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__ = '24.07.12'

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

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 = _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

722 class GeoidError(HeightError):

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

724 '''

725 pass

726

727

728 class 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

834 class 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

845 def _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

851 def _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

859 class 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

1270 class 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

1397 class _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

1426 class _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

1669 class PGMError(GeoidError):

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

1671 '''

1672 pass

1673

1674

1675 def 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

1714 if __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

1768 del _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