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

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.interns import MISSING, NN, _4_, _COLONSPACE_, _COMMASPACE_, \

96 _cubic_, _E_, _height_, _in_, _kind_, _knots_, \

97 _lat_, _linear_, _lon_, _mean_, _N_, _n_a_, \

98 _not_, _numpy_, _on_, _outside_, _S_, _s_, \

99 _scipy_, _SPACE_, _stdev_, _supported_, _tbd_, \

100 _W_, _width_, _version2

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

102 from pygeodesy.named import _Named, _NamedTuple

103# from pygeodesy.namedTuples import LatLon3Tuple # _MODS

104 from pygeodesy.props import deprecated_method, Property_RO, property_RO

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

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

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

108

109 from math import floor

110 import os.path as _os_path

111 from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET

112 from struct import calcsize as _calcsize, unpack as _unpack

113 try:

114 from StringIO import StringIO as _BytesIO # reads bytes

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

116

117 except ImportError: # Python 3+

118 from io import BytesIO as _BytesIO # PYCHOK expected

119

120__all__ = _ALL_LAZY.geoids

121__version__ = '24.04.07'

122

123_assert_ = 'assert'

124_bHASH_ = b'#'

125_endian_ = 'endian'

126_format_ = '%s %r'

127_header_ = 'header'

128# temporarily hold a single instance for each int value

129_intCs = {}

130_interp2d_ks = {-2: _linear_,

131 -3: _cubic_,

132 -5: 'quintic'}

133_lli_ = 'lli'

134_non_increasing_ = 'non-increasing'

135_rb_ = 'rb'

136

137

138 class _GeoidBase(_HeightsBase):

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

140 '''

141 _cropped = None

142# _datum = _WGS84 # from _HeightsBase

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

144 _endian = _tbd_

145 _geoid = _n_a_

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

147 _interp2d = None # interp2d interpolation

148 _kind = 3 # order for interp2d, RectBivariateSpline

149# _kmin = 2 # min number of knots

150 _knots = 0 # nlat * nlon

151 _mean = None # fixed in GeoidKarney

152# _name = NN # _Named

153 _nBytes = 0 # numpy size in bytes, float64

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

155 _sizeB = 0 # geoid file size in bytes

156 _smooth = 0 # used only for RectBivariateSpline

157 _stdev = None # fixed in GeoidKarney

158 _u2B = 0 # np.itemsize or undefined

159

160 _lat_d = _0_0 # increment, +tive

161 _lat_lo = _0_0 # lower lat, south

162 _lat_hi = _0_0 # upper lat, noth

163 _lon_d = _0_0 # increment, +tive

164 _lon_lo = _0_0 # left lon, west

165 _lon_hi = _0_0 # right lon, east

166 _lon_of = _0_0 # forward lon offset

167 _lon_og = _0_0 # reverse lon offset

168

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

170 _yx_hits = None # cache hits, ala Karney

171

172 def __init__(self, hs, p):

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

174 and several internal geoid attributes.

175

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

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

178 other geoid parameters (C{INTERNAL}).

179

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

181 invalid B{C{kind}}.

182

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

184

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

186 C{-.RectBivariateSpline} issue.

187

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

189 C{-.RectBivariateSpline} warning as

190 exception.

191

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

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

194 C{scipy.interpolate.RectBivariateSpline}.

195 '''

196 spi = self.scipy_interpolate

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

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

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

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

201 if (p.nlat, p.nlon) != hs.shape:

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

203

204 # both axes and bounding box

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

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

207

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

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

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

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

212 k = self.kind

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

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

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

216 else: # call and overwrite the DEPRECATED .interp2d

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

218 elif 1 <= k <= 5:

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

220 s=self._smooth).ev

221 else:

222 raise GeoidError(kind=k)

223

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

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

226 self._knots = p.knots # grid knots

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

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

229 # shrink the box by 1 unit on every side

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

231 self._lat_lo = float(bb[0])

232 self._lat_hi = float(bb[1])

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

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

235

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

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

238

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

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

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

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

243 return the I{orthometric} height instead of the

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

245

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

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

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

249

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

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

252 geoid file is closed.

253

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

255 or longitude range.

256

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

258 C{-.RectBivariateSpline} issue.

259

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

261 C{-.RectBivariateSpline} warning as

262 exception.

263

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

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

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

267

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

269 '''

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

271

272 def __enter__(self):

273 '''Open context.

274 '''

275 return self

276

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

278 '''Close context.

279 '''

280 self.close()

281 # return None # XXX False

282

283 def __repr__(self):

284 return self.toStr()

285

286 def __str__(self):

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

288

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

290 # handle __call__

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

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

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

294 _a, _h = hs.append, self._hGeoid

295 try:

296 for i, lli in enumerate(llis):

297 N = _h(*_w(lli.lat, lli.lon))

298 # orthometric or geoid height

299 _a(_H(lli, N) if _H else N)

300 return _as(hs)

301

302 except (GeoidError, RangeError) as x:

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

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

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

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

307 except Exception as x:

308 if scipy and self.scipy:

309 raise _SciPyIssue(x)

310 else:

311 raise

312

313 @Property_RO

314 def _center(self):

315 ''' Cache for method L{center}.

316 '''

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

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

319

320 def center(self, LatLon=None):

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

322

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

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

325

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

327 lon, height)} otherwise a B{C{LatLon}} instance

328 with the lat-, longitude and geoid height of the

329 center grid location.

330 '''

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

332

333 def close(self):

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

335 '''

336 if not self.closed:

337 self._egm.close()

338 self._egm = None

339

340 @property_RO

341 def closed(self):

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

343 '''

344 return self._egm is None

345

346 @Property_RO

347 def cropped(self):

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

349 '''

350 return self._cropped

351

352 @Property_RO

353 def dtype(self):

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

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

356 '''

357 return self._hs_y_x.dtype

358

359 @Property_RO

360 def endian(self):

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

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

363 '''

364 return self._endian

365

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

367 # only used for .interpolate.interp2d, but

368 # overwritten for .RectBivariateSpline,

369 # note (y, x) must be flipped!

370 return self._interp2d(x, y)

371

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

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

374 m, a = len2(frange(lo, n, d))

375 if m != n:

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

377 if d < 0:

378 d, a = -d, list(reversed(a))

379 for i in range(1, m):

380 e = a[i] - a[i-1]

381 if e < EPS: # non-increasing axis

382 i = Fmt.INDEX(name, i)

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

384 return self.numpy.array(a), d

385

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

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

388 self._notOverloaded(lat, lon)

389

390 def _gyx2g2(self, y, x):

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

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

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

394

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

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

397

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

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

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

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

402

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

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

405

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

407 B{C{lats}} and B{C{lons}}.

408

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

410 geoid's lat- or longitude range.

411

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

413 C{-.RectBivariateSpline} issue.

414

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

416 C{-.RectBivariateSpline} warning as

417 exception.

418 '''

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

420

421 def _hGeoid(self, lat, lon):

422 out = self.outside(lat, lon)

423 if out:

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

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

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

427

428 @Property_RO

429 def _highest(self):

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

431 '''

432 return self._llh3minmax(True)

433

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

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

436

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

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

439

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

441 lon, height)} otherwise a B{C{LatLon}} instance

442 with the lat-, longitude and geoid height of the

443 highest grid location.

444 '''

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

446

447 @Property_RO

448 def hits(self):

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

450 '''

451 return self._yx_hits

452

453 @deprecated_method

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

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

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

457 try:

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

459 except AttributeError as x:

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

461

462 @Property_RO

463 def kind(self):

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

465 '''

466 return self._kind

467

468 @Property_RO

469 def knots(self):

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

471 '''

472 return self._knots

473

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

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

476 self._notOverloaded(lat, lon)

477

478 @property_RO

479 def _LL3T(self):

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

481 '''

482 _GeoidBase._LL3T = T = _MODS.namedTuples.LatLon3Tuple # overwrite poperty_RO

483 return T

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 B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

517 lon, height)} otherwise a B{C{LatLon}} instance

518 with the lat-, longitude and geoid height of the

519 lower-left, SW grid corner.

520 '''

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

522

523 @Property_RO

524 def _loweright(self):

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

526 '''

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

528

529 def loweright(self, LatLon=None):

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

531

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

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

534

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

536 lon, height)} otherwise a B{C{LatLon}} instance

537 with the lat-, longitude and geoid height of the

538 lower-right, SE grid corner.

539 '''

540

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

542

543 lowerright = loweright # synonymous

544

545 @Property_RO

546 def _lowest(self):

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

548 '''

549 return self._llh3minmax(False)

550

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

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

553

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

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

556

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

558 lon, height)} otherwise a B{C{LatLon}} instance

559 with the lat-, longitude and geoid height of the

560 lowest grid location.

561 '''

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

563

564 @Property_RO

565 def mean(self):

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

567 '''

568 if self._mean is None: # see GeoidKarney

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

570 return self._mean

571

572 @property_RO

573 def name(self):

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

575 '''

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

577

578 @Property_RO

579 def nBytes(self):

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

581 '''

582 return self._nBytes

583

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

585 # open the geoid file

586 try:

587 self._geoid = _os_path.basename(geoid)

588 self._sizeB = _os_path.getsize(geoid)

589 g = open(geoid, _rb_)

590 except (IOError, OSError) as x:

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

592

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

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

595 self._kind = int(kind)

596 if name:

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

598 if smooth:

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

600

601 return g

602

603 def outside(self, lat, lon):

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

605 lat-/longitude or crop range.

606

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

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

609

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

611 empty C{str} if inside.

612 '''

613 return (_S_ if lat < self._lat_lo else

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

615 (_W_ if lon < self._lon_lo else

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

617

618 @Property_RO

619 def pgm(self):

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

621 '''

622 return self._pgm

623

624 @Property_RO

625 def sizeB(self):

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

627 '''

628 return self._sizeB

629

630 @Property_RO

631 def smooth(self):

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

633 '''

634 return self._smooth

635

636 @Property_RO

637 def stdev(self):

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

639 '''

640 if self._stdev is None: # see GeoidKarney

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

642 return self._stdev

643

644 def _swne(self, crop):

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

646 try:

647 if len(crop) == 2:

648 try: # sw, ne LatLons

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

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

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

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

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

654 swne = crop

655 if len(swne) == 4:

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

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

658 -180 <= w <= (e - _1_0) <= 179:

659 return s, w, n, e

660 except (IndexError, TypeError, ValueError):

661 pass

662 raise GeoidError(crop=crop)

663

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

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

666

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

668 default). Trailing zero decimals are stripped

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

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

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

672

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

674 '''

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

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

677 (self.lowerleft, self.upperright,

678 self.center,

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

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

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

682 attrs( 'cropped', 'dtype', _endian_, 'hits', _knots_, 'nBytes',

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

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

685

686 @Property_RO

687 def u2B(self):

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

689 '''

690 return self._u2B

691

692 @Property_RO

693 def _upperleft(self):

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

695 '''

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

697

698 def upperleft(self, LatLon=None):

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

700

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

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

703

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

705 lon, height)} otherwise a B{C{LatLon}} instance

706 with the lat-, longitude and geoid height of the

707 upper-left, NW grid corner.

708 '''

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

710

711 @Property_RO

712 def _upperright(self):

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

714 '''

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

716

717 def upperright(self, LatLon=None):

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

719

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

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

722

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

724 lon, height)} otherwise a B{C{LatLon}} instance

725 with the lat-, longitude and geoid height of the

726 upper-right, NE grid corner.

727 '''

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

729

730

731 class GeoidError(HeightError):

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

733 '''

734 pass

735

736

737 class GeoidG2012B(_GeoidBase):

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

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

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

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

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

743 U{Guam and Northern Mariana Islands

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

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

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

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

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

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

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

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

752

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

754 C{g2012b*.bin} grid files.

755 '''

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

757 kind=3, name=NN, smooth=0):

758 '''New L{GeoidG2012B} interpolator.

759

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

761 @kwarg crop: Optional crop box, not supported (C{None}).

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

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

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

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

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

767 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

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

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

770 @kwarg name: Optional geoid name (C{str}).

771 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

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

773 scipy.interpolate.RectBivariateSpline.html>}

774 only (C{int}).

775

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

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

778

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

780 not installed.

781

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

783

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

785

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

787 warning as exception.

788

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

790

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

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

793 '''

794 if crop is not None:

795 raise GeoidError(crop=crop, txt=_not_(_supported_))

796

797 g = self._open(g2012b_bin, datum, kind, name, smooth)

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

799

800 try:

801 p = _Gpars()

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

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

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

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

806 # skip 4xf8, get 3xi4

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

808 if ien == 1: # correct endian

809 p.knots = p.nlat * p.nlon

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

811 and 1 < p.nlon < n:

812 self._endian = en_+'f4'

813 break

814 else: # couldn't validate endian

815 raise GeoidError(_endian_)

816

817 # get the first 4xf8

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

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

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

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

822 _GeoidBase.__init__(self, hs, p)

823

824 except Exception as x:

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

826 finally:

827 g.close()

828

829 def _g2ll2(self, lat, lon):

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

831 return lat, lon

832

833 def _ll2g2(self, lat, lon):

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

835 return lat, lon

836

837 if _FOR_DOCS:

838 __call__ = _GeoidBase.__call__

839 height = _GeoidBase.height

840

841

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

843 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat

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

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

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

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

848 '''

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

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

851

852

853 def _I(i):

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

855 '''

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

857

858

859 def _T(*cs):

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

861 '''

862 return map1(_I, *cs)

863

864_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)

865

866

867 class GeoidKarney(_GeoidBase):

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

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

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

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

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

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

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

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

876

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

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

879 datasets.

880 '''

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

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

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

884 _T0s12,

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

886 _T0s12,

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

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

889 _T0s12,

890 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),

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

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

893

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

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

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

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

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

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

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

901 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),

902 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),

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

904

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

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

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

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

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

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

911 _T0s12,

912 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),

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

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

915

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

917 _T(1, 0),

918 _T(0, 1),

919 _T(1, 1))

920

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

922 _T( 1, -1),

923 _T(-1, 0),

924 _T( 0, 0),

925 _T( 1, 0),

926 _T( 2, 0),

927 _T(-1, 1),

928 _T( 0, 1),

929 _T( 1, 1),

930 _T( 2, 1),

931 _T( 0, 2),

932 _T( 1, 2))

933

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

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

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

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

938# (-8.167, 147.25, 85.422) if egm96-5.pgm else

939# (-4.5, 148.75, 81.33)) # egm84-15.pgm

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

941# (4.667, 78.833, -107.043) if egm96-5.pgm else

942# (4.75, 79.25, -107.34)) # egm84-15.pgm

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

944 _nBytes = None # not applicable

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

946 _smooth = None # not applicable

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

948 _u2B = _calcsize(_endian) # pixelsize_ in bytes

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

950 _Ru2B = 0 # row of pixelsize_s in bytes

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

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

953 _yx_hits = 0 # cache hits

954

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

956 kind=3, name=NN, smooth=None):

957 '''New L{GeoidKarney} interpolator.

958

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

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

961 note below.

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

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

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

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

966 C{LatLon} instances.

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

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

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

970 for C{cubic}.

971 @kwarg name: Optional geoid name (C{str}).

972 @kwarg smooth: Smoothing factor, unsupported (C{None}).

973

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

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

976

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

978

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

980

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

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

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

984 '''

985 if smooth is not None:

986 raise GeoidError(smooth=smooth, txt=_not_(_supported_))

987

988 if kind in (2,):

989 self._evH = self._ev2H

990 elif kind not in (3,):

991 raise GeoidError(kind=kind)

992

993 self._egm = g = self._open(egm_pgm, datum, kind, name, smooth)

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

995

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

997 self._Ru2B = _calcsize(self._Rendian)

998

999 self._knots = p.knots # grid knots

1000 self._lon_of = float(p.flon) # forward offset

1001 self._lon_og = float(p.glon) # reverse offset

1002 # set earth (lat, lon) limits (s, w, n, e)

1003 self._lat_lo, self._lon_lo, \

1004 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)

1005 self._cropped = True if crop else False

1006

1007 def __call__(self, *llis, **wrap_H):

1008 '''Interpolate the geoid height for one or several locations.

1009

1010 @arg llis: One or more locations (C{LatLon}s), all positional.

1011 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.

1012 If C{B{wrap} is True}, wrap or I{normalize} all

1013 B{C{llis}} locations (C{bool}). If C{B{H} is True},

1014 return the I{orthometric} height instead of the

1015 I{geoid} height at each location (C{bool}).

1016

1017 @return: A single interpolated geoid (or orthometric) height

1018 (C{float}) or a list or tuple of interpolated geoid

1019 (or orthometric) heights (C{float}s).

1020

1021 @raise GeoidError: Insufficient number of B{C{llis}}, an

1022 invalid B{C{lli}} or the C{egm*.pgm}

1023 geoid file is closed.

1024

1025 @raise RangeError: An B{C{lli}} is outside this geoid's lat-

1026 or longitude range.

1027

1028 @note: To obtain I{orthometric} heights, each B{C{llis}}

1029 location must have an ellipsoid C{height} or C{h}

1030 attribute, otherwise C{height=0} is used.

1031

1032 @see: Function L{pygeodesy.heightOrthometric}.

1033 '''

1034 return self._called(llis, False, **wrap_H)

1035

1036 def _c0c3v(self, y, x):

1037 # get the common denominator, the 10x12 cubic matrix and

1038 # the 12 cubic v-coefficients around geoid index (y, x)

1039 p = self._pgm

1040 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):

1041 # read 4x4 ushorts, drop the 4 corners

1042 g = self._egm

1043 e = self._4endian

1044 n = self._4u2B

1045 R = self._Ru2B

1046

1047 b = self._seek(y - 1, x - 1)

1048 v = _unpack(e, g.read(n))[1:3]

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))

1055 b += R

1056 g.seek(b, _SEEK_SET)

1057 v += _unpack(e, g.read(n))[1:3]

1058 j = 1

1059

1060 else: # likely some wrapped y and/or x's

1061 v = self._raws(y, x, GeoidKarney._CM)

1062 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)

1063

1064 return GeoidKarney._C0[j], GeoidKarney._C3[j], v

1065

1066 @Property_RO

1067 def dtype(self):

1068 '''Get the geoid's grid data type (C{str}).

1069 '''

1070 return 'ushort'

1071

1072 def _ev(self, lat, lon): # PYCHOK expected

1073 # interpolate the geoid height at grid (lat, lon)

1074 fy, fx = self._g2yx2(lat, lon)

1075 y, x = int(floor(fy)), int(floor(fx))

1076 fy -= y

1077 fx -= x

1078 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H

1079 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)

1080 H += self._pgm.Offset # H.fadd(self._pgm.Offset)

1081 return H.fsum()

1082

1083 def _ev2H(self, fy, fx, *yx):

1084 # compute the bilinear 4-tuple and interpolate raw H

1085 if self._yxH == yx:

1086 t = self._yxHt

1087 self._yx_hits += 1

1088 else:

1089 y, x = self._yxH = yx

1090 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)

1091 v = _1_0, -fx, fx

1092 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)

1093 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy

1094 return H

1095

1096 def _ev3H(self, fy, fx, *yx):

1097 # compute the cubic 10-tuple and interpolate raw H

1098 if self._yxH == yx:

1099 t = self._yxHt

1100 self._yx_hits += 1

1101 else:

1102 self._yxH = yx

1103 c0, c3, v = self._c0c3v(*yx)

1104 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]

1105 self._yxHt = t = tuple(t)

1106 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...

1107 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +

1108 # fy * (t[2] + fx * (t[4] + fx * t[7]) +

1109 # fy * (t[5] + fx * t[8] + fy * t[9]));

1110 v = _1_0, fx, fy

1111 H = Fdot(v, t[5], t[8], t[9])

1112 H *= fy

1113 H += Fhorner(fx, t[2], t[4], t[7])

1114 H *= fy

1115 H += Fhorner(fx, t[0], t[1], t[3], t[6])

1116 return H

1117

1118 _evH = _ev3H # overriden for kind == 2

1119

1120 def _g2ll2(self, lat, lon):

1121 # convert grid (lat, lon) to earth (lat, lon), uncropped

1122 while lon > _180_0:

1123 lon -= _360_0

1124 return lat, lon

1125

1126 def _g2yx2(self, lat, lon):

1127 # convert grid (lat, lon) to grid (y, x) indices

1128 p = self._pgm

1129 # note, slat = +90, rlat < 0 makes y >=0

1130 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)

1131

1132 def _gyx2g2(self, y, x):

1133 # convert grid (y, x) indices to grid (lat, lon)

1134 p = self._pgm

1135 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)

1136

1137 def height(self, lats, lons, **wrap):

1138 '''Interpolate the geoid height for one or several lat-/longitudes.

1139

1140 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).

1141 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).

1142 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}

1143 and B{C{lons}} locations (C{bool}).

1144

1145 @return: A single interpolated geoid height (C{float}) or a

1146 list of interpolated geoid heights (C{float}s).

1147

1148 @raise GeoidError: Insufficient or non-matching number of

1149 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}

1150 geoid file is closed.

1151

1152 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this

1153 geoid's lat- or longitude range.

1154 '''

1155 return _height_called(self, lats, lons, Error=GeoidError, **wrap)

1156

1157 @Property_RO

1158 def _highest_ltd(self):

1159 '''(INTERNAL) Cache for L{highest} mesthod.

1160 '''

1161 return self._llh3minmax(True, -12, -4)

1162

1163 def highest(self, LatLon=None, full=False): # PYCHOK full

1164 '''Return the location and largest height of this geoid.

1165

1166 @kwarg LatLon: Optional class to return the location and height

1167 (C{LatLon}) or C{None}.

1168 @kwarg full: Search the full or limited latitude range (C{bool}).

1169

1170 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1171 lon, height)} otherwise a B{C{LatLon}} instance

1172 with the lat-, longitude and geoid height at the

1173 highest grid location.

1174 '''

1175 llh = self._highest if full or self.cropped else self._highest_ltd

1176 return self._llh3LL(llh, LatLon)

1177

1178 def _lat2y2(self, lat2):

1179 # convert earth lat(s) to min and max grid y indices

1180 ys, m = [], self._pgm.nlat - 1

1181 for lat in lat2:

1182 y, _ = self._g2yx2(*self._ll2g2(lat, 0))

1183 ys.append(max(min(int(y), m), 0))

1184 return min(ys), max(ys) + 1

1185

1186 def _ll2g2(self, lat, lon):

1187 # convert earth (lat, lon) to grid (lat, lon), uncropped

1188 while lon < 0:

1189 lon += _360_0

1190 return lat, lon

1191

1192 def _llh3minmax(self, highest=True, *lat2):

1193 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid

1194 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)

1195 y = x = 0

1196 h = self._raw(y, x)

1197 if highest:

1198 for j, r in self._raw2(*lat2):

1199 m = max(r)

1200 if m > h:

1201 h, y, x = m, j, r.index(m)

1202 else: # lowest

1203 for j, r in self._raw2(*lat2):

1204 m = min(r)

1205 if m < h:

1206 h, y, x = m, j, r.index(m)

1207 h *= self._pgm.Scale

1208 h += self._pgm.Offset

1209 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)

1210

1211 @Property_RO

1212 def _lowest_ltd(self):

1213 '''(INTERNAL) Cache for L{lowest}.

1214 '''

1215 return self._llh3minmax(False, 0, 8)

1216

1217 def lowest(self, LatLon=None, full=False): # PYCHOK full

1218 '''Return the location and lowest height of this geoid.

1219

1220 @kwarg LatLon: Optional class to return the location and height

1221 (C{LatLon}) or C{None}.

1222 @kwarg full: Search the full or limited latitude range (C{bool}).

1223

1224 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1225 lon, height)} otherwise a B{C{LatLon}} instance

1226 with the lat-, longitude and geoid height of the

1227 lowest grid location.

1228 '''

1229 llh = self._lowest if full or self.cropped else self._lowest_ltd

1230 return self._llh3LL(llh, LatLon)

1231

1232 def _raw(self, y, x):

1233 # get the ushort geoid height at geoid index (y, x),

1234 # like GeographicLib/Geoid.hpp real rawval(is, iy)

1235 p = self._pgm

1236 if x < 0:

1237 x += p.nlon

1238 elif x >= p.nlon:

1239 x -= p.nlon

1240 h = p.nlon // 2

1241 if y < 0:

1242 y = -y

1243 elif y >= p.nlat:

1244 y = (p.nlat - 1) * 2 - y

1245 else:

1246 h = 0

1247 x += h if x < h else -h

1248 self._seek(y, x)

1249 h = _unpack(self._endian, self._egm.read(self._u2B))

1250 return h[0]

1251

1252 def _raws(self, y, x, ijs):

1253 # get bilinear 4-tuple or 10x12 cubic matrix

1254 return tuple(self._raw(y + j, x + i) for i, j in ijs)

1255

1256 def _raw2(self, *lat2):

1257 # yield a 2-tuple (y, ushorts) for each row or for

1258 # the rows between two (or more) earth lat values

1259 p = self._pgm

1260 g = self._egm

1261 e = self._Rendian

1262 n = self._Ru2B

1263 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat

1264 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)

1265 self._seek(s, 0) # to start of row s

1266 for y in range(s, t):

1267 yield y, _unpack(e, g.read(n))

1268

1269 def _seek(self, y, x):

1270 # position geoid to grid index (y, x)

1271 p, g = self._pgm, self._egm

1272 if g:

1273 b = p.skip + (y * p.nlon + x) * self._u2B

1274 g.seek(b, _SEEK_SET)

1275 return b # position

1276 raise GeoidError('closed file', txt=repr(p.egm)) # IOError

1277

1278

1279 class GeoidPGM(_GeoidBase):

1280 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth

1281 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/

1282 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1283 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}

1284 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/

1285 generated/scipy.interpolate.RectBivariateSpline.html>} or

1286 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1287 scipy.interpolate.interp2d.html>} interpolation.

1288

1289 Use any of the U{egm84-, egm96- or egm2008-*.pgm

1290 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}

1291 datasets. However, unless cropped, an entire C{egm*.pgm} dataset

1292 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/

1293 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}

1294 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1295 scipy.interpolate.interp2d.html>} interpolator and converted from

1296 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory

1297 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/

1298 geoid.html#geoidinst>} file size and may exceed the available memory,

1299 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.

1300 '''

1301 _cropped = False

1302 _endian = '>u2'

1303

1304 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84

1305 kind=3, name=NN, smooth=0):

1306 '''New L{GeoidPGM} interpolator.

1307

1308 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/

1309 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).

1310 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,

1311 north, east}) or 2-tuple (C{(south, west), (north, east)}),

1312 in C{degrees90} lat- and C{degrees180} longitudes or a

1313 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.

1314 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

1315 or L{a_f2Tuple}), default C{WGS84}.

1316 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for

1317 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/

1318 reference/generated/scipy.interpolate.RectBivariateSpline.html>},

1319 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

1320 reference/generated/scipy.interpolate.interp2d.html>}, -3

1321 for C{interp2d cubic} or -5 for C{interp2d quintic}.

1322 @kwarg name: Optional geoid name (C{str}).

1323 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

1324 <https://docs.SciPy.org/doc/scipy/reference/generated/

1325 scipy.interpolate.RectBivariateSpline.html>}

1326 only (C{int}).

1327

1328 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},

1329 B{C{kind}} or B{C{smooth}}.

1330

1331 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

1332

1333 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.

1334

1335 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.

1336

1337 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}

1338 warning as exception.

1339

1340 @raise TypeError: Invalid B{C{datum}}.

1341

1342 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify

1343 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.

1344

1345 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/

1346 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte

1347 C{int} height converted to 8-byte C{dtype float64} for C{scipy}

1348 interpolators. Therefore, internal memory usage is 4 times the

1349 C{egm*.pgm} file size and may exceed the available memory,

1350 especially with 32-bit Python. To reduce memory usage, set

1351 keyword argument B{C{crop}} to the region of interest. For example

1352 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://

1353 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}

1354 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.

1355

1356 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.

1357 '''

1358 np = self.numpy

1359 self._u2B = np.dtype(self.endian).itemsize

1360

1361 g = self._open(egm_pgm, datum, kind, name, smooth)

1362 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)

1363 if crop:

1364 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))

1365 if _version2(np.__version__) < (1, 9):

1366 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-

1367 self._cropped = True

1368 try:

1369 # U{numpy dtype formats are different from Python struct formats

1370 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}

1371 # read all heights, skipping the PGM header lines, converted to float

1372 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale

1373 if p.Offset: # offset

1374 hs = p.Offset + hs

1375 if p.dlat < 0: # flip the rows

1376 hs = np.flipud(hs)

1377 _GeoidBase.__init__(self, hs, p)

1378 except Exception as x:

1379 raise _SciPyIssue(x, _in_, repr(egm_pgm))

1380 finally:

1381 g.close()

1382

1383 def _g2ll2(self, lat, lon):

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

1385 if self._cropped:

1386 lon -= self._lon_of

1387 else:

1388 while lon > _180_0:

1389 lon -= _360_0

1390 return lat, lon

1391

1392 def _ll2g2(self, lat, lon):

1393 # convert earth (lat, lon) to grid (lat, lon), un-/cropped

1394 if self._cropped:

1395 lon += self._lon_of

1396 else:

1397 while lon < 0:

1398 lon += _360_0

1399 return lat, lon

1400

1401 if _FOR_DOCS:

1402 __call__ = _GeoidBase.__call__

1403 height = _GeoidBase.height

1404

1405

1406 class _Gpars(_Named):

1407 '''(INTERNAL) Basic geoid parameters.

1408 '''

1409 # interpolator parameters

1410 dlat = 0 # +/- latitude resolution in C{degrees}

1411 dlon = 0 # longitude resolution in C{degrees}

1412 nlat = 1 # number of latitude knots (C{int})

1413 nlon = 0 # number of longitude knots (C{int})

1414 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat

1415 rlon = 0 # longitude resolution in C{float}, 1 / .dlon

1416 slat = 0 # nothern- or southern most latitude (C{degrees90})

1417 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})

1418

1419 flon = 0 # forward, earth to grid longitude offset

1420 glon = 0 # reverse, grid to earth longitude offset

1421

1422 knots = 0 # number of knots, nlat * nlon (C{int})

1423 skip = 0 # header bytes to skip (C{int})

1424

1425 def __repr__(self):

1426 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for

1427 a in dir(self.__class__)

1428 if a[:1].isupper()))

1429 return _COLONSPACE_(self, t)

1430

1431 def __str__(self):

1432 return Fmt.PAREN(self.classname, repr(self.name))

1433

1434

1435 class _PGM(_Gpars):

1436 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.

1437

1438 # Geoid file in PGM format for the GeographicLib::Geoid class

1439 # Description WGS84 EGM96, 5-minute grid

1440 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html

1441 # DateTime 2009-08-29 18:45:03

1442 # MaxBilinearError 0.140

1443 # RMSBilinearError 0.005

1444 # MaxCubicError 0.003

1445 # RMSCubicError 0.001

1446 # Offset -108

1447 # Scale 0.003

1448 # Origin 90N 0E

1449 # AREA_OR_POINT Point

1450 # Vertical_Datum WGS84

1451 <width> <height>

1452 <pixel>

1453 ...

1454 '''

1455 crop4 = () # 4-tuple (C{south, west, north, east}).

1456 egm = None

1457 glon = 180 # reverse offset, uncropped

1458# pgm = NN # name

1459 sizeB = 0

1460 u2B = 2 # item size of grid height (C{int}).

1461

1462 @staticmethod

1463 def _llstr2floats(latlon):

1464 # llstr to (lat, lon) floats

1465 lat, lon = latlon.split()

1466 return _MODS.dms.parseDMS2(lat, lon)

1467

1468 # PGM file attributes, CamelCase but not .istitle()

1469 AREA_OR_POINT = str

1470 DateTime = str

1471 Description = str # 'WGS84 EGM96, 5-minute grid'

1472 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'

1473 MaxBilinearError = float

1474 MaxCubicError = float

1475 Offset = float

1476 Origin = _llstr2floats

1477 Pixel = 0

1478 RMSBilinearError = float

1479 RMSCubicError = float

1480 Scale = float

1481 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'

1482 Vertical_Datum = str

1483

1484 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22

1485 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.

1486 '''

1487 self.name = pgm # geoid file name

1488 if itemsize:

1489 self._u2B = itemsize

1490 if sizeB:

1491 self.sizeB = sizeB

1492

1493 t = g.readline() # make sure newline == '\n'

1494 if t != b'P5\n' and t.strip() != b'P5':

1495 raise self._Errorf(_format_, _header_, t)

1496

1497 while True: # read all # Attr ... lines,

1498 try: # ignore empty ones or comments

1499 t = g.readline().strip()

1500 if t.startswith(_bHASH_):

1501 t = t.lstrip(_bHASH_).lstrip()

1502 a, v = map(_ub2str, t.split(None, 1))

1503 f = getattr(_PGM, a, None)

1504 if callable(f) and a[:1].isupper():

1505 setattr(self, a, f(v))

1506 elif t:

1507 break

1508 except (TypeError, ValueError):

1509 raise self._Errorf(_format_, 'Attr', t)

1510 else: # should never get here

1511 raise self._Errorf(_format_, _header_, g.tell())

1512

1513 try: # must be (even) width and (odd) height

1514 nlon, nlat = map(int, t.split())

1515 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \

1516 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):

1517 raise ValueError

1518 except (TypeError, ValueError):

1519 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)

1520

1521 try: # must be 16 bit pixel height

1522 t = g.readline().strip()

1523 self.Pixel = int(t)

1524 if not 255 < self.Pixel < 65536: # >u2 or >H only

1525 raise ValueError

1526 except (TypeError, ValueError):

1527 raise self._Errorf(_format_, 'pixel', t)

1528

1529 for a in dir(_PGM): # set undefined # Attr ... to None

1530 if a[:1].isupper() and callable(getattr(self, a)):

1531 setattr(self, a, None)

1532

1533 if self.Origin is None:

1534 raise self._Errorf(_format_, 'Origin', self.Origin)

1535 if self.Offset is None or self.Offset > 0:

1536 raise self._Errorf(_format_, 'Offset', self.Offset)

1537 if self.Scale is None or self.Scale < EPS:

1538 raise self._Errorf(_format_, 'Scale', self.Scale)

1539

1540 self.skip = g.tell()

1541 self.knots = nlat * nlon

1542

1543 self.nlat, self.nlon = nlat, nlon

1544 self.slat, self.wlon = self.Origin

1545 # note, negative .dlat and .rlat since rows

1546 # are from .slat 90N down in decreasing lat

1547 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon

1548 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0

1549

1550 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0

1551 n = float(self.slat)

1552 s = n + self.dlat * (nlat - 1)

1553 w = self.wlon - self.glon

1554 e = w + self.dlon * nlon

1555 self.crop4 = s, w, n, e

1556

1557 n = self.sizeB - self.skip

1558 if n > 0 and n != (self.knots * self.u2B):

1559 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)

1560

1561 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15

1562 '''Crop the geoid to (south, west, north, east) box.

1563 '''

1564 # flon offset for both west and east

1565 f = 360 if west < 0 else 0

1566 # earth (lat, lon) to grid indices (y, x),

1567 # note y is decreasing, i.e. n < s

1568 s, w = self._lle2yx2(south, west, f)

1569 n, e = self._lle2yx2(north, east, f)

1570 s += 1 # s > n

1571 e += 1 # e > w

1572

1573 hi, wi = self.nlat, self.nlon

1574 # handle special cases

1575 if (s - n) > hi:

1576 n, s = 0, hi # entire lat range

1577 if (e - w) > wi:

1578 w, e, f = 0, wi, 180 # entire lon range

1579 if s == hi and w == n == 0 and e == wi:

1580 return g # use entire geoid as-is

1581

1582 if (e - w) < k1 or (s - n) < (k1 + 1):

1583 raise self._Errorf(_format_, 'swne', (north - south, east - west))

1584

1585 if e > wi > w: # wrap around

1586 # read w..wi and 0..e

1587 r, p = (wi - w), (e - wi)

1588 elif e > w:

1589 r, p = (e - w), 0

1590 else:

1591 raise self._Errorf('%s(%s < %s)', _assert_, w, e)

1592

1593 # convert to bytes

1594 r *= self.u2B

1595 p *= self.u2B

1596 q = wi * self.u2B # stride

1597 # number of rows and cols to skip from

1598 # the original (.slat, .wlon) origin

1599 z = self.skip + (n * wi + w) * self.u2B

1600 # sanity check

1601 if r < 2 or p < 0 or q < 2 or z < self.skip \

1602 or z > self.sizeB:

1603 raise self._Errorf(_format_, _assert_, (r, p, q, z))

1604

1605 # can't use _BytesIO since numpy

1606 # needs .fileno attr in .fromfile

1607 t, c = 0, self._tmpfile()

1608 # reading (s - n) rows, forward

1609 for y in range(n, s): # PYCHOK y unused

1610 g.seek(z, _SEEK_SET)

1611 # Python 2 tmpfile.write returns None

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

1613 if p: # wrap around to start of row

1614 g.seek(-q, _SEEK_CUR)

1615 # assert(g.tell() == (z - w * self.u2B))

1616 # Python 2 tmpfile.write returns None

1617 t += c.write(g.read(p)) or p

1618 z += q

1619 c.flush()

1620 g.close()

1621

1622 s -= n # nlat

1623 e -= w # nlon

1624 k = s * e # knots

1625 z = k * self.u2B

1626 if t != z:

1627 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)

1628

1629 # update the _Gpars accordingly, note attributes

1630 # .dlat, .dlon, .rlat and .rlon remain unchanged

1631 self.slat += n * self.dlat

1632 self.wlon += w * self.dlon

1633 self.nlat = s

1634 self.nlon = e

1635 self.flon = self.glon = f

1636

1637 self.crop4 = south, west, north, east

1638 self.knots = k

1639 self.skip = 0 # no header lines in c

1640

1641 c.seek(0, _SEEK_SET)

1642 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-

1643 return c

1644

1645 def _Errorf(self, fmt, *args): # PYCHOK no cover

1646 t = fmt % args

1647 e = self.pgm or NN

1648 if e:

1649 t = _SPACE_(t, _in_, repr(e))

1650 return PGMError(t)

1651

1652 def _lle2yx2(self, lat, lon, flon):

1653 # earth (lat, lon) to grid indices (y, x)

1654 # with .dlat decreasing from 90N .slat

1655 lat -= self.slat

1656 lon += flon - self.wlon

1657 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),

1658 max(0, int(lon * self.rlon)))

1659

1660 def _tmpfile(self):

1661 # create a tmpfile to hold the cropped geoid grid

1662 try:

1663 from tempfile import NamedTemporaryFile as tmpfile

1664 except ImportError: # Python 2.7.16-

1665 from os import tmpfile

1666 t = _os_path.splitext(_os_path.basename(self.pgm))[0]

1667 f = tmpfile(mode='w+b', prefix=t or 'egm')

1668 f.seek(0, _SEEK_SET) # force overwrite

1669 return f

1670

1671 @Property_RO

1672 def pgm(self):

1673 '''Get the geoid file name (C{str}).

1674 '''

1675 return self.name

1676

1677

1678 class PGMError(GeoidError):

1679 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.

1680 '''

1681 pass

1682

1683

1684 def egmGeoidHeights(GeoidHeights_dat):

1685 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1686 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat

1687 <https://SourceForge.net/projects/geographiclib/files/testdata/>}

1688 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/

1689 geoid.html#testgeoid>}.

1690

1691 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file

1692 (C{str} or C{file} handle).

1693

1694 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,

1695 egm84, egm96, egm2008)}.

1696

1697 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.

1698

1699 @note: Function L{egmGeoidHeights} is used to test the geoids

1700 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module

1701 C{test/testGeoids.py}.

1702 '''

1703 dat = GeoidHeights_dat

1704 if isinstance(dat, bytes):

1705 dat = _BytesIO(dat)

1706

1707 try:

1708 dat.seek(0, _SEEK_SET) # reset

1709 except AttributeError as x:

1710 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)

1711

1712 for t in dat.readlines():

1713 t = t.strip()

1714 if t and not t.startswith(_bHASH_):

1715 lat, lon, egm84, egm96, egm2008 = map(float, t.split())

1716 while lon > _180_0: # EasternLon to earth lon

1717 lon -= _360_0

1718 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)

1719

1720

1721__all__ += _ALL_DOCS(_GeoidBase)

1722

1723 if __name__ == '__main__':

1724

1725 from pygeodesy.lazily import printf, _sys

1726

1727 _crop = ()

1728 _GeoidEGM = GeoidKarney

1729 _kind = 3

1730

1731 geoids = _sys.argv[1:]

1732 while geoids:

1733 geoid = geoids.pop(0)

1734

1735 if '-crop'.startswith(geoid.lower()):

1736 _crop = 20, -125, 50, -65 # CONUS

1737

1738 elif '-karney'.startswith(geoid.lower()):

1739 _GeoidEGM = GeoidKarney

1740

1741 elif '-kind'.startswith(geoid.lower()):

1742 _kind = int(geoids.pop(0))

1743

1744 elif '-pgm'.startswith(geoid.lower()):

1745 _GeoidEGM = GeoidPGM

1746

1747 elif geoid[-4:].lower() in ('.pgm',):

1748 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)

1749 printf(g.toStr(), nt=1, nl=1)

1750 printf(repr(g.pgm), nt=1)

1751 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:

1752 # The height of the EGM96 geoid at Timbuktu

1753 # echo 16:46:33N 3:00:34W | GeoidEval

1754 # => 28.7068 -0.02e-6 -1.73e-6

1755 # The 1st number is the height of the geoid, the 2nd and

1756 # 3rd are its slopes in northerly and easterly direction

1757 t = 'Timbuktu %s' % (g,)

1758 k = {'egm84-15.pgm': '31.2979',

1759 'egm96-5.pgm': '28.7067',

1760 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')

1761 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')

1762 for ll in (ll, (16.776, -3.009),):

1763 try:

1764 h, ll = g.height(*ll), fstr(ll, prec=6)

1765 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)

1766 except (GeoidError, RangeError) as x:

1767 printf(_COLONSPACE_(t, str(x)))

1768

1769 elif geoid[-4:].lower() in ('.bin',):

1770 g = GeoidG2012B(geoid, kind=_kind)

1771 printf(g.toStr())

1772

1773 else:

1774 raise GeoidError(grid=repr(geoid))

1775

1776_I = int # PYCHOK unused _I

1777 del _intCs # trash ints cache

1778

1779# **) MIT License

1780#

1781# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1782#

1783# Permission is hereby granted, free of charge, to any person obtaining a

1784# copy of this software and associated documentation files (the "Software"),

1785# to deal in the Software without restriction, including without limitation

1786# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1787# and/or sell copies of the Software, and to permit persons to whom the

1788# Software is furnished to do so, subject to the following conditions:

1789#

1790# The above copyright notice and this permission notice shall be included

1791# in all copies or substantial portions of the Software.

1792#

1793# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1794# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1795# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1796# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1797# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1798# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1799# OTHER DEALINGS IN THE SOFTWARE.

1800

1801# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>

1802# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm

1803# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm

1804# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm

1805

1806# _center = 0, 0, 17.2260 # egm2008-1.pgm

1807# _center = 0, 0, 17.1630 # egm96-5.pgm

1808# _center = 0, 0, 18.3296 # egm84-15.pgm

1809

1810# _upperright = 90, 180, 14.8980 # egm2008-1.pgm

1811# _upperright = 90, 180, 13.6050 # egm96-5.pgm

1812# _upperright = 90, 180, 13.0980 # egm84-15.pgm

1813

1814

1815# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm

1816#

1817# 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)

1818#

1819# _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'

1820#

1821# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1822# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1823#

1824# 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)

1825#

1826# _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'

1827#

1828# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1829# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1830#

1831# 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)

1832#

1833# _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'

1834#

1835# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1836# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1837

1838

1839# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm

1840#

1841# 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)

1842#

1843# _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'

1844#

1845# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1846# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1847#

1848# 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)

1849#

1850# _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'

1851#

1852# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1853# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1854#

1855# 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)

1856#

1857# _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'

1858#

1859# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1860# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1861

1862

1863# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm

1864#

1865# 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)

1866#

1867# _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'

1868#

1869# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1870# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1871#

1872# 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)

1873#

1874# _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'

1875#

1876# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979

1877# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979

1878#

1879# 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)

1880#

1881# _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'

1882#

1883# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067

1884# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067