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_, \

97 _cubic_, _E_, _height_, _in_, _kind_, _lat_, \

98 _linear_, _lon_, _mean_, _N_, _n_a_, _numpy_, \

99 _on_, _outside_, _S_, _s_, _scipy_, _SPACE_, \

100 _stdev_, _tbd_, _W_, _width_

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

102 from pygeodesy.named import _name__, _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__ = '24.05.23'

122

123_assert_ = 'assert'

124_bHASH_ = b'#'

125_endian_ = 'endian'

126_format_ = '%s %r'

127_header_ = 'header'

128_intCs = {} # cache int value

129_interp2d_ks = {-2: _linear_,

130 -3: _cubic_,

131 -5: 'quintic'}

132_lli_ = 'lli'

133_non_increasing_ = 'non-increasing'

134_rb_ = 'rb'

135_supported_ = 'supported'

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} (C{bool}) and

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

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

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

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

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, datum=None, # NAD 83 Ellipsoid

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

758 '''New L{GeoidG2012B} interpolator.

759

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

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

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

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

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

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

766 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

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

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

769 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

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

771 scipy.interpolate.RectBivariateSpline.html>}

772 only (C{int}).

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

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

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 not

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

795 if crop is not None:

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

797

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

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

800

801 try:

802 p = _Gpars()

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

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

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

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

807 # skip 4xf8, get 3xi4

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

809 if ien == 1: # correct endian

810 p.knots = p.nlat * p.nlon

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

812 and 1 < p.nlon < n:

813 self._endian = en_+'f4'

814 break

815 else: # couldn't validate endian

816 raise GeoidError(_endian_)

817

818 # get the first 4xf8

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

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

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

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

823 _GeoidBase.__init__(self, hs, p)

824

825 except Exception as x:

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

827 finally:

828 g.close()

829

830 def _g2ll2(self, lat, lon):

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

832 return lat, lon

833

834 def _ll2g2(self, lat, lon):

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

836 return lat, lon

837

838 if _FOR_DOCS:

839 __call__ = _GeoidBase.__call__

840 height = _GeoidBase.height

841

842

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

844 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat

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

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

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

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

849 '''

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

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

852

853

854 def _I(i):

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

856 '''

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

858

859

860 def _T(*cs):

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

862 '''

863 return map1(_I, *cs)

864

865_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)

866

867

868 class GeoidKarney(_GeoidBase):

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

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

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

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

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

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

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

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

877

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

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

880 datasets.

881 '''

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

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

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

885 _T0s12,

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

887 _T0s12,

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

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

890 _T0s12,

891 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),

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

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

894

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

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

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

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

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

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

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

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

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

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

905

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

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

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

909 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),

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

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

912 _T0s12,

913 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),

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

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

916

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

918 _T(1, 0),

919 _T(0, 1),

920 _T(1, 1))

921

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

923 _T( 1, -1),

924 _T(-1, 0),

925 _T( 0, 0),

926 _T( 1, 0),

927 _T( 2, 0),

928 _T(-1, 1),

929 _T( 0, 1),

930 _T( 1, 1),

931 _T( 2, 1),

932 _T( 0, 2),

933 _T( 1, 2))

934

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

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

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

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

939# (-8.167, 147.25, 85.422) if egm96-5.pgm else

940# (-4.5, 148.75, 81.33)) # egm84-15.pgm

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

942# (4.667, 78.833, -107.043) if egm96-5.pgm else

943# (4.75, 79.25, -107.34)) # egm84-15.pgm

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

945 _nBytes = None # not applicable

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

947 _smooth = None # not applicable

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

949 _u2B = _calcsize(_endian) # pixelsize_ in bytes

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

951 _Ru2B = 0 # row of pixelsize_s in bytes

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

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

954 _yx_hits = 0 # cache hits

955

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

957 kind=3, **name_smooth):

958 '''New L{GeoidKarney} interpolator.

959

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

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

962 note below.

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

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

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

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

967 C{LatLon} instances.

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

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

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

971 for C{cubic}.

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

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

974

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

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

977

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

979

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

981

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

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

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

985 '''

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

987 if smooth is not None:

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

989

990 if kind in (2,):

991 self._evH = self._ev2H

992 elif kind not in (3,):

993 raise GeoidError(kind=kind)

994

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

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

997

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

999 self._Ru2B = _calcsize(self._Rendian)

1000

1001 self._knots = p.knots # grid knots

1002 self._lon_of = float(p.flon) # forward offset

1003 self._lon_og = float(p.glon) # reverse offset

1004 # set earth (lat, lon) limits (s, w, n, e)

1005 self._lat_lo, self._lon_lo, \

1006 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)

1007 self._cropped = True if crop else False

1008

1009 def __call__(self, *llis, **wrap_H):

1010 '''Interpolate the geoid height for one or several locations.

1011

1012 @arg llis: One or more locations (C{LatLon}s), all positional.

1013 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.

1014 If C{B{wrap} is True}, wrap or I{normalize} all

1015 B{C{llis}} locations (C{bool}). If C{B{H} is True},

1016 return the I{orthometric} height instead of the

1017 I{geoid} height at each location (C{bool}).

1018

1019 @return: A single interpolated geoid (or orthometric) height

1020 (C{float}) or a list or tuple of interpolated geoid

1021 (or orthometric) heights (C{float}s).

1022

1023 @raise GeoidError: Insufficient number of B{C{llis}}, an

1024 invalid B{C{lli}} or the C{egm*.pgm}

1025 geoid file is closed.

1026

1027 @raise RangeError: An B{C{lli}} is outside this geoid's lat-

1028 or longitude range.

1029

1030 @note: To obtain I{orthometric} heights, each B{C{llis}}

1031 location must have an ellipsoid C{height} or C{h}

1032 attribute, otherwise C{height=0} is used.

1033

1034 @see: Function L{pygeodesy.heightOrthometric}.

1035 '''

1036 return self._called(llis, False, **wrap_H)

1037

1038 def _c0c3v(self, y, x):

1039 # get the common denominator, the 10x12 cubic matrix and

1040 # the 12 cubic v-coefficients around geoid index (y, x)

1041 p = self._pgm

1042 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):

1043 # read 4x4 ushorts, drop the 4 corners

1044 g = self._egm

1045 e = self._4endian

1046 n = self._4u2B

1047 R = self._Ru2B

1048

1049 b = self._seek(y - 1, x - 1)

1050 v = _unpack(e, g.read(n))[1:3]

1051 b += R

1052 g.seek(b, _SEEK_SET)

1053 v += _unpack(e, g.read(n))

1054 b += R

1055 g.seek(b, _SEEK_SET)

1056 v += _unpack(e, g.read(n))

1057 b += R

1058 g.seek(b, _SEEK_SET)

1059 v += _unpack(e, g.read(n))[1:3]

1060 j = 1

1061

1062 else: # likely some wrapped y and/or x's

1063 v = self._raws(y, x, GeoidKarney._CM)

1064 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)

1065

1066 return GeoidKarney._C0[j], GeoidKarney._C3[j], v

1067

1068 @Property_RO

1069 def dtype(self):

1070 '''Get the geoid's grid data type (C{str}).

1071 '''

1072 return 'ushort'

1073

1074 def _ev(self, lat, lon): # PYCHOK expected

1075 # interpolate the geoid height at grid (lat, lon)

1076 fy, fx = self._g2yx2(lat, lon)

1077 y, x = int(floor(fy)), int(floor(fx))

1078 fy -= y

1079 fx -= x

1080 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H

1081 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)

1082 H += self._pgm.Offset # H.fadd(self._pgm.Offset)

1083 return H.fsum()

1084

1085 def _ev2H(self, fy, fx, *yx):

1086 # compute the bilinear 4-tuple and interpolate raw H

1087 if self._yxH == yx:

1088 t = self._yxHt

1089 self._yx_hits += 1

1090 else:

1091 y, x = self._yxH = yx

1092 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)

1093 v = _1_0, -fx, fx

1094 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)

1095 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy

1096 return H

1097

1098 def _ev3H(self, fy, fx, *yx):

1099 # compute the cubic 10-tuple and interpolate raw H

1100 if self._yxH == yx:

1101 t = self._yxHt

1102 self._yx_hits += 1

1103 else:

1104 self._yxH = yx

1105 c0, c3, v = self._c0c3v(*yx)

1106 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]

1107 self._yxHt = t = tuple(t)

1108 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...

1109 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +

1110 # fy * (t[2] + fx * (t[4] + fx * t[7]) +

1111 # fy * (t[5] + fx * t[8] + fy * t[9]));

1112 v = _1_0, fx, fy

1113 H = Fdot(v, t[5], t[8], t[9])

1114 H *= fy

1115 H += Fhorner(fx, t[2], t[4], t[7])

1116 H *= fy

1117 H += Fhorner(fx, t[0], t[1], t[3], t[6])

1118 return H

1119

1120 _evH = _ev3H # overriden for kind == 2

1121

1122 def _g2ll2(self, lat, lon):

1123 # convert grid (lat, lon) to earth (lat, lon), uncropped

1124 while lon > _180_0:

1125 lon -= _360_0

1126 return lat, lon

1127

1128 def _g2yx2(self, lat, lon):

1129 # convert grid (lat, lon) to grid (y, x) indices

1130 p = self._pgm

1131 # note, slat = +90, rlat < 0 makes y >=0

1132 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)

1133

1134 def _gyx2g2(self, y, x):

1135 # convert grid (y, x) indices to grid (lat, lon)

1136 p = self._pgm

1137 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)

1138

1139 def height(self, lats, lons, **wrap):

1140 '''Interpolate the geoid height for one or several lat-/longitudes.

1141

1142 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).

1143 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).

1144 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}

1145 and B{C{lons}} locations (C{bool}).

1146

1147 @return: A single interpolated geoid height (C{float}) or a

1148 list of interpolated geoid heights (C{float}s).

1149

1150 @raise GeoidError: Insufficient or non-matching number of

1151 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}

1152 geoid file is closed.

1153

1154 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this

1155 geoid's lat- or longitude range.

1156 '''

1157 return _height_called(self, lats, lons, Error=GeoidError, **wrap)

1158

1159 @Property_RO

1160 def _highest_ltd(self):

1161 '''(INTERNAL) Cache for L{highest} mesthod.

1162 '''

1163 return self._llh3minmax(True, -12, -4)

1164

1165 def highest(self, LatLon=None, full=False): # PYCHOK full

1166 '''Return the location and largest height of this geoid.

1167

1168 @kwarg LatLon: Optional class to return the location and height

1169 (C{LatLon}) or C{None}.

1170 @kwarg full: Search the full or limited latitude range (C{bool}).

1171

1172 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1173 lon, height)} otherwise a B{C{LatLon}} instance

1174 with the lat-, longitude and geoid height at the

1175 highest grid location.

1176 '''

1177 llh = self._highest if full or self.cropped else self._highest_ltd

1178 return self._llh3LL(llh, LatLon)

1179

1180 def _lat2y2(self, lat2):

1181 # convert earth lat(s) to min and max grid y indices

1182 ys, m = [], self._pgm.nlat - 1

1183 for lat in lat2:

1184 y, _ = self._g2yx2(*self._ll2g2(lat, 0))

1185 ys.append(max(min(int(y), m), 0))

1186 return min(ys), max(ys) + 1

1187

1188 def _ll2g2(self, lat, lon):

1189 # convert earth (lat, lon) to grid (lat, lon), uncropped

1190 while lon < 0:

1191 lon += _360_0

1192 return lat, lon

1193

1194 def _llh3minmax(self, highest=True, *lat2):

1195 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid

1196 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)

1197 y = x = 0

1198 h = self._raw(y, x)

1199 if highest:

1200 for j, r in self._raw2(*lat2):

1201 m = max(r)

1202 if m > h:

1203 h, y, x = m, j, r.index(m)

1204 else: # lowest

1205 for j, r in self._raw2(*lat2):

1206 m = min(r)

1207 if m < h:

1208 h, y, x = m, j, r.index(m)

1209 h *= self._pgm.Scale

1210 h += self._pgm.Offset

1211 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)

1212

1213 @Property_RO

1214 def _lowest_ltd(self):

1215 '''(INTERNAL) Cache for L{lowest}.

1216 '''

1217 return self._llh3minmax(False, 0, 8)

1218

1219 def lowest(self, LatLon=None, full=False): # PYCHOK full

1220 '''Return the location and lowest height of this geoid.

1221

1222 @kwarg LatLon: Optional class to return the location and height

1223 (C{LatLon}) or C{None}.

1224 @kwarg full: Search the full or limited latitude range (C{bool}).

1225

1226 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1227 lon, height)} otherwise a B{C{LatLon}} instance

1228 with the lat-, longitude and geoid height of the

1229 lowest grid location.

1230 '''

1231 llh = self._lowest if full or self.cropped else self._lowest_ltd

1232 return self._llh3LL(llh, LatLon)

1233

1234 def _raw(self, y, x):

1235 # get the ushort geoid height at geoid index (y, x),

1236 # like GeographicLib/Geoid.hpp real rawval(is, iy)

1237 p = self._pgm

1238 if x < 0:

1239 x += p.nlon

1240 elif x >= p.nlon:

1241 x -= p.nlon

1242 h = p.nlon // 2

1243 if y < 0:

1244 y = -y

1245 elif y >= p.nlat:

1246 y = (p.nlat - 1) * 2 - y

1247 else:

1248 h = 0

1249 x += h if x < h else -h

1250 self._seek(y, x)

1251 h = _unpack(self._endian, self._egm.read(self._u2B))

1252 return h[0]

1253

1254 def _raws(self, y, x, ijs):

1255 # get bilinear 4-tuple or 10x12 cubic matrix

1256 return tuple(self._raw(y + j, x + i) for i, j in ijs)

1257

1258 def _raw2(self, *lat2):

1259 # yield a 2-tuple (y, ushorts) for each row or for

1260 # the rows between two (or more) earth lat values

1261 p = self._pgm

1262 g = self._egm

1263 e = self._Rendian

1264 n = self._Ru2B

1265 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat

1266 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)

1267 self._seek(s, 0) # to start of row s

1268 for y in range(s, t):

1269 yield y, _unpack(e, g.read(n))

1270

1271 def _seek(self, y, x):

1272 # position geoid to grid index (y, x)

1273 p, g = self._pgm, self._egm

1274 if g:

1275 b = p.skip + (y * p.nlon + x) * self._u2B

1276 g.seek(b, _SEEK_SET)

1277 return b # position

1278 raise GeoidError('closed file', txt=repr(p.egm)) # IOError

1279

1280

1281 class GeoidPGM(_GeoidBase):

1282 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth

1283 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/

1284 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1285 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}

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

1287 generated/scipy.interpolate.RectBivariateSpline.html>} or

1288 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1289 scipy.interpolate.interp2d.html>} interpolation.

1290

1291 Use any of the U{egm84-, egm96- or egm2008-*.pgm

1292 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}

1293 datasets. However, unless cropped, an entire C{egm*.pgm} dataset

1294 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/

1295 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}

1296 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1297 scipy.interpolate.interp2d.html>} interpolator and converted from

1298 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory

1299 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/

1300 geoid.html#geoidinst>} file size and may exceed the available memory,

1301 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.

1302 '''

1303 _cropped = False

1304 _endian = '>u2'

1305

1306 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84

1307 kind=3, smooth=0, **name):

1308 '''New L{GeoidPGM} interpolator.

1309

1310 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/

1311 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).

1312 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,

1313 north, east}) or 2-tuple (C{(south, west), (north, east)}),

1314 in C{degrees90} lat- and C{degrees180} longitudes or a

1315 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.

1316 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

1317 or L{a_f2Tuple}), default C{WGS84}.

1318 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for

1319 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/

1320 reference/generated/scipy.interpolate.RectBivariateSpline.html>},

1321 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

1322 reference/generated/scipy.interpolate.interp2d.html>}, -3

1323 for C{interp2d cubic} or -5 for C{interp2d quintic}.

1324 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

1325 <https://docs.SciPy.org/doc/scipy/reference/generated/

1326 scipy.interpolate.RectBivariateSpline.html>}

1327 only (C{int}).

1328 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).

1329

1330 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},

1331 B{C{kind}} or B{C{smooth}}.

1332

1333 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

1334

1335 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.

1336

1337 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.

1338

1339 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}

1340 warning as exception.

1341

1342 @raise TypeError: Invalid B{C{datum}} or unexpected argument.

1343

1344 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify

1345 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.

1346

1347 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/

1348 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte

1349 C{int} height converted to 8-byte C{dtype float64} for C{scipy}

1350 interpolators. Therefore, internal memory usage is 4 times the

1351 C{egm*.pgm} file size and may exceed the available memory,

1352 especially with 32-bit Python. To reduce memory usage, set

1353 keyword argument B{C{crop}} to the region of interest. For example

1354 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://

1355 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}

1356 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.

1357

1358 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.

1359 '''

1360 np = self.numpy

1361 self._u2B = np.dtype(self.endian).itemsize

1362

1363 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)

1364 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)

1365 if crop:

1366 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))

1367 if _MODS.internals._version2(np.__version__) < (1, 9):

1368 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-

1369 self._cropped = True

1370 try:

1371 # U{numpy dtype formats are different from Python struct formats

1372 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}

1373 # read all heights, skipping the PGM header lines, converted to float

1374 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale

1375 if p.Offset: # offset

1376 hs = p.Offset + hs

1377 if p.dlat < 0: # flip the rows

1378 hs = np.flipud(hs)

1379 _GeoidBase.__init__(self, hs, p)

1380 except Exception as x:

1381 raise _SciPyIssue(x, _in_, repr(egm_pgm))

1382 finally:

1383 g.close()

1384

1385 def _g2ll2(self, lat, lon):

1386 # convert grid (lat, lon) to earth (lat, lon), un-/cropped

1387 if self._cropped:

1388 lon -= self._lon_of

1389 else:

1390 while lon > _180_0:

1391 lon -= _360_0

1392 return lat, lon

1393

1394 def _ll2g2(self, lat, lon):

1395 # convert earth (lat, lon) to grid (lat, lon), un-/cropped

1396 if self._cropped:

1397 lon += self._lon_of

1398 else:

1399 while lon < 0:

1400 lon += _360_0

1401 return lat, lon

1402

1403 if _FOR_DOCS:

1404 __call__ = _GeoidBase.__call__

1405 height = _GeoidBase.height

1406

1407

1408 class _Gpars(_Named):

1409 '''(INTERNAL) Basic geoid parameters.

1410 '''

1411 # interpolator parameters

1412 dlat = 0 # +/- latitude resolution in C{degrees}

1413 dlon = 0 # longitude resolution in C{degrees}

1414 nlat = 1 # number of latitude knots (C{int})

1415 nlon = 0 # number of longitude knots (C{int})

1416 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat

1417 rlon = 0 # longitude resolution in C{float}, 1 / .dlon

1418 slat = 0 # nothern- or southern most latitude (C{degrees90})

1419 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})

1420

1421 flon = 0 # forward, earth to grid longitude offset

1422 glon = 0 # reverse, grid to earth longitude offset

1423

1424 knots = 0 # number of knots, nlat * nlon (C{int})

1425 skip = 0 # header bytes to skip (C{int})

1426

1427 def __repr__(self):

1428 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for

1429 a in dir(self.__class__)

1430 if a[:1].isupper()))

1431 return _COLONSPACE_(self, t)

1432

1433 def __str__(self):

1434 return Fmt.PAREN(self.classname, repr(self.name))

1435

1436

1437 class _PGM(_Gpars):

1438 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.

1439

1440 # Geoid file in PGM format for the GeographicLib::Geoid class

1441 # Description WGS84 EGM96, 5-minute grid

1442 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html

1443 # DateTime 2009-08-29 18:45:03

1444 # MaxBilinearError 0.140

1445 # RMSBilinearError 0.005

1446 # MaxCubicError 0.003

1447 # RMSCubicError 0.001

1448 # Offset -108

1449 # Scale 0.003

1450 # Origin 90N 0E

1451 # AREA_OR_POINT Point

1452 # Vertical_Datum WGS84

1453 <width> <height>

1454 <pixel>

1455 ...

1456 '''

1457 crop4 = () # 4-tuple (C{south, west, north, east}).

1458 egm = None

1459 glon = 180 # reverse offset, uncropped

1460# pgm = NN # name

1461 sizeB = 0

1462 u2B = 2 # item size of grid height (C{int}).

1463

1464 @staticmethod

1465 def _llstr2floats(latlon):

1466 # llstr to (lat, lon) floats

1467 lat, lon = latlon.split()

1468 return _MODS.dms.parseDMS2(lat, lon)

1469

1470 # PGM file attributes, CamelCase but not .istitle()

1471 AREA_OR_POINT = str

1472 DateTime = str

1473 Description = str # 'WGS84 EGM96, 5-minute grid'

1474 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'

1475 MaxBilinearError = float

1476 MaxCubicError = float

1477 Offset = float

1478 Origin = _llstr2floats

1479 Pixel = 0

1480 RMSBilinearError = float

1481 RMSCubicError = float

1482 Scale = float

1483 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'

1484 Vertical_Datum = str

1485

1486 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22

1487 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.

1488 '''

1489 self.name = pgm # geoid file name

1490 if itemsize:

1491 self._u2B = itemsize

1492 if sizeB:

1493 self.sizeB = sizeB

1494

1495 t = g.readline() # make sure newline == '\n'

1496 if t != b'P5\n' and t.strip() != b'P5':

1497 raise self._Errorf(_format_, _header_, t)

1498

1499 while True: # read all # Attr ... lines,

1500 try: # ignore empty ones or comments

1501 t = g.readline().strip()

1502 if t.startswith(_bHASH_):

1503 t = t.lstrip(_bHASH_).lstrip()

1504 a, v = map(_ub2str, t.split(None, 1))

1505 f = getattr(_PGM, a, None)

1506 if callable(f) and a[:1].isupper():

1507 setattr(self, a, f(v))

1508 elif t:

1509 break

1510 except (TypeError, ValueError):

1511 raise self._Errorf(_format_, 'Attr', t)

1512 else: # should never get here

1513 raise self._Errorf(_format_, _header_, g.tell())

1514

1515 try: # must be (even) width and (odd) height

1516 nlon, nlat = map(int, t.split())

1517 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \

1518 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):

1519 raise ValueError

1520 except (TypeError, ValueError):

1521 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)

1522

1523 try: # must be 16 bit pixel height

1524 t = g.readline().strip()

1525 self.Pixel = int(t)

1526 if not 255 < self.Pixel < 65536: # >u2 or >H only

1527 raise ValueError

1528 except (TypeError, ValueError):

1529 raise self._Errorf(_format_, 'pixel', t)

1530

1531 for a in dir(_PGM): # set undefined # Attr ... to None

1532 if a[:1].isupper() and callable(getattr(self, a)):

1533 setattr(self, a, None)

1534

1535 if self.Origin is None:

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

1537 if self.Offset is None or self.Offset > 0:

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

1539 if self.Scale is None or self.Scale < EPS:

1540 raise self._Errorf(_format_, 'Scale', self.Scale)

1541

1542 self.skip = g.tell()

1543 self.knots = nlat * nlon

1544

1545 self.nlat, self.nlon = nlat, nlon

1546 self.slat, self.wlon = self.Origin

1547 # note, negative .dlat and .rlat since rows

1548 # are from .slat 90N down in decreasing lat

1549 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon

1550 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0

1551

1552 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0

1553 n = float(self.slat)

1554 s = n + self.dlat * (nlat - 1)

1555 w = self.wlon - self.glon

1556 e = w + self.dlon * nlon

1557 self.crop4 = s, w, n, e

1558

1559 n = self.sizeB - self.skip

1560 if n > 0 and n != (self.knots * self.u2B):

1561 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)

1562

1563 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15

1564 '''Crop the geoid to (south, west, north, east) box.

1565 '''

1566 # flon offset for both west and east

1567 f = 360 if west < 0 else 0

1568 # earth (lat, lon) to grid indices (y, x),

1569 # note y is decreasing, i.e. n < s

1570 s, w = self._lle2yx2(south, west, f)

1571 n, e = self._lle2yx2(north, east, f)

1572 s += 1 # s > n

1573 e += 1 # e > w

1574

1575 hi, wi = self.nlat, self.nlon

1576 # handle special cases

1577 if (s - n) > hi:

1578 n, s = 0, hi # entire lat range

1579 if (e - w) > wi:

1580 w, e, f = 0, wi, 180 # entire lon range

1581 if s == hi and w == n == 0 and e == wi:

1582 return g # use entire geoid as-is

1583

1584 if (e - w) < k1 or (s - n) < (k1 + 1):

1585 raise self._Errorf(_format_, 'swne', (north - south, east - west))

1586

1587 if e > wi > w: # wrap around

1588 # read w..wi and 0..e

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

1590 elif e > w:

1591 r, p = (e - w), 0

1592 else:

1593 raise self._Errorf('%s(%s < %s)', _assert_, w, e)

1594

1595 # convert to bytes

1596 r *= self.u2B

1597 p *= self.u2B

1598 q = wi * self.u2B # stride

1599 # number of rows and cols to skip from

1600 # the original (.slat, .wlon) origin

1601 z = self.skip + (n * wi + w) * self.u2B

1602 # sanity check

1603 if r < 2 or p < 0 or q < 2 or z < self.skip \

1604 or z > self.sizeB:

1605 raise self._Errorf(_format_, _assert_, (r, p, q, z))

1606

1607 # can't use _BytesIO since numpy

1608 # needs .fileno attr in .fromfile

1609 t, c = 0, self._tmpfile()

1610 # reading (s - n) rows, forward

1611 for y in range(n, s): # PYCHOK y unused

1612 g.seek(z, _SEEK_SET)

1613 # Python 2 tmpfile.write returns None

1614 t += c.write(g.read(r)) or r

1615 if p: # wrap around to start of row

1616 g.seek(-q, _SEEK_CUR)

1617 # assert(g.tell() == (z - w * self.u2B))

1618 # Python 2 tmpfile.write returns None

1619 t += c.write(g.read(p)) or p

1620 z += q

1621 c.flush()

1622 g.close()

1623

1624 s -= n # nlat

1625 e -= w # nlon

1626 k = s * e # knots

1627 z = k * self.u2B

1628 if t != z:

1629 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)

1630

1631 # update the _Gpars accordingly, note attributes

1632 # .dlat, .dlon, .rlat and .rlon remain unchanged

1633 self.slat += n * self.dlat

1634 self.wlon += w * self.dlon

1635 self.nlat = s

1636 self.nlon = e

1637 self.flon = self.glon = f

1638

1639 self.crop4 = south, west, north, east

1640 self.knots = k

1641 self.skip = 0 # no header lines in c

1642

1643 c.seek(0, _SEEK_SET)

1644 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-

1645 return c

1646

1647 def _Errorf(self, fmt, *args): # PYCHOK no cover

1648 t = fmt % args

1649 e = self.pgm or NN

1650 if e:

1651 t = _SPACE_(t, _in_, repr(e))

1652 return PGMError(t)

1653

1654 def _lle2yx2(self, lat, lon, flon):

1655 # earth (lat, lon) to grid indices (y, x)

1656 # with .dlat decreasing from 90N .slat

1657 lat -= self.slat

1658 lon += flon - self.wlon

1659 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),

1660 max(0, int(lon * self.rlon)))

1661

1662 def _tmpfile(self):

1663 # create a tmpfile to hold the cropped geoid grid

1664 try:

1665 from tempfile import NamedTemporaryFile as tmpfile

1666 except ImportError: # Python 2.7.16-

1667 from os import tmpfile

1668 t = _os_path.splitext(_os_path.basename(self.pgm))[0]

1669 f = tmpfile(mode='w+b', prefix=t or 'egm')

1670 f.seek(0, _SEEK_SET) # force overwrite

1671 return f

1672

1673 @Property_RO

1674 def pgm(self):

1675 '''Get the geoid file name (C{str}).

1676 '''

1677 return self.name

1678

1679

1680 class PGMError(GeoidError):

1681 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.

1682 '''

1683 pass

1684

1685

1686 def egmGeoidHeights(GeoidHeights_dat):

1687 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1688 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat

1689 <https://SourceForge.net/projects/geographiclib/files/testdata/>}

1690 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/

1691 geoid.html#testgeoid>}.

1692

1693 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file

1694 (C{str} or C{file} handle).

1695

1696 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,

1697 egm84, egm96, egm2008)}.

1698

1699 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.

1700

1701 @note: Function L{egmGeoidHeights} is used to test the geoids

1702 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module

1703 C{test/testGeoids.py}.

1704 '''

1705 dat = GeoidHeights_dat

1706 if isinstance(dat, bytes):

1707 dat = _BytesIO(dat)

1708

1709 try:

1710 dat.seek(0, _SEEK_SET) # reset

1711 except AttributeError as x:

1712 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)

1713

1714 for t in dat.readlines():

1715 t = t.strip()

1716 if t and not t.startswith(_bHASH_):

1717 lat, lon, egm84, egm96, egm2008 = map(float, t.split())

1718 while lon > _180_0: # EasternLon to earth lon

1719 lon -= _360_0

1720 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)

1721

1722

1723__all__ += _ALL_DOCS(_GeoidBase)

1724

1725 if __name__ == '__main__':

1726

1727 from pygeodesy.internals import printf, _sys

1728

1729 _crop = ()

1730 _GeoidEGM = GeoidKarney

1731 _kind = 3

1732

1733 geoids = _sys.argv[1:]

1734 while geoids:

1735 geoid = geoids.pop(0)

1736

1737 if '-crop'.startswith(geoid.lower()):

1738 _crop = 20, -125, 50, -65 # CONUS

1739

1740 elif '-karney'.startswith(geoid.lower()):

1741 _GeoidEGM = GeoidKarney

1742

1743 elif '-kind'.startswith(geoid.lower()):

1744 _kind = int(geoids.pop(0))

1745

1746 elif '-pgm'.startswith(geoid.lower()):

1747 _GeoidEGM = GeoidPGM

1748

1749 elif geoid[-4:].lower() in ('.pgm',):

1750 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)

1751 printf(g.toStr(), nt=1, nl=1)

1752 printf(repr(g.pgm), nt=1)

1753 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:

1754 # The height of the EGM96 geoid at Timbuktu

1755 # echo 16:46:33N 3:00:34W | GeoidEval

1756 # => 28.7068 -0.02e-6 -1.73e-6

1757 # The 1st number is the height of the geoid, the 2nd and

1758 # 3rd are its slopes in northerly and easterly direction

1759 t = 'Timbuktu %s' % (g,)

1760 k = {'egm84-15.pgm': '31.2979',

1761 'egm96-5.pgm': '28.7067',

1762 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')

1763 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')

1764 for ll in (ll, (16.776, -3.009),):

1765 try:

1766 h, ll = g.height(*ll), fstr(ll, prec=6)

1767 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)

1768 except (GeoidError, RangeError) as x:

1769 printf(_COLONSPACE_(t, str(x)))

1770

1771 elif geoid[-4:].lower() in ('.bin',):

1772 g = GeoidG2012B(geoid, kind=_kind)

1773 printf(g.toStr())

1774

1775 else:

1776 raise GeoidError(grid=repr(geoid))

1777

1778_I = int # PYCHOK unused _I

1779 del _intCs # trash ints cache

1780

1781# **) MIT License

1782#

1783# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1784#

1785# Permission is hereby granted, free of charge, to any person obtaining a

1786# copy of this software and associated documentation files (the "Software"),

1787# to deal in the Software without restriction, including without limitation

1788# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1789# and/or sell copies of the Software, and to permit persons to whom the

1790# Software is furnished to do so, subject to the following conditions:

1791#

1792# The above copyright notice and this permission notice shall be included

1793# in all copies or substantial portions of the Software.

1794#

1795# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1796# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1797# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1798# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1799# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1800# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1801# OTHER DEALINGS IN THE SOFTWARE.

1802

1803# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>

1804# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm

1805# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm

1806# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm

1807

1808# _center = 0, 0, 17.2260 # egm2008-1.pgm

1809# _center = 0, 0, 17.1630 # egm96-5.pgm

1810# _center = 0, 0, 18.3296 # egm84-15.pgm

1811

1812# _upperright = 90, 180, 14.8980 # egm2008-1.pgm

1813# _upperright = 90, 180, 13.6050 # egm96-5.pgm

1814# _upperright = 90, 180, 13.0980 # egm84-15.pgm

1815

1816

1817# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm

1818#

1819# 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)

1820#

1821# _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'

1822#

1823# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1824# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1825#

1826# 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)

1827#

1828# _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'

1829#

1830# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1831# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1832#

1833# 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)

1834#

1835# _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'

1836#

1837# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1838# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1839

1840

1841# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm

1842#

1843# 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)

1844#

1845# _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'

1846#

1847# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1848# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1849#

1850# 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)

1851#

1852# _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'

1853#

1854# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1855# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1856#

1857# 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)

1858#

1859# _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'

1860#

1861# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1862# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1863

1864

1865# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm

1866#

1867# 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)

1868#

1869# _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'

1870#

1871# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1872# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1873#

1874# 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)

1875#

1876# _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'

1877#

1878# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979

1879# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979

1880#

1881# 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)

1882#

1883# _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'

1884#

1885# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067

1886# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067