1

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

3

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

5

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

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

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

9 and C{geoid} model files.

10

11 L{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.

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

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

15 require those packages to be installed.

16

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

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

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

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

21

22 Typical usage

23=============

24

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

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

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

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

29

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

31

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

33 arguments to select different interpolation options

34

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

36

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

38

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

40

41 C{>>> h = ginterpolator(ll)}

42

43 or

44

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

46

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

48

49 C{>>> hs = ginterpolator(lls)}

50

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

52

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

54

55 or as 2 lists, 2 tuples, etc.

56

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

58

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

60 courtesy 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

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

84

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

86 from 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

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

90 _SciPyIssue, _xkwds_pop2

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

92# from pygoedesy.formy import heightOrthometric # _MODS

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

94 _HeightsBase, _ellipsoidal_datum, _Wrap

95# from pygeodesy.internals import _version2 # _MODS

96 from 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_

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

101 from pygeodesy.named import _name__, _Named, _NamedTuple

102# from pygeodesy.namedTuples import LatLon3Tuple # _MODS

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

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

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

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

107

108 from math import floor

109 import os.path as _os_path

110 from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET

111 from struct import calcsize as _calcsize, unpack as _unpack

112 try:

113 from StringIO import StringIO as _BytesIO # reads bytes

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

115

116 except ImportError: # Python 3+

117 from io import BytesIO as _BytesIO # PYCHOK expected

118

119__all__ = _ALL_LAZY.geoids

120__version__ = '24.07.25'

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

137 class _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 = self._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 @property_ROver

420 def _heightOrthometric(self):

421 return _MODS.formy.heightOrthometric # overwrite property_ROver

422

423 def _hGeoid(self, lat, lon):

424 out = self.outside(lat, lon)

425 if out:

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

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

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

429

430 @Property_RO

431 def _highest(self):

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

433 '''

434 return self._llh3minmax(True)

435

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

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

438

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

440 (C{LatLon}) or C{None}.

441

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

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

444 longitude and geoid height of the highest grid location.

445 '''

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

447

448 @Property_RO

449 def hits(self):

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

451 '''

452 return self._yx_hits

453

454 @deprecated_method

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

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

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

458 try:

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

460 except AttributeError as x:

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

462

463 @Property_RO

464 def kind(self):

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

466 '''

467 return self._kind

468

469 @Property_RO

470 def knots(self):

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

472 '''

473 return self._knots

474

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

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

477 self._notOverloaded(lat, lon)

478

479 @property_ROver

480 def _LL3T(self):

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

482 '''

483 return _MODS.namedTuples.LatLon3Tuple # overwrite property_ROver

484

485 def _llh3(self, lat, lon):

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

487

488 def _llh3LL(self, llh, LatLon):

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

490

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

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

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

494 # numpy.argmin.html#numpy.argmin>

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

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

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

498

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

500 # numpy.fromfile, like .frombuffer

501 g.seek(offset, _SEEK_SET)

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

503

504 @Property_RO

505 def _lowerleft(self):

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

507 '''

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

509

510 def lowerleft(self, LatLon=None):

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

512

513 @kwarg LatLon: Optional class to return the location

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

515

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

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

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

519 '''

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

521

522 @Property_RO

523 def _loweright(self):

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

525 '''

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

527

528 def loweright(self, LatLon=None):

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

530

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

532 (C{LatLon}) or C{None}.

533

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

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

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

537 '''

538

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

540

541 lowerright = loweright # synonymous

542

543 @Property_RO

544 def _lowest(self):

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

546 '''

547 return self._llh3minmax(False)

548

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

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

551

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

553 (C{LatLon}) or C{None}.

554

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

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

557 longitude and geoid height of the lowest grid location.

558 '''

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

560

561 @Property_RO

562 def mean(self):

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

564 '''

565 if self._mean is None: # see GeoidKarney

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

567 return self._mean

568

569 @property_RO

570 def name(self):

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

572 '''

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

574

575 @Property_RO

576 def nBytes(self):

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

578 '''

579 return self._nBytes

580

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

582 # open the geoid file

583 try:

584 self._geoid = _os_path.basename(geoid)

585 self._sizeB = _os_path.getsize(geoid)

586 g = open(geoid, _rb_)

587 except (IOError, OSError) as x:

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

589

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

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

592 self._kind = int(kind)

593 if name:

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

595 if smooth:

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

597

598 return g

599

600 def outside(self, lat, lon):

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

602 lat-/longitude or crop range.

603

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

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

606

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

608 empty C{str} if inside.

609 '''

610 return (_S_ if lat < self._lat_lo else

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

612 (_W_ if lon < self._lon_lo else

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

614

615 @Property_RO

616 def pgm(self):

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

618 '''

619 return self._pgm

620

621 @Property_RO

622 def sizeB(self):

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

624 '''

625 return self._sizeB

626

627 @Property_RO

628 def smooth(self):

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

630 '''

631 return self._smooth

632

633 @Property_RO

634 def stdev(self):

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

636 '''

637 if self._stdev is None: # see GeoidKarney

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

639 return self._stdev

640

641 def _swne(self, crop):

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

643 try:

644 if len(crop) == 2:

645 try: # sw, ne LatLons

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

647 crop[1].lat, crop[1].lon)

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

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

650 else: # (s, w, n, e)

651 swne = crop

652 if len(swne) == 4:

653 s, w, n, e = map(float, swne)

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

655 -180 <= w <= (e - _1_0) <= 179:

656 return s, w, n, e

657 except (IndexError, TypeError, ValueError):

658 pass

659 raise GeoidError(crop=crop)

660

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

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

663

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

665 default). Trailing zero decimals are stripped

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

667 for negative B{C{prec}} values.

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

669

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

671 '''

672 s = 1 if self.kind < 0 else 2

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

674 (self.lowerleft, self.upperright,

675 self.center,

676 self.highest, self.lowest)) + \

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

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

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

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

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

682

683 @Property_RO

684 def u2B(self):

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

686 '''

687 return self._u2B

688

689 @Property_RO

690 def _upperleft(self):

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

692 '''

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

694

695 def upperleft(self, LatLon=None):

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

697

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

699 (C{LatLon}) or C{None}.

700

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

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

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

704 '''

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

706

707 @Property_RO

708 def _upperright(self):

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

710 '''

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

712

713 def upperright(self, LatLon=None):

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

715

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

717 (C{LatLon}) or C{None}.

718

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

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

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

722 '''

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

724

725

726 class GeoidError(HeightError):

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

728 '''

729 pass

730

731

732 class GeoidG2012B(_GeoidBase):

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

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

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

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

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

738 U{Guam and Northern Mariana Islands

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

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

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

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

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

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

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

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

747

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

749 C{g2012b*.bin} grid files.

750 '''

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

752 kind=3, smooth=0, **name_crop):

753 '''New L{GeoidG2012B} interpolator.

754

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

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

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

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

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

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

761 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

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

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

764 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

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

766 scipy.interpolate.RectBivariateSpline.html>}

767 only (C{int}).

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

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

770

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

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

773

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

775 installed.

776

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

778

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

780

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

782 warning as exception.

783

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

785

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

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

788 '''

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

790 if crop is not None:

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

792

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

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

795

796 try:

797 p = _Gpars()

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

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

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

801 for en_ in ('<', '>'):

802 # skip 4xf8, get 3xi4

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

804 if ien == 1: # correct endian

805 p.knots = p.nlat * p.nlon

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

807 and 1 < p.nlon < n:

808 self._endian = en_+'f4'

809 break

810 else: # couldn't validate endian

811 raise GeoidError(_endian_)

812

813 # get the first 4xf8

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

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

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

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

818 _GeoidBase.__init__(self, hs, p)

819

820 except Exception as x:

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

822 finally:

823 g.close()

824

825 def _g2ll2(self, lat, lon):

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

827 return lat, lon

828

829 def _ll2g2(self, lat, lon):

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

831 return lat, lon

832

833 if _FOR_DOCS:

834 __call__ = _GeoidBase.__call__

835 height = _GeoidBase.height

836

837

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

839 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat

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

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

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

843 C{0 <= EasterLon <= 360}).

844 '''

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

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

847

848

849 def _I(i):

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

851 '''

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

853

854

855 def _T(*cs):

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

857 '''

858 return map1(_I, *cs)

859

860_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)

861

862

863 class GeoidKarney(_GeoidBase):

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

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

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

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

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

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

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

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

872

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

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

875 datasets.

876 '''

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

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

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

880 _T0s12,

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

882 _T0s12,

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

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

885 _T0s12,

886 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),

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

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

889

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

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

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

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

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

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

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

897 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),

898 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),

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

900

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

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

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

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

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

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

907 _T0s12,

908 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),

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

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

911

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

913 _T(1, 0),

914 _T(0, 1),

915 _T(1, 1))

916

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

918 _T( 1, -1),

919 _T(-1, 0),

920 _T( 0, 0),

921 _T( 1, 0),

922 _T( 2, 0),

923 _T(-1, 1),

924 _T( 0, 1),

925 _T( 1, 1),

926 _T( 2, 1),

927 _T( 0, 2),

928 _T( 1, 2))

929

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

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

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

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

934# (-8.167, 147.25, 85.422) if egm96-5.pgm else

935# (-4.5, 148.75, 81.33)) # egm84-15.pgm

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

937# (4.667, 78.833, -107.043) if egm96-5.pgm else

938# (4.75, 79.25, -107.34)) # egm84-15.pgm

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

940 _nBytes = None # not applicable

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

942 _smooth = None # not applicable

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

944 _u2B = _calcsize(_endian) # pixelsize_ in bytes

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

946 _Ru2B = 0 # row of pixelsize_s in bytes

947 _yxH = () # cache (y, x) indices

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

949 _yx_hits = 0 # cache hits

950

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

952 kind=3, **name_smooth):

953 '''New L{GeoidKarney} interpolator.

954

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

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

957 note below.

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

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

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

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

962 C{LatLon} instances.

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

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

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

966 for C{cubic}.

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

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

969

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

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

972

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

974

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

976

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

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

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

980 '''

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

982 if smooth is not None:

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

984

985 if kind in (2,):

986 self._evH = self._ev2H

987 elif kind not in (3,):

988 raise GeoidError(kind=kind)

989

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

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

992

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

994 self._Ru2B = _calcsize(self._Rendian)

995

996 self._knots = p.knots # grid knots

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

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

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

1000 self._lat_lo, self._lon_lo, \

1001 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)

1002 self._cropped = True if crop else False

1003

1004 def __call__(self, *llis, **wrap_H):

1005 '''Interpolate the geoid height for one or several locations.

1006

1007 @arg llis: One or more locations (C{LatLon}s), all positional.

1008 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.

1009 If C{B{wrap} is True}, wrap or I{normalize} all

1010 B{C{llis}} locations (C{bool}). If C{B{H} is True},

1011 return the I{orthometric} height instead of the

1012 I{geoid} height at each location (C{bool}).

1013

1014 @return: A single interpolated geoid (or orthometric) height

1015 (C{float}) or a list or tuple of interpolated geoid

1016 (or orthometric) heights (C{float}s).

1017

1018 @raise GeoidError: Insufficient number of B{C{llis}}, an

1019 invalid B{C{lli}} or the C{egm*.pgm}

1020 geoid file is closed.

1021

1022 @raise RangeError: An B{C{lli}} is outside this geoid's lat-

1023 or longitude range.

1024

1025 @note: To obtain I{orthometric} heights, each B{C{llis}}

1026 location must have an ellipsoid C{height} or C{h}

1027 attribute, otherwise C{height=0} is used.

1028

1029 @see: Function L{pygeodesy.heightOrthometric}.

1030 '''

1031 return self._called(llis, False, **wrap_H)

1032

1033 def _c0c3v(self, y, x):

1034 # get the common denominator, the 10x12 cubic matrix and

1035 # the 12 cubic v-coefficients around geoid index (y, x)

1036 p = self._pgm

1037 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):

1038 # read 4x4 ushorts, drop the 4 corners

1039 g = self._egm

1040 e = self._4endian

1041 n = self._4u2B

1042 R = self._Ru2B

1043

1044 b = self._seek(y - 1, x - 1)

1045 v = _unpack(e, g.read(n))[1:3]

1046 b += R

1047 g.seek(b, _SEEK_SET)

1048 v += _unpack(e, g.read(n))

1049 b += R

1050 g.seek(b, _SEEK_SET)

1051 v += _unpack(e, g.read(n))

1052 b += R

1053 g.seek(b, _SEEK_SET)

1054 v += _unpack(e, g.read(n))[1:3]

1055 j = 1

1056

1057 else: # likely some wrapped y and/or x's

1058 v = self._raws(y, x, GeoidKarney._CM)

1059 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)

1060

1061 return GeoidKarney._C0[j], GeoidKarney._C3[j], v

1062

1063 @Property_RO

1064 def dtype(self):

1065 '''Get the geoid's grid data type (C{str}).

1066 '''

1067 return 'ushort'

1068

1069 def _ev(self, lat, lon): # PYCHOK expected

1070 # interpolate the geoid height at grid (lat, lon)

1071 fy, fx = self._g2yx2(lat, lon)

1072 y, x = int(floor(fy)), int(floor(fx))

1073 fy -= y

1074 fx -= x

1075 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H

1076 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)

1077 H += self._pgm.Offset # H.fadd(self._pgm.Offset)

1078 return H.fsum()

1079

1080 def _ev2H(self, fy, fx, *yx):

1081 # compute the bilinear 4-tuple and interpolate raw H

1082 if self._yxH == yx:

1083 t = self._yxHt

1084 self._yx_hits += 1

1085 else:

1086 y, x = self._yxH = yx

1087 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)

1088 v = _1_0, -fx, fx

1089 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)

1090 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy

1091 return H

1092

1093 def _ev3H(self, fy, fx, *yx):

1094 # compute the cubic 10-tuple and interpolate raw H

1095 if self._yxH == yx:

1096 t = self._yxHt

1097 self._yx_hits += 1

1098 else:

1099 self._yxH = yx

1100 c0, c3, v = self._c0c3v(*yx)

1101 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]

1102 self._yxHt = t = tuple(t)

1103 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...

1104 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +

1105 # fy * (t[2] + fx * (t[4] + fx * t[7]) +

1106 # fy * (t[5] + fx * t[8] + fy * t[9]));

1107 v = _1_0, fx, fy

1108 H = Fdot(v, t[5], t[8], t[9])

1109 H *= fy

1110 H += Fhorner(fx, t[2], t[4], t[7])

1111 H *= fy

1112 H += Fhorner(fx, t[0], t[1], t[3], t[6])

1113 return H

1114

1115 _evH = _ev3H # overriden for kind == 2

1116

1117 def _g2ll2(self, lat, lon):

1118 # convert grid (lat, lon) to earth (lat, lon), uncropped

1119 while lon > _180_0:

1120 lon -= _360_0

1121 return lat, lon

1122

1123 def _g2yx2(self, lat, lon):

1124 # convert grid (lat, lon) to grid (y, x) indices

1125 p = self._pgm

1126 # note, slat = +90, rlat < 0 makes y >=0

1127 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)

1128

1129 def _gyx2g2(self, y, x):

1130 # convert grid (y, x) indices to grid (lat, lon)

1131 p = self._pgm

1132 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)

1133

1134 def height(self, lats, lons, **wrap):

1135 '''Interpolate the geoid height for one or several lat-/longitudes.

1136

1137 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).

1138 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).

1139 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}

1140 and B{C{lons}} locations (C{bool}).

1141

1142 @return: A single interpolated geoid height (C{float}) or a

1143 list of interpolated geoid heights (C{float}s).

1144

1145 @raise GeoidError: Insufficient or non-matching number of

1146 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}

1147 geoid file is closed.

1148

1149 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this

1150 geoid's lat- or longitude range.

1151 '''

1152 return _height_called(self, lats, lons, Error=GeoidError, **wrap)

1153

1154 @Property_RO

1155 def _highest_ltd(self):

1156 '''(INTERNAL) Cache for L{highest} mesthod.

1157 '''

1158 return self._llh3minmax(True, -12, -4)

1159

1160 def highest(self, LatLon=None, full=False): # PYCHOK full

1161 '''Return the location and largest height of this geoid.

1162

1163 @kwarg LatLon: Optional class to return the location and height

1164 (C{LatLon}) or C{None}.

1165 @kwarg full: Search the full or limited latitude range (C{bool}).

1166

1167 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,

1168 height)} otherwise a B{C{LatLon}} instance with the lat-,

1169 longitude and geoid height of the highest grid location.

1170 '''

1171 llh = self._highest if full or self.cropped else self._highest_ltd

1172 return self._llh3LL(llh, LatLon)

1173

1174 def _lat2y2(self, lat2):

1175 # convert earth lat(s) to min and max grid y indices

1176 ys, m = [], self._pgm.nlat - 1

1177 for lat in lat2:

1178 y, _ = self._g2yx2(*self._ll2g2(lat, 0))

1179 ys.append(max(min(int(y), m), 0))

1180 return min(ys), max(ys) + 1

1181

1182 def _ll2g2(self, lat, lon):

1183 # convert earth (lat, lon) to grid (lat, lon), uncropped

1184 while lon < 0:

1185 lon += _360_0

1186 return lat, lon

1187

1188 def _llh3minmax(self, highest=True, *lat2):

1189 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid

1190 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)

1191 y = x = 0

1192 h = self._raw(y, x)

1193 if highest:

1194 for j, r in self._raw2(*lat2):

1195 m = max(r)

1196 if m > h:

1197 h, y, x = m, j, r.index(m)

1198 else: # lowest

1199 for j, r in self._raw2(*lat2):

1200 m = min(r)

1201 if m < h:

1202 h, y, x = m, j, r.index(m)

1203 h *= self._pgm.Scale

1204 h += self._pgm.Offset

1205 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)

1206

1207 @Property_RO

1208 def _lowest_ltd(self):

1209 '''(INTERNAL) Cache for L{lowest}.

1210 '''

1211 return self._llh3minmax(False, 0, 8)

1212

1213 def lowest(self, LatLon=None, full=False): # PYCHOK full

1214 '''Return the location and lowest height of this geoid.

1215

1216 @kwarg LatLon: Optional class to return the location and height

1217 (C{LatLon}) or C{None}.

1218 @kwarg full: Search the full or limited latitude range (C{bool}).

1219

1220 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,

1221 height)} otherwise a B{C{LatLon}} instance with the lat-,

1222 longitude and geoid height of the lowest grid location.

1223 '''

1224 llh = self._lowest if full or self.cropped else self._lowest_ltd

1225 return self._llh3LL(llh, LatLon)

1226

1227 def _raw(self, y, x):

1228 # get the ushort geoid height at geoid index (y, x),

1229 # like GeographicLib/Geoid.hpp real rawval(is, iy)

1230 p = self._pgm

1231 if x < 0:

1232 x += p.nlon

1233 elif x >= p.nlon:

1234 x -= p.nlon

1235 h = p.nlon // 2

1236 if y < 0:

1237 y = -y

1238 elif y >= p.nlat:

1239 y = (p.nlat - 1) * 2 - y

1240 else:

1241 h = 0

1242 x += h if x < h else -h

1243 self._seek(y, x)

1244 h = _unpack(self._endian, self._egm.read(self._u2B))

1245 return h[0]

1246

1247 def _raws(self, y, x, ijs):

1248 # get bilinear 4-tuple or 10x12 cubic matrix

1249 return tuple(self._raw(y + j, x + i) for i, j in ijs)

1250

1251 def _raw2(self, *lat2):

1252 # yield a 2-tuple (y, ushorts) for each row or for

1253 # the rows between two (or more) earth lat values

1254 p = self._pgm

1255 g = self._egm

1256 e = self._Rendian

1257 n = self._Ru2B

1258 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat

1259 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)

1260 self._seek(s, 0) # to start of row s

1261 for y in range(s, t):

1262 yield y, _unpack(e, g.read(n))

1263

1264 def _seek(self, y, x):

1265 # position geoid to grid index (y, x)

1266 p, g = self._pgm, self._egm

1267 if g:

1268 b = p.skip + (y * p.nlon + x) * self._u2B

1269 g.seek(b, _SEEK_SET)

1270 return b # position

1271 raise GeoidError('closed file', txt=repr(p.egm)) # IOError

1272

1273

1274 class GeoidPGM(_GeoidBase):

1275 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth

1276 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/

1277 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1278 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}

1279 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/

1280 generated/scipy.interpolate.RectBivariateSpline.html>} or

1281 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1282 scipy.interpolate.interp2d.html>} interpolation.

1283

1284 Use any of the U{egm84-, egm96- or egm2008-*.pgm

1285 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}

1286 datasets. However, unless cropped, an entire C{egm*.pgm} dataset

1287 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/

1288 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}

1289 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1290 scipy.interpolate.interp2d.html>} interpolator and converted from

1291 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory

1292 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/

1293 geoid.html#geoidinst>} file size and may exceed the available memory,

1294 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.

1295 '''

1296 _cropped = False

1297 _endian = '>u2'

1298

1299 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84

1300 kind=3, smooth=0, **name):

1301 '''New L{GeoidPGM} interpolator.

1302

1303 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/

1304 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).

1305 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,

1306 north, east}) or 2-tuple (C{(south, west), (north, east)}),

1307 in C{degrees90} lat- and C{degrees180} longitudes or a

1308 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.

1309 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

1310 or L{a_f2Tuple}), default C{WGS84}.

1311 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for

1312 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/

1313 reference/generated/scipy.interpolate.RectBivariateSpline.html>},

1314 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

1315 reference/generated/scipy.interpolate.interp2d.html>}, -3

1316 for C{interp2d cubic} or -5 for C{interp2d quintic}.

1317 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

1318 <https://docs.SciPy.org/doc/scipy/reference/generated/

1319 scipy.interpolate.RectBivariateSpline.html>}

1320 only (C{int}).

1321 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).

1322

1323 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},

1324 B{C{kind}} or B{C{smooth}}.

1325

1326 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

1327

1328 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.

1329

1330 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.

1331

1332 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}

1333 warning as exception.

1334

1335 @raise TypeError: Invalid B{C{datum}} or unexpected argument.

1336

1337 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify

1338 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.

1339

1340 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/

1341 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte

1342 C{int} height converted to 8-byte C{dtype float64} for C{scipy}

1343 interpolators. Therefore, internal memory usage is 4 times the

1344 C{egm*.pgm} file size and may exceed the available memory,

1345 especially with 32-bit Python. To reduce memory usage, set

1346 keyword argument B{C{crop}} to the region of interest. For example

1347 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://

1348 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}

1349 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.

1350

1351 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.

1352 '''

1353 np = self.numpy

1354 self._u2B = np.dtype(self.endian).itemsize

1355

1356 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)

1357 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)

1358 if crop:

1359 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))

1360 if _MODS.internals._version2(np.__version__) < (1, 9):

1361 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-

1362 self._cropped = True

1363 try:

1364 # U{numpy dtype formats are different from Python struct formats

1365 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}

1366 # read all heights, skipping the PGM header lines, converted to float

1367 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale

1368 if p.Offset: # offset

1369 hs = p.Offset + hs

1370 if p.dlat < 0: # flip the rows

1371 hs = np.flipud(hs)

1372 _GeoidBase.__init__(self, hs, p)

1373 except Exception as x:

1374 raise _SciPyIssue(x, _in_, repr(egm_pgm))

1375 finally:

1376 g.close()

1377

1378 def _g2ll2(self, lat, lon):

1379 # convert grid (lat, lon) to earth (lat, lon), un-/cropped

1380 if self._cropped:

1381 lon -= self._lon_of

1382 else:

1383 while lon > _180_0:

1384 lon -= _360_0

1385 return lat, lon

1386

1387 def _ll2g2(self, lat, lon):

1388 # convert earth (lat, lon) to grid (lat, lon), un-/cropped

1389 if self._cropped:

1390 lon += self._lon_of

1391 else:

1392 while lon < 0:

1393 lon += _360_0

1394 return lat, lon

1395

1396 if _FOR_DOCS:

1397 __call__ = _GeoidBase.__call__

1398 height = _GeoidBase.height

1399

1400

1401 class _Gpars(_Named):

1402 '''(INTERNAL) Basic geoid parameters.

1403 '''

1404 # interpolator parameters

1405 dlat = 0 # +/- latitude resolution in C{degrees}

1406 dlon = 0 # longitude resolution in C{degrees}

1407 nlat = 1 # number of latitude knots (C{int})

1408 nlon = 0 # number of longitude knots (C{int})

1409 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat

1410 rlon = 0 # longitude resolution in C{float}, 1 / .dlon

1411 slat = 0 # nothern- or southern most latitude (C{degrees90})

1412 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})

1413

1414 flon = 0 # forward, earth to grid longitude offset

1415 glon = 0 # reverse, grid to earth longitude offset

1416

1417 knots = 0 # number of knots, nlat * nlon (C{int})

1418 skip = 0 # header bytes to skip (C{int})

1419

1420 def __repr__(self):

1421 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for

1422 a in dir(self.__class__)

1423 if a[:1].isupper()))

1424 return _COLONSPACE_(self, t)

1425

1426 def __str__(self):

1427 return Fmt.PAREN(self.classname, repr(self.name))

1428

1429

1430 class _PGM(_Gpars):

1431 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.

1432

1433 # Geoid file in PGM format for the GeographicLib::Geoid class

1434 # Description WGS84 EGM96, 5-minute grid

1435 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html

1436 # DateTime 2009-08-29 18:45:03

1437 # MaxBilinearError 0.140

1438 # RMSBilinearError 0.005

1439 # MaxCubicError 0.003

1440 # RMSCubicError 0.001

1441 # Offset -108

1442 # Scale 0.003

1443 # Origin 90N 0E

1444 # AREA_OR_POINT Point

1445 # Vertical_Datum WGS84

1446 <width> <height>

1447 <pixel>

1448 ...

1449 '''

1450 crop4 = () # 4-tuple (C{south, west, north, east}).

1451 egm = None

1452 glon = 180 # reverse offset, uncropped

1453# pgm = NN # name

1454 sizeB = 0

1455 u2B = 2 # item size of grid height (C{int}).

1456

1457 @staticmethod

1458 def _llstr2floats(latlon):

1459 # llstr to (lat, lon) floats

1460 lat, lon = latlon.split()

1461 return _MODS.dms.parseDMS2(lat, lon)

1462

1463 # PGM file attributes, CamelCase but not .istitle()

1464 AREA_OR_POINT = str

1465 DateTime = str

1466 Description = str # 'WGS84 EGM96, 5-minute grid'

1467 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'

1468 MaxBilinearError = float

1469 MaxCubicError = float

1470 Offset = float

1471 Origin = _llstr2floats

1472 Pixel = 0

1473 RMSBilinearError = float

1474 RMSCubicError = float

1475 Scale = float

1476 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'

1477 Vertical_Datum = str

1478

1479 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22

1480 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.

1481 '''

1482 self.name = pgm # geoid file name

1483 if itemsize:

1484 self._u2B = itemsize

1485 if sizeB:

1486 self.sizeB = sizeB

1487

1488 t = g.readline() # make sure newline == '\n'

1489 if t != b'P5\n' and t.strip() != b'P5':

1490 raise self._Errorf(_format_, _header_, t)

1491

1492 while True: # read all # Attr ... lines,

1493 try: # ignore empty ones or comments

1494 t = g.readline().strip()

1495 if t.startswith(_bHASH_):

1496 t = t.lstrip(_bHASH_).lstrip()

1497 a, v = map(_ub2str, t.split(None, 1))

1498 f = getattr(_PGM, a, None)

1499 if callable(f) and a[:1].isupper():

1500 setattr(self, a, f(v))

1501 elif t:

1502 break

1503 except (TypeError, ValueError):

1504 raise self._Errorf(_format_, 'Attr', t)

1505 else: # should never get here

1506 raise self._Errorf(_format_, _header_, g.tell())

1507

1508 try: # must be (even) width and (odd) height

1509 nlon, nlat = map(int, t.split())

1510 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \

1511 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):

1512 raise ValueError

1513 except (TypeError, ValueError):

1514 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)

1515

1516 try: # must be 16 bit pixel height

1517 t = g.readline().strip()

1518 self.Pixel = int(t)

1519 if not 255 < self.Pixel < 65536: # >u2 or >H only

1520 raise ValueError

1521 except (TypeError, ValueError):

1522 raise self._Errorf(_format_, 'pixel', t)

1523

1524 for a in dir(_PGM): # set undefined # Attr ... to None

1525 if a[:1].isupper() and callable(getattr(self, a)):

1526 setattr(self, a, None)

1527

1528 if self.Origin is None:

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

1530 if self.Offset is None or self.Offset > 0:

1531 raise self._Errorf(_format_, 'Offset', self.Offset)

1532 if self.Scale is None or self.Scale < EPS:

1533 raise self._Errorf(_format_, 'Scale', self.Scale)

1534

1535 self.skip = g.tell()

1536 self.knots = nlat * nlon

1537

1538 self.nlat, self.nlon = nlat, nlon

1539 self.slat, self.wlon = self.Origin

1540 # note, negative .dlat and .rlat since rows

1541 # are from .slat 90N down in decreasing lat

1542 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon

1543 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0

1544

1545 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0

1546 n = float(self.slat)

1547 s = n + self.dlat * (nlat - 1)

1548 w = self.wlon - self.glon

1549 e = w + self.dlon * nlon

1550 self.crop4 = s, w, n, e

1551

1552 n = self.sizeB - self.skip

1553 if n > 0 and n != (self.knots * self.u2B):

1554 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)

1555

1556 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15

1557 '''Crop the geoid to (south, west, north, east) box.

1558 '''

1559 # flon offset for both west and east

1560 f = 360 if west < 0 else 0

1561 # earth (lat, lon) to grid indices (y, x),

1562 # note y is decreasing, i.e. n < s

1563 s, w = self._lle2yx2(south, west, f)

1564 n, e = self._lle2yx2(north, east, f)

1565 s += 1 # s > n

1566 e += 1 # e > w

1567

1568 hi, wi = self.nlat, self.nlon

1569 # handle special cases

1570 if (s - n) > hi:

1571 n, s = 0, hi # entire lat range

1572 if (e - w) > wi:

1573 w, e, f = 0, wi, 180 # entire lon range

1574 if s == hi and w == n == 0 and e == wi:

1575 return g # use entire geoid as-is

1576

1577 if (e - w) < k1 or (s - n) < (k1 + 1):

1578 raise self._Errorf(_format_, 'swne', (north - south, east - west))

1579

1580 if e > wi > w: # wrap around

1581 # read w..wi and 0..e

1582 r, p = (wi - w), (e - wi)

1583 elif e > w:

1584 r, p = (e - w), 0

1585 else:

1586 raise self._Errorf('%s(%s < %s)', _assert_, w, e)

1587

1588 # convert to bytes

1589 r *= self.u2B

1590 p *= self.u2B

1591 q = wi * self.u2B # stride

1592 # number of rows and cols to skip from

1593 # the original (.slat, .wlon) origin

1594 z = self.skip + (n * wi + w) * self.u2B

1595 # sanity check

1596 if r < 2 or p < 0 or q < 2 or z < self.skip \

1597 or z > self.sizeB:

1598 raise self._Errorf(_format_, _assert_, (r, p, q, z))

1599

1600 # can't use _BytesIO since numpy

1601 # needs .fileno attr in .fromfile

1602 t, c = 0, self._tmpfile()

1603 # reading (s - n) rows, forward

1604 for y in range(n, s): # PYCHOK y unused

1605 g.seek(z, _SEEK_SET)

1606 # Python 2 tmpfile.write returns None

1607 t += c.write(g.read(r)) or r

1608 if p: # wrap around to start of row

1609 g.seek(-q, _SEEK_CUR)

1610 # assert(g.tell() == (z - w * self.u2B))

1611 # Python 2 tmpfile.write returns None

1612 t += c.write(g.read(p)) or p

1613 z += q

1614 c.flush()

1615 g.close()

1616

1617 s -= n # nlat

1618 e -= w # nlon

1619 k = s * e # knots

1620 z = k * self.u2B

1621 if t != z:

1622 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)

1623

1624 # update the _Gpars accordingly, note attributes

1625 # .dlat, .dlon, .rlat and .rlon remain unchanged

1626 self.slat += n * self.dlat

1627 self.wlon += w * self.dlon

1628 self.nlat = s

1629 self.nlon = e

1630 self.flon = self.glon = f

1631

1632 self.crop4 = south, west, north, east

1633 self.knots = k

1634 self.skip = 0 # no header lines in c

1635

1636 c.seek(0, _SEEK_SET)

1637 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-

1638 return c

1639

1640 def _Errorf(self, fmt, *args): # PYCHOK no cover

1641 t = fmt % args

1642 e = self.pgm or NN

1643 if e:

1644 t = _SPACE_(t, _in_, repr(e))

1645 return PGMError(t)

1646

1647 def _lle2yx2(self, lat, lon, flon):

1648 # earth (lat, lon) to grid indices (y, x)

1649 # with .dlat decreasing from 90N .slat

1650 lat -= self.slat

1651 lon += flon - self.wlon

1652 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),

1653 max(0, int(lon * self.rlon)))

1654

1655 def _tmpfile(self):

1656 # create a tmpfile to hold the cropped geoid grid

1657 try:

1658 from tempfile import NamedTemporaryFile as tmpfile

1659 except ImportError: # Python 2.7.16-

1660 from os import tmpfile

1661 t = _os_path.splitext(_os_path.basename(self.pgm))[0]

1662 f = tmpfile(mode='w+b', prefix=t or 'egm')

1663 f.seek(0, _SEEK_SET) # force overwrite

1664 return f

1665

1666 @Property_RO

1667 def pgm(self):

1668 '''Get the geoid file name (C{str}).

1669 '''

1670 return self.name

1671

1672

1673 class PGMError(GeoidError):

1674 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.

1675 '''

1676 pass

1677

1678

1679 def egmGeoidHeights(GeoidHeights_dat):

1680 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1681 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat

1682 <https://SourceForge.net/projects/geographiclib/files/testdata/>}

1683 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/

1684 geoid.html#testgeoid>}.

1685

1686 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file

1687 (C{str} or C{file} handle).

1688

1689 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,

1690 egm84, egm96, egm2008)}.

1691

1692 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.

1693

1694 @note: Function L{egmGeoidHeights} is used to test the geoids

1695 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module

1696 C{test/testGeoids.py}.

1697 '''

1698 dat = GeoidHeights_dat

1699 if isinstance(dat, bytes):

1700 dat = _BytesIO(dat)

1701

1702 try:

1703 dat.seek(0, _SEEK_SET) # reset

1704 except AttributeError as x:

1705 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)

1706

1707 for t in dat.readlines():

1708 t = t.strip()

1709 if t and not t.startswith(_bHASH_):

1710 lat, lon, egm84, egm96, egm2008 = map(float, t.split())

1711 while lon > _180_0: # EasternLon to earth lon

1712 lon -= _360_0

1713 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)

1714

1715

1716__all__ += _ALL_DOCS(_GeoidBase)

1717

1718 if __name__ == '__main__':

1719

1720 from pygeodesy.internals import printf, _sys

1721

1722 _crop = ()

1723 _GeoidEGM = GeoidKarney

1724 _kind = 3

1725

1726 geoids = _sys.argv[1:]

1727 while geoids:

1728 geoid = geoids.pop(0)

1729

1730 if '-crop'.startswith(geoid.lower()):

1731 _crop = 20, -125, 50, -65 # CONUS

1732

1733 elif '-karney'.startswith(geoid.lower()):

1734 _GeoidEGM = GeoidKarney

1735

1736 elif '-kind'.startswith(geoid.lower()):

1737 _kind = int(geoids.pop(0))

1738

1739 elif '-pgm'.startswith(geoid.lower()):

1740 _GeoidEGM = GeoidPGM

1741

1742 elif geoid[-4:].lower() in ('.pgm',):

1743 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)

1744 printf(g.toStr(), nt=1, nl=1)

1745 printf(repr(g.pgm), nt=1)

1746 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:

1747 # The height of the EGM96 geoid at Timbuktu

1748 # echo 16:46:33N 3:00:34W | GeoidEval

1749 # => 28.7068 -0.02e-6 -1.73e-6

1750 # The 1st number is the height of the geoid, the 2nd and

1751 # 3rd are its slopes in northerly and easterly direction

1752 t = 'Timbuktu %s' % (g,)

1753 k = {'egm84-15.pgm': '31.2979',

1754 'egm96-5.pgm': '28.7067',

1755 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')

1756 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')

1757 for ll in (ll, (16.776, -3.009),):

1758 try:

1759 h, ll = g.height(*ll), fstr(ll, prec=6)

1760 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)

1761 except (GeoidError, RangeError) as x:

1762 printf(_COLONSPACE_(t, str(x)))

1763

1764 elif geoid[-4:].lower() in ('.bin',):

1765 g = GeoidG2012B(geoid, kind=_kind)

1766 printf(g.toStr())

1767

1768 else:

1769 raise GeoidError(grid=repr(geoid))

1770

1771_I = int # PYCHOK unused _I

1772 del _intCs # trash ints cache

1773

1774# **) MIT License

1775#

1776# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1777#

1778# Permission is hereby granted, free of charge, to any person obtaining a

1779# copy of this software and associated documentation files (the "Software"),

1780# to deal in the Software without restriction, including without limitation

1781# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1782# and/or sell copies of the Software, and to permit persons to whom the

1783# Software is furnished to do so, subject to the following conditions:

1784#

1785# The above copyright notice and this permission notice shall be included

1786# in all copies or substantial portions of the Software.

1787#

1788# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1789# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1790# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1791# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1792# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1793# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1794# OTHER DEALINGS IN THE SOFTWARE.

1795

1796# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>

1797# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm

1798# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm

1799# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm

1800

1801# _center = 0, 0, 17.2260 # egm2008-1.pgm

1802# _center = 0, 0, 17.1630 # egm96-5.pgm

1803# _center = 0, 0, 18.3296 # egm84-15.pgm

1804

1805# _upperright = 90, 180, 14.8980 # egm2008-1.pgm

1806# _upperright = 90, 180, 13.6050 # egm96-5.pgm

1807# _upperright = 90, 180, 13.0980 # egm84-15.pgm

1808

1809

1810# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm

1811#

1812# 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)

1813#

1814# _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'

1815#

1816# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1817# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1818#

1819# 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)

1820#

1821# _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'

1822#

1823# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1824# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1825#

1826# 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)

1827#

1828# _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'

1829#

1830# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1831# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1832

1833

1834# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm

1835#

1836# 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)

1837#

1838# _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'

1839#

1840# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1841# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1842#

1843# 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)

1844#

1845# _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'

1846#

1847# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1848# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1849#

1850# 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)

1851#

1852# _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'

1853#

1854# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1855# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1856

1857

1858# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm

1859#

1860# 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)

1861#

1862# _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'

1863#

1864# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1865# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1866#

1867# 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)

1868#

1869# _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'

1870#

1871# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979

1872# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979

1873#

1874# 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)

1875#

1876# _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'

1877#

1878# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067

1879# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067