

1670 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset. 

1671 ''' 

1672 pass 

1673 

1674 

1675def egmGeoidHeights(GeoidHeights_dat): 

1676 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ 

1677 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat 

1678 <https://SourceForge.net/projects/geographiclib/files/testdata/>} 

1679 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/ 

1680 geoid.html#testgeoid>}. 

1681 

1682 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file 

1683 (C{str} or C{file} handle). 

1684 

1685 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon, 

1686 egm84, egm96, egm2008)}. 

1687 

1688 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}. 

1689 

1690 @note: Function L{egmGeoidHeights} is used to test the geoids 

1691 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module 

1692 C{test/testGeoids.py}. 

1693 ''' 

1694 dat = GeoidHeights_dat 

1695 if isinstance(dat, bytes): 

1696 dat = _BytesIO(dat) 

1697 

1698 try: 

1699 dat.seek(0, _SEEK_SET) # reset 

1700 except AttributeError as x: 

1701 raise GeoidError(GeoidHeights_dat=type(dat), cause=x) 

1702 

1703 for t in dat.readlines(): 

1704 t = t.strip() 

1705 if t and not t.startswith(_bHASH_): 

1706 lat, lon, egm84, egm96, egm2008 = map(float, t.split()) 

1707 while lon > _180_0: # EasternLon to earth lon 

1708 lon -= _360_0 

1709 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008) 

1710 

1711 

1712__all__ += _ALL_DOCS(_GeoidBase) 

1713 

1714if __name__ == '__main__': 

1715 

1716 from pygeodesy.internals import printf, _sys 

1717 

1718 _crop = () 

1719 _GeoidEGM = GeoidKarney 

1720 _kind = 3 

1721 

1722 geoids = _sys.argv[1:] 

1723 while geoids: 

1724 geoid = geoids.pop(0) 

1725 

1726 if '-crop'.startswith(geoid.lower()): 

1727 _crop = 20, -125, 50, -65 # CONUS 

1728 

1729 elif '-karney'.startswith(geoid.lower()): 

1730 _GeoidEGM = GeoidKarney 

1731 

1732 elif '-kind'.startswith(geoid.lower()): 

1733 _kind = int(geoids.pop(0)) 

1734 

1735 elif '-pgm'.startswith(geoid.lower()): 

1736 _GeoidEGM = GeoidPGM 

1737 

1738 elif geoid[-4:].lower() in ('.pgm',): 

1739 g = _GeoidEGM(geoid, crop=_crop, kind=_kind) 

1740 printf(g.toStr(), nt=1, nl=1) 

1741 printf(repr(g.pgm), nt=1) 

1742 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>: 

1743 # The height of the EGM96 geoid at Timbuktu 

1744 # echo 16:46:33N 3:00:34W | GeoidEval 

1745 # => 28.7068 -0.02e-6 -1.73e-6 

1746 # The 1st number is the height of the geoid, the 2nd and 

1747 # 3rd are its slopes in northerly and easterly direction 

1748 t = 'Timbuktu %s' % (g,) 

1749 k = {'egm84-15.pgm': '31.2979', 

1750 'egm96-5.pgm': '28.7067', 

1751 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880') 

1752 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':') 

1753 for ll in (ll, (16.776, -3.009),): 

1754 try: 

1755 h, ll = g.height(*ll), fstr(ll, prec=6) 

1756 printf('%s.height(%s): %.4F vs %s', t, ll, h, k) 

1757 except (GeoidError, RangeError) as x: 

1758 printf(_COLONSPACE_(t, str(x))) 

1759 

1760 elif geoid[-4:].lower() in ('.bin',): 

1761 g = GeoidG2012B(geoid, kind=_kind) 

1762 printf(g.toStr()) 

1763 

1764 else: 

1765 raise GeoidError(grid=repr(geoid)) 

1766 

1767_I = int # PYCHOK unused _I 

1768del _intCs # trash ints cache 

1769 

1770# **) MIT License 

1771# 

1772# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1773# 

1774# Permission is hereby granted, free of charge, to any person obtaining a 

1775# copy of this software and associated documentation files (the "Software"), 

1776# to deal in the Software without restriction, including without limitation 

1777# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1778# and/or sell copies of the Software, and to permit persons to whom the 

1779# Software is furnished to do so, subject to the following conditions: 

1780# 

1781# The above copyright notice and this permission notice shall be included 

1782# in all copies or substantial portions of the Software. 

1783# 

1784# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1785# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1786# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1787# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1788# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1789# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1790# OTHER DEALINGS IN THE SOFTWARE. 

1791 

1792# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval> 

1793# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm 

1794# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm 

1795# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm 

1796 

1797# _center = 0, 0, 17.2260 # egm2008-1.pgm 

1798# _center = 0, 0, 17.1630 # egm96-5.pgm 

1799# _center = 0, 0, 18.3296 # egm84-15.pgm 

1800 

1801# _upperright = 90, 180, 14.8980 # egm2008-1.pgm 

1802# _upperright = 90, 180, 13.6050 # egm96-5.pgm 

1803# _upperright = 90, 180, 13.0980 # egm84-15.pgm 

1804 

1805 

1806# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm 

1807# 

1808# GeoidKarney('egm2008-1.pgm'): lowerleft(-90.0, -180.0, -30.15), upperright(90.0, 180.0, 14.898), center(0.0, 0.0, 17.226), highest(-8.4, 147.367, 85.839), lowest(4.7, 78.767, -106.911) 

1809# 

1810# _PGM('../testGeoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84' 

1811# 

1812# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 

1813# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 

1814# 

1815# GeoidKarney('egm84-15.pgm'): lowerleft(-90.0, -180.0, -29.712), upperright(90.0, 180.0, 13.098), center(0.0, 0.0, 18.33), highest(-4.5, 148.75, 81.33), lowest(4.75, 79.25, -107.34) 

1816# 

1817# _PGM('../testGeoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84' 

1818# 

1819# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979 

1820# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979 

1821# 

1822# GeoidKarney('egm96-5.pgm'): lowerleft(-90.0, -180.0, -29.535), upperright(90.0, 180.0, 13.605), center(0.0, 0.0, 17.163), highest(-8.167, 147.25, 85.422), lowest(4.667, 78.833, -107.043) 

1823# 

1824# _PGM('../testGeoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84' 

1825# 

1826# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067 

1827# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067 

1828 

1829 

1830# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm 

1831# 

1832# GeoidKarney('egm2008-1.pgm'): lowerleft(-90.0, -180.0, -30.15), upperright(90.0, 180.0, 14.898), center(0.0, 0.0, 17.226), highest(-8.4, 147.367, 85.839), lowest(4.7, 78.767, -106.911) 

1833# 

1834# _PGM('../testGeoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84' 

1835# 

1836# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 

1837# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 

1838# 

1839# GeoidKarney('egm84-15.pgm'): lowerleft(-90.0, -180.0, -29.712), upperright(90.0, 180.0, 13.098), center(0.0, 0.0, 18.33), highest(-4.5, 148.75, 81.33), lowest(4.75, 79.25, -107.34) 

1840# 

1841# _PGM('../testGeoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84' 

1842# 

1843# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979 

1844# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979 

1845# 

1846# GeoidKarney('egm96-5.pgm'): lowerleft(-90.0, -180.0, -29.535), upperright(90.0, 180.0, 13.605), center(0.0, 0.0, 17.163), highest(-8.167, 147.25, 85.422), lowest(4.667, 78.833, -107.043) 

1847# 

1848# _PGM('../testGeoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84' 

1849# 

1850# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067 

1851# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067 

1852 

1853 

1854# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm 

1855# 

1856# GeoidPGM('egm2008-1.pgm'): lowerleft(-90.0, -180.0, -30.15), upperright(90.0, 180.0, 14.898), center(0.0, 0.0, 17.226), highest(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911) 

1857# 

1858# _PGM('../testGeoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84' 

1859# 

1860# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 

1861# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 

1862# 

1863# GeoidPGM('egm84-15.pgm'): lowerleft(-90.0, -180.0, -29.712), upperright(90.0, 180.0, 13.098), center(0.0, 0.0, 18.33), highest(-4.5, -31.25, 81.33), lowest(4.75, -100.75, -107.34) 

1864# 

1865# _PGM('../testGeoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84' 

1866# 

1867# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979 

1868# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979 

1869# 

1870# GeoidPGM('egm96-5.pgm'): lowerleft(-90.0, -180.0, -29.535), upperright(90.0, 180.0, 13.605), center(0.0, -0.0, 17.179), highest(-8.167, -32.75, 85.422), lowest(4.667, -101.167, -107.043) 

1871# 

1872# _PGM('../testGeoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84' 

1873# 

1874# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067 

1875# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067