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

41

42 or

43

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

45

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

47

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

49

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

51

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

53

54 or as 2 lists, 2 tuples, etc.

55

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

57

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

59 courtesy of SBFRF.

60

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

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

63 to be installed.

64

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

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

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

68

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

70 U{Geoid height<https://GeographicLib.SourceForge.io/html/geoid.html>} and U{Installing

71 the Geoid datasets<https://GeographicLib.SourceForge.io/html/geoid.html#geoidinst>},

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

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

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

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

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

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

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

79 Avoiding_Pitfalls_Related_to_Ellipsoid_Height_and_Height_Above_Mean_Sea_Level>}.

80'''

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

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

83

84 from pygeodesy.basics import len2, map1, map2, isodd, ub2str as _ub2str

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

86 from pygeodesy.datums import _ellipsoidal_datum, _WGS84

87 from pygeodesy.dms import parseDMS2

88 from pygeodesy.errors import _incompatible, LenError, RangeError, _SciPyIssue

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

90 from pygeodesy.heights import _allis2, _ascalar, _HeightBase, HeightError

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

92 _DOT_, _E_, _height_, _in_, _kind_, _knots_, \

93 _lat_, _linear_, _lon_, _mean_, _N_, _n_a_, _not_, \

94 _numpy_, _on_, _outside_, _S_, _s_, _scipy_, \

95 _SPACE_, _stdev_, _supported_, _tbd_, _W_, _width_

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

97 from pygeodesy.named import _Named, _NamedTuple, notOverloaded

98# from pygeodesy.namedTuples import LatLon3Tuple # _MODS

99 from pygeodesy.props import Property_RO, property_RO

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

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

102

103 from math import floor

104 import os.path as _os_path

105 from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET

106 from struct import calcsize as _calcsize, unpack as _unpack

107

108 try:

109 from StringIO import StringIO as _BytesIO # reads bytes

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

111

112 except ImportError: # Python 3+

113 from io import BytesIO as _BytesIO # PYCHOK expected

114

115__all__ = _ALL_LAZY.geoids

116__version__ = '22.10.23'

117

118_assert_ = 'assert'

119_bHASH_ = b'#'

120_endian_ = 'endian'

121_format_ = '%s %r'

122_header_ = 'header'

123# temporarily hold a single instance for each int value

124_intCs = {}

125_interp2d_ks = {-2: _linear_,

126 -3: _cubic_,

127 -5: 'quintic'}

128_lli_ = 'lli'

129_non_increasing_ = 'non-increasing'

130_rb_ = 'rb'

131

132

133 class _GeoidBase(_HeightBase):

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

135 '''

136 _cropped = None

137 _datum = _WGS84

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

139 _endian = _tbd_

140 _geoid = _n_a_

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

142 _interp2d = None # interp2d interpolation

143 _kind = 3 # order for interp2d, RectBivariateSpline

144 _knots = 0 # nlat * nlon

145 _mean = None # fixed in GeoidKarney

146# _name = NN # _Named

147 _nBytes = 0 # numpy size in bytes, float64

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

149 _sizeB = 0 # geoid file size in bytes

150 _smooth = 0 # used only for RectBivariateSpline

151 _stdev = None # fixed in GeoidKarney

152 _u2B = 0 # np.itemsize or undefined

153

154 _lat_d = _0_0 # increment, +tive

155 _lat_lo = _0_0 # lower lat, south

156 _lat_hi = _0_0 # upper lat, noth

157 _lon_d = _0_0 # increment, +tive

158 _lon_lo = _0_0 # left lon, west

159 _lon_hi = _0_0 # right lon, east

160 _lon_of = _0_0 # forward lon offset

161 _lon_og = _0_0 # reverse lon offset

162

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

164 _yx_hits = None # cache hits, ala Karney

165

166 def __init__(self, hs, p):

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

168 and several internal geoid attributes.

169

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

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

172 other geoid parameters (C{INTERNAL}).

173

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

175 invalid B{C{kind}}.

176

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

178

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

180 C{-.RectBivariateSpline} issue.

181

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

183 C{-.RectBivariateSpline} warning as

184 exception.

185 '''

186 spi = self.scipy_interpolate

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

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

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

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

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

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

193

194 # both axes and bounding box

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

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

197

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

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

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

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

202 k = self.kind

203 if k in _interp2d_ks:

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

205 elif 1 <= k <= 5:

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

207 s=self._smooth).ev

208 else:

209 raise GeoidError(kind=k)

210

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

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

213 self._knots = p.knots # grid knots

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

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

216 # shrink the box by 1 unit on every side

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

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

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

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

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

222

223 def __call__(self, *llis):

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

225

226 @arg llis: The location or locations (C{LatLon}, ... or

227 C{LatLon}s).

228

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

230 a list or tuple of interpolated geoid heights

231 (C{float}s).

232

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

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

235 geoid file is closed.

236

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

238 or longitude range.

239

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

241 C{-.RectBivariateSpline} issue.

242

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

244 C{-.RectBivariateSpline} warning as

245 exception.

246 '''

247 return self._called(llis, True)

248

249 def __enter__(self):

250 '''Open context.

251 '''

252 return self

253

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

255 '''Close context.

256 '''

257 self.close()

258 # return None # XXX False

259

260 def __repr__(self):

261 return self.toStr()

262

263 def __str__(self):

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

265

266 def _called(self, llis, scipy):

267 # handle __call__

268 _as, llis = _allis2(llis, Error=GeoidError)

269 try:

270 hs = []

271 for i, lli in enumerate(llis):

272 hs.append(self._hGeoid(lli.lat, lli.lon))

273 return _as(hs)

274

275 except (GeoidError, RangeError) as x:

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

277 t = _lli_ if _as is _ascalar else Fmt.SQUARE(llis=i)

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

279 raise type(x)(t, lli, cause=x)

280 except Exception as x:

281 if scipy and self.scipy:

282 raise _SciPyIssue(x)

283 else:

284 raise

285

286 @Property_RO

287 def _center(self):

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

289 '''

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

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

292

293 def center(self, LatLon=None):

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

295

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

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

298

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

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

301 with the lat-, longitude and height of the grid

302 center location.

303 '''

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

305

306 def close(self):

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

308 '''

309 if not self.closed:

310 self._egm.close()

311 self._egm = None

312

313 @property_RO

314 def closed(self):

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

316 '''

317 return self._egm is None

318

319 @Property_RO

320 def cropped(self):

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

322 '''

323 return self._cropped

324

325 @Property_RO

326 def dtype(self):

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

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

329 '''

330 return self._hs_y_x.dtype

331

332 @Property_RO

333 def endian(self):

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

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

336 '''

337 return self._endian

338

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

340 # only used for .interpolate.interp2d, but

341 # overwritten for .RectBivariateSpline,

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

343 return self._interp2d(x, y)

344

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

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

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

348 if m != n:

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

350 if d < 0:

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

352 for i in range(1, m):

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

354 if e < EPS: # non-increasing axis

355 i = Fmt.SQUARE(name, i)

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

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

358

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

360 notOverloaded(self, lat, lon)

361

362 def _gyx2g2(self, y, x):

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

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

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

366

367 def height(self, lats, lons):

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

369

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

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

372

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

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

375

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

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

378

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

380 geoid's lat- or longitude range.

381

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

383 C{-.RectBivariateSpline} issue.

384

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

386 C{-.RectBivariateSpline} warning as

387 exception.

388 '''

389 return _HeightBase._height(self, lats, lons, Error=GeoidError)

390

391 def _hGeoid(self, lat, lon):

392 out = self.outside(lat, lon)

393 if out:

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

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

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

397

398 @Property_RO

399 def _highest(self):

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

401 '''

402 return self._llh3minmax(True)

403

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

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

406

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

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

409

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

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

412 with the lat-, longitude and height of the highest

413 grid location.

414 '''

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

416

417 @Property_RO

418 def hits(self):

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

420 '''

421 return self._yx_hits

422

423 @Property_RO

424 def kind(self):

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

426 '''

427 return self._kind

428

429 @Property_RO

430 def knots(self):

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

432 '''

433 return self._knots

434

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

436 notOverloaded(self, lat, lon)

437

438 @property_RO

439 def _LL3T(self):

440 '''(INTERNAL) Get L{LatLon3Tuple} once.

441 '''

442 T = _MODS.namedTuples.LatLon3Tuple

443 _GeoidBase._LL3T = T # overwrite poperty_RO

444 return T

445

446 def _llh3(self, lat, lon):

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

448

449 def _llh3LL(self, llh, LatLon):

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

451

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

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

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

455 # numpy.argmin.html#numpy.argmin>

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

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

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

459

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

461 # numpy.fromfile, like .frombuffer

462 g.seek(offset, _SEEK_SET)

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

464

465 @Property_RO

466 def _lowerleft(self):

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

468 '''

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

470

471 def lowerleft(self, LatLon=None):

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

473

474 @kwarg LatLon: Optional class to return the location

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

476

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

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

479 with the lat-, longitude and height of the lower-left,

480 SW grid corner.

481 '''

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

483

484 @Property_RO

485 def _loweright(self):

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

487 '''

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

489

490 def loweright(self, LatLon=None):

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

492

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

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

495

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

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

498 with the lat-, longitude and height of the lower-right,

499 SE grid corner.

500 '''

501

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

503

504 lowerright = loweright # synonymous

505

506 @Property_RO

507 def _lowest(self):

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

509 '''

510 return self._llh3minmax(False)

511

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

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

514

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

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

517

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

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

520 with the lat-, longitude and height of the lowest

521 grid location.

522 '''

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

524

525 @Property_RO

526 def mean(self):

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

528 '''

529 if self._mean is None: # see GeoidKarney

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

531 return self._mean

532

533 @property_RO

534 def name(self):

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

536 '''

537 return _HeightBase.name.fget(self) or self._geoid # recursion

538

539 @Property_RO

540 def nBytes(self):

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

542 '''

543 return self._nBytes

544

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

546 # open the geoid file

547 try:

548 self._geoid = _os_path.basename(geoid)

549 self._sizeB = _os_path.getsize(geoid)

550 g = open(geoid, _rb_)

551 except (IOError, OSError) as x:

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

553

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

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

556 self._kind = int(kind)

557 if name:

558 _HeightBase.name.fset(self, name) # rename

559 if smooth:

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

561

562 return g

563

564 def outside(self, lat, lon):

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

566 lat-/longitude or crop range.

567

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

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

570

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

572 empty C{str} if inside.

573 '''

574 return (_S_ if lat < self._lat_lo else

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

576 (_W_ if lon < self._lon_lo else

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

578

579 @Property_RO

580 def pgm(self):

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

582 '''

583 return self._pgm

584

585 @Property_RO

586 def sizeB(self):

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

588 '''

589 return self._sizeB

590

591 @Property_RO

592 def smooth(self):

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

594 '''

595 return self._smooth

596

597 @Property_RO

598 def stdev(self):

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

600 '''

601 if self._stdev is None: # see GeoidKarney

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

603 return self._stdev

604

605 def _swne(self, crop):

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

607 try:

608 if len(crop) == 2:

609 try: # sw, ne LatLons

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

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

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

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

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

615 swne = crop

616 if len(swne) == 4:

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

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

619 -180 <= w <= (e - _1_0) <= 179:

620 return s, w, n, e

621 except (IndexError, TypeError, ValueError):

622 pass

623 raise GeoidError(crop=crop)

624

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

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

627

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

629 default). Trailing zero decimals are stripped

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

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

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

633

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

635 '''

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

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

638 (self.lowerleft, self.upperright,

639 self.center,

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

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

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

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

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

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

646

647 @Property_RO

648 def u2B(self):

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

650 '''

651 return self._u2B

652

653 @Property_RO

654 def _upperleft(self):

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

656 '''

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

658

659 def upperleft(self, LatLon=None):

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

661

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

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

664

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

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

667 with the lat-, longitude and height of the upper-left,

668 NW grid corner.

669 '''

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

671

672 @Property_RO

673 def _upperright(self):

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

675 '''

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

677

678 def upperright(self, LatLon=None):

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

680

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

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

683

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

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

686 with the lat-, longitude and height of the upper-right,

687 NE grid corner.

688 '''

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

690

691

692 class GeoidError(HeightError):

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

694 '''

695 pass

696

697

698 class GeoidG2012B(_GeoidBase):

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

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

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

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

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

704 U{Guam and Northern Mariana Islands

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

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

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

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

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

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

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

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

713

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

715 C{g2012b*.bin} grid files.

716 '''

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

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

719 '''New L{GeoidG2012B} interpolator.

720

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

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

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

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

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

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

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

728 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

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

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

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

732 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

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

734 scipy.interpolate.RectBivariateSpline.html>}

735 only (C{int}).

736

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

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

739

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

741 not installed.

742

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

744

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

746

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

748 warning as exception.

749

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

751 '''

752 if crop is not None:

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

754

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

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

757

758 try:

759 p = _Gpars()

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

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

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

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

764 # skip 4xf8, get 3xi4

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

766 if ien == 1: # correct endian

767 p.knots = p.nlat * p.nlon

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

769 and 1 < p.nlon < n:

770 self._endian = en_+'f4'

771 break

772 else: # couldn't validate endian

773 raise GeoidError(_endian_)

774

775 # get the first 4xf8

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

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

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

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

780 _GeoidBase.__init__(self, hs, p)

781

782 except Exception as x:

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

784 finally:

785 g.close()

786

787 def _g2ll2(self, lat, lon):

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

789 return lat, lon

790

791 def _ll2g2(self, lat, lon):

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

793 return lat, lon

794

795 if _FOR_DOCS:

796 __call__ = _GeoidBase.__call__

797 height = _GeoidBase.height

798

799

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

801 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat

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

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

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

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

806 '''

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

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

809

810

811 def _I(i):

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

813 '''

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

815

816

817 def _T(*cs):

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

819 '''

820 return map1(_I, *cs)

821

822

823 class GeoidKarney(_GeoidBase):

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

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

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

827 html/geoid.html#geoidinst>} datasets using bilinear or U{cubic

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

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

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

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

832

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

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

835 datasets.

836 '''

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

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

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

840 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

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

842 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

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

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

845 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

846 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),

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

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

849

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

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

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

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

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

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

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

857 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),

858 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),

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

860

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

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

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

864 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),

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

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

867 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

868 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),

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

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

871

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

873 _T(1, 0),

874 _T(0, 1),

875 _T(1, 1))

876

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

878 _T( 1, -1),

879 _T(-1, 0),

880 _T( 0, 0),

881 _T( 1, 0),

882 _T( 2, 0),

883 _T(-1, 1),

884 _T( 0, 1),

885 _T( 1, 1),

886 _T( 2, 1),

887 _T( 0, 2),

888 _T( 1, 2))

889

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

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

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

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

894# (-8.167, 147.25, 85.422) if egm96-5.pgm else

895# (-4.5, 148.75, 81.33)) # egm84-15.pgm

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

897# (4.667, 78.833, -107.043) if egm96-5.pgm else

898# (4.75, 79.25, -107.34)) # egm84-15.pgm

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

900 _nBytes = None # not applicable

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

902 _smooth = None # not applicable

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

904 _u2B = _calcsize(_endian) # pixelsize_ in bytes

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

906 _Ru2B = 0 # row of pixelsize_s in bytes

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

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

909 _yx_hits = 0 # cache hits

910

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

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

913 '''New L{GeoidKarney} interpolator.

914

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

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

917 note below.

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

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

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

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

922 C{LatLon} instances.

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

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

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

926 for C{cubic}.

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

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

929

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

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

932

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

934

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

936

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

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

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

940 '''

941 if smooth is not None:

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

943

944 if kind in (2,):

945 self._evH = self._ev2H

946 elif kind not in (3,):

947 raise GeoidError(kind=kind)

948

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

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

951

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

953 self._Ru2B = _calcsize(self._Rendian)

954

955 self._knots = p.knots # grid knots

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

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

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

959 self._lat_lo, \

960 self._lon_lo, \

961 self._lat_hi, \

962 self._lon_hi = self._swne(crop if crop else p.crop4)

963 self._cropped = True if crop else False

964

965 def __call__(self, *llis):

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

967

968 @arg llis: The location or locations (C{LatLon}, ... or

969 C{LatLon}s).

970

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

972 a list or tuple of interpolated geoid heights

973 (C{float}s).

974

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

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

977 geoid file is closed.

978

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

980 or longitude range.

981 '''

982 return self._called(llis, False)

983

984 def _c0c3v(self, y, x):

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

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

987 p = self._pgm

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

989 # read 4x4 ushorts, drop the 4 corners

990 g = self._egm

991 e = self._4endian

992 n = self._4u2B

993 R = self._Ru2B

994

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

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

997 b += R

998 g.seek(b, _SEEK_SET)

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

1000 b += R

1001 g.seek(b, _SEEK_SET)

1002 v += _unpack(e, g.read(n))

1003 b += R

1004 g.seek(b, _SEEK_SET)

1005 v += _unpack(e, g.read(n))[1:3]

1006 j = 1

1007

1008 else: # likely some wrapped y and/or x's

1009 v = self._raws(y, x, GeoidKarney._CM)

1010 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)

1011

1012 return GeoidKarney._C0[j], GeoidKarney._C3[j], v

1013

1014 @Property_RO

1015 def dtype(self):

1016 '''Get the geoid's grid data type (C{str}).

1017 '''

1018 return 'ushort'

1019

1020 def _ev(self, lat, lon): # PYCHOK expected

1021 # interpolate the geoid height at grid (lat, lon)

1022 fy, fx = self._g2yx2(lat, lon)

1023 y, x = int(floor(fy)), int(floor(fx))

1024 fy -= y

1025 fx -= x

1026 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H

1027 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)

1028 H += self._pgm.Offset # H.fadd(self._pgm.Offset)

1029 return H.fsum()

1030

1031 def _ev2H(self, fy, fx, *yx):

1032 # compute the bilinear 4-tuple and interpolate raw H

1033 if self._yxH == yx:

1034 t = self._yxHt

1035 self._yx_hits += 1

1036 else:

1037 y, x = self._yxH = yx

1038 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)

1039 v = _1_0, -fx, fx

1040 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)

1041 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy

1042 return H

1043

1044 def _ev3H(self, fy, fx, *yx):

1045 # compute the cubic 10-tuple and interpolate raw H

1046 if self._yxH == yx:

1047 t = self._yxHt

1048 self._yx_hits += 1

1049 else:

1050 self._yxH = yx

1051 c0, c3, v = self._c0c3v(*yx)

1052 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]

1053 self._yxHt = t = tuple(t)

1054 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...

1055 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +

1056 # fy * (t[2] + fx * (t[4] + fx * t[7]) +

1057 # fy * (t[5] + fx * t[8] + fy * t[9]));

1058 v = _1_0, fx, fy

1059 H = Fdot(v, t[5], t[8], t[9])

1060 H *= fy

1061 H += Fhorner(fx, t[2], t[4], t[7])

1062 H *= fy

1063 H += Fhorner(fx, t[0], t[1], t[3], t[6])

1064 return H

1065

1066 _evH = _ev3H # overriden for kind == 2

1067

1068 def _g2ll2(self, lat, lon):

1069 # convert grid (lat, lon) to earth (lat, lon), uncropped

1070 while lon > _180_0:

1071 lon -= _360_0

1072 return lat, lon

1073

1074 def _g2yx2(self, lat, lon):

1075 # convert grid (lat, lon) to grid (y, x) indices

1076 p = self._pgm

1077 # note, slat = +90, rlat < 0 makes y >=0

1078 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)

1079

1080 def _gyx2g2(self, y, x):

1081 # convert grid (y, x) indices to grid (lat, lon)

1082 p = self._pgm

1083 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)

1084

1085 def height(self, lats, lons):

1086 '''Interpolate the geoid height for one or several lat-/longitudes.

1087

1088 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).

1089 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).

1090

1091 @return: A single interpolated geoid height (C{float}) or a

1092 list of interpolated geoid heights (C{float}s).

1093

1094 @raise GeoidError: Insufficient or non-matching number of

1095 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}

1096 geoid file is closed.

1097

1098 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this

1099 geoid's lat- or longitude range.

1100 '''

1101 return _HeightBase._height(self, lats, lons, Error=GeoidError)

1102

1103 @Property_RO

1104 def _highest_ltd(self):

1105 '''(INTERNAL) Cache for L{highest} mesthod.

1106 '''

1107 return self._llh3minmax(True, -12, -4)

1108

1109 def highest(self, LatLon=None, full=False): # PYCHOK full

1110 '''Return the location and largest height of this geoid.

1111

1112 @kwarg LatLon: Optional class to return the location and height

1113 (C{LatLon}) or C{None}.

1114 @kwarg full: Search the full or limited latitude range (C{bool}).

1115

1116 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1117 lon, height)} otherwise a B{C{LatLon}} instance

1118 with the lat-, longitude and height of the highest

1119 grid location.

1120 '''

1121 llh = self._highest if full or self.cropped else self._highest_ltd

1122 return self._llh3LL(llh, LatLon)

1123

1124 def _lat2y2(self, lat2):

1125 # convert earth lat(s) to min and max grid y indices

1126 ys, m = [], self._pgm.nlat - 1

1127 for lat in lat2:

1128 y, _ = self._g2yx2(*self._ll2g2(lat, 0))

1129 ys.append(max(min(int(y), m), 0))

1130 return min(ys), max(ys) + 1

1131

1132 def _ll2g2(self, lat, lon):

1133 # convert earth (lat, lon) to grid (lat, lon), uncropped

1134 while lon < 0:

1135 lon += _360_0

1136 return lat, lon

1137

1138 def _llh3minmax(self, highest=True, *lat2):

1139 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid

1140 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)

1141 y = x = 0

1142 h = self._raw(y, x)

1143 if highest:

1144 for j, r in self._raw2(*lat2):

1145 m = max(r)

1146 if m > h:

1147 h, y, x = m, j, r.index(m)

1148 else: # lowest

1149 for j, r in self._raw2(*lat2):

1150 m = min(r)

1151 if m < h:

1152 h, y, x = m, j, r.index(m)

1153 h *= self._pgm.Scale

1154 h += self._pgm.Offset

1155 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)

1156

1157 @Property_RO

1158 def _lowest_ltd(self):

1159 '''(INTERNAL) Cache for L{lowest}.

1160 '''

1161 return self._llh3minmax(False, 0, 8)

1162

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

1164 '''Return the location and lowest 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 height of the lowest

1173 grid location.

1174 '''

1175 llh = self._lowest if full or self.cropped else self._lowest_ltd

1176 return self._llh3LL(llh, LatLon)

1177

1178 def _raw(self, y, x):

1179 # get the ushort geoid height at geoid index (y, x),

1180 # like GeographicLib/Geoid.hpp real rawval(is, iy)

1181 p = self._pgm

1182 if x < 0:

1183 x += p.nlon

1184 elif x >= p.nlon:

1185 x -= p.nlon

1186 h = p.nlon // 2

1187 if y < 0:

1188 y = -y

1189 elif y >= p.nlat:

1190 y = (p.nlat - 1) * 2 - y

1191 else:

1192 h = 0

1193 x += h if x < h else -h

1194 self._seek(y, x)

1195 h = _unpack(self._endian, self._egm.read(self._u2B))

1196 return h[0]

1197

1198 def _raws(self, y, x, ijs):

1199 # get bilinear 4-tuple or 10x12 cubic matrix

1200 return tuple(self._raw(y + j, x + i) for i, j in ijs)

1201

1202 def _raw2(self, *lat2):

1203 # yield a 2-tuple (y, ushorts) for each row or for

1204 # the rows between two (or more) earth lat values

1205 p = self._pgm

1206 g = self._egm

1207 e = self._Rendian

1208 n = self._Ru2B

1209 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat

1210 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)

1211 self._seek(s, 0) # to start of row s

1212 for y in range(s, t):

1213 yield y, _unpack(e, g.read(n))

1214

1215 def _seek(self, y, x):

1216 # position geoid to grid index (y, x)

1217 p, g = self._pgm, self._egm

1218 if g:

1219 b = p.skip + (y * p.nlon + x) * self._u2B

1220 g.seek(b, _SEEK_SET)

1221 return b # position

1222 raise GeoidError('closed file: %r' % (p.egm,)) # IOError

1223

1224

1225 class GeoidPGM(_GeoidBase):

1226 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth

1227 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/

1228 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1229 html/geoid.html#geoidinst>} datasets but based on C{SciPy}

1230 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/

1231 generated/scipy.interpolate.RectBivariateSpline.html>} or

1232 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1233 scipy.interpolate.interp2d.html>} interpolation.

1234

1235 Use any of the U{egm84-, egm96- or egm2008-*.pgm

1236 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}

1237 datasets. However, unless cropped, an entire C{egm*.pgm} dataset

1238 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/

1239 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}

1240 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1241 scipy.interpolate.interp2d.html>} interpolator and converted from

1242 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory

1243 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/

1244 geoid.html#geoidinst>} file size and may exceed the available memory,

1245 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.

1246 '''

1247 _endian = '>u2'

1248

1249 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84

1250 kind=3, name=NN, smooth=0):

1251 '''New L{GeoidPGM} interpolator.

1252

1253 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/

1254 html/geoid.html#geoidinst>} file name (C{egm*.pgm}).

1255 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,

1256 north, east}) or 2-tuple (C{(south, west), (north, east)}),

1257 in C{degrees90} lat- and C{degrees180} longitudes or a

1258 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.

1259 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

1260 or L{a_f2Tuple}), default C{WGS84}.

1261 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for

1262 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/

1263 reference/generated/scipy.interpolate.RectBivariateSpline.html>},

1264 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

1265 reference/generated/scipy.interpolate.interp2d.html>}, -3

1266 for C{interp2d cubic} or -5 for C{interp2d quintic}.

1267 @kwarg name: Optional geoid name (C{str}).

1268 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

1269 <https://docs.SciPy.org/doc/scipy/reference/generated/

1270 scipy.interpolate.RectBivariateSpline.html>}

1271 only (C{int}).

1272

1273 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},

1274 B{C{kind}} or B{C{smooth}}.

1275

1276 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

1277

1278 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.

1279

1280 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.

1281

1282 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}

1283 warning as exception.

1284

1285 @raise TypeError: Invalid B{C{datum}}.

1286

1287 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/

1288 html/geoid.html#geoidinst>} file sizes are based on a 2-byte

1289 C{int} height converted to 8-byte C{dtype float64} for C{scipy}

1290 interpolators. Therefore, internal memory usage is 4 times the

1291 C{egm*.pgm} file size and may exceed the available memory,

1292 especially with 32-bit Python. To reduce memory usage, set

1293 keyword argument B{C{crop}} to the region of interest. For example

1294 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://

1295 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}

1296 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.

1297

1298 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.

1299 '''

1300 np = self.numpy

1301 self._u2B = np.dtype(self.endian).itemsize

1302

1303 g = self._open(egm_pgm, datum, kind, name, smooth)

1304 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)

1305 if crop:

1306 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))

1307 self._g2ll2 = self._g2ll2_cropped

1308 self._ll2g2 = self._ll2g2_cropped

1309 if map2(int, np.__version__.split(_DOT_)[:2]) < (1, 9):

1310 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-

1311 self._cropped = True

1312 else:

1313 self._cropped = False

1314

1315 try:

1316 # U{numpy dtype formats are different from Python struct formats

1317 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}

1318 # read all heights, skipping the PGM header lines, converted to float

1319 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale

1320 if p.Offset: # offset

1321 hs = p.Offset + hs

1322 if p.dlat < 0: # flip the rows

1323 hs = np.flipud(hs)

1324 _GeoidBase.__init__(self, hs, p)

1325 except Exception as x:

1326 raise _SciPyIssue(x, _in_, repr(egm_pgm))

1327 finally:

1328 g.close()

1329

1330 def _g2ll2(self, lat, lon):

1331 # convert grid (lat, lon) to earth (lat, lon), uncropped

1332 while lon > _180_0:

1333 lon -= _360_0

1334 return lat, lon

1335

1336 def _g2ll2_cropped(self, lat, lon):

1337 # convert cropped grid (lat, lon) to earth (lat, lon)

1338 return lat, lon - self._lon_og

1339

1340 def _ll2g2(self, lat, lon):

1341 # convert earth (lat, lon) to grid (lat, lon), uncropped

1342 while lon < 0:

1343 lon += _360_0

1344 return lat, lon

1345

1346 def _ll2g2_cropped(self, lat, lon):

1347 # convert earth (lat, lon) to cropped grid (lat, lon)

1348 return lat, lon + self._lon_of

1349

1350 if _FOR_DOCS:

1351 __call__ = _GeoidBase.__call__

1352 height = _GeoidBase.height

1353

1354

1355 class _Gpars(_Named):

1356 '''(INTERNAL) Basic geoid parameters.

1357 '''

1358 # interpolator parameters

1359 dlat = 0 # +/- latitude resolution in C{degrees}

1360 dlon = 0 # longitude resolution in C{degrees}

1361 nlat = 1 # number of latitude knots (C{int})

1362 nlon = 0 # number of longitude knots (C{int})

1363 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat

1364 rlon = 0 # longitude resolution in C{float}, 1 / .dlon

1365 slat = 0 # nothern- or southern most latitude (C{degrees90})

1366 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})

1367

1368 flon = 0 # forward, earth to grid longitude offset

1369 glon = 0 # reverse, grid to earth longitude offset

1370

1371 knots = 0 # number of knots, nlat * nlon (C{int})

1372 skip = 0 # header bytes to skip (C{int})

1373

1374 def __repr__(self):

1375 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for

1376 a in dir(self.__class__)

1377 if a[:1].isupper()))

1378 return _COLONSPACE_(self, t)

1379

1380 def __str__(self):

1381 return Fmt.PAREN(self.classname, repr(self.name))

1382

1383

1384 class _PGM(_Gpars):

1385 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.

1386

1387 # Geoid file in PGM format for the GeographicLib::Geoid class

1388 # Description WGS84 EGM96, 5-minute grid

1389 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html

1390 # DateTime 2009-08-29 18:45:03

1391 # MaxBilinearError 0.140

1392 # RMSBilinearError 0.005

1393 # MaxCubicError 0.003

1394 # RMSCubicError 0.001

1395 # Offset -108

1396 # Scale 0.003

1397 # Origin 90N 0E

1398 # AREA_OR_POINT Point

1399 # Vertical_Datum WGS84

1400 <width> <height>

1401 <pixel>

1402 ...

1403 '''

1404 crop4 = () # 4-tuple (C{south, west, north, east}).

1405 egm = None

1406 glon = 180 # reverse offset, uncropped

1407# pgm = NN # name

1408 sizeB = 0

1409 u2B = 2 # item size of grid height (C{int}).

1410

1411 @staticmethod

1412 def _llstr2floats(latlon):

1413 # llstr to (lat, lon) floats

1414 lat, lon = latlon.split()

1415 return parseDMS2(lat, lon)

1416

1417 # PGM file attributes, CamelCase but not .istitle()

1418 AREA_OR_POINT = str

1419 DateTime = str

1420 Description = str # 'WGS84 EGM96, 5-minute grid'

1421 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'

1422 MaxBilinearError = float

1423 MaxCubicError = float

1424 Offset = float

1425 Origin = _llstr2floats

1426 Pixel = 0

1427 RMSBilinearError = float

1428 RMSCubicError = float

1429 Scale = float

1430 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'

1431 Vertical_Datum = str

1432

1433 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22

1434 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.

1435 '''

1436 self.name = pgm # geoid file name

1437 if itemsize:

1438 self._u2B = itemsize

1439 if sizeB:

1440 self.sizeB = sizeB

1441

1442 t = g.readline() # make sure newline == '\n'

1443 if t != b'P5\n' and t.strip() != b'P5':

1444 raise self._Errorf(_format_, _header_, t)

1445

1446 while True: # read all # Attr ... lines,

1447 try: # ignore empty ones or comments

1448 t = g.readline().strip()

1449 if t.startswith(_bHASH_):

1450 t = t.lstrip(_bHASH_).lstrip()

1451 a, v = map(_ub2str, t.split(None, 1))

1452 f = getattr(_PGM, a, None)

1453 if callable(f) and a[:1].isupper():

1454 setattr(self, a, f(v))

1455 elif t:

1456 break

1457 except (TypeError, ValueError):

1458 raise self._Errorf(_format_, 'Attr', t)

1459 else: # should never get here

1460 raise self._Errorf(_format_, _header_, g.tell())

1461

1462 try: # must be (even) width and (odd) height

1463 nlon, nlat = map(int, t.split())

1464 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \

1465 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):

1466 raise ValueError

1467 except (TypeError, ValueError):

1468 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)

1469

1470 try: # must be 16 bit pixel height

1471 t = g.readline().strip()

1472 self.Pixel = int(t)

1473 if not 255 < self.Pixel < 65536: # >u2 or >H only

1474 raise ValueError

1475 except (TypeError, ValueError):

1476 raise self._Errorf(_format_, 'pixel', t)

1477

1478 for a in dir(_PGM): # set undefined # Attr ... to None

1479 if a[:1].isupper() and callable(getattr(self, a)):

1480 setattr(self, a, None)

1481

1482 if self.Origin is None:

1483 raise self._Errorf(_format_, 'Origin', self.Origin)

1484 if self.Offset is None or self.Offset > 0:

1485 raise self._Errorf(_format_, 'Offset', self.Offset)

1486 if self.Scale is None or self.Scale < EPS:

1487 raise self._Errorf(_format_, 'Scale', self.Scale)

1488

1489 self.skip = g.tell()

1490 self.knots = nlat * nlon

1491

1492 self.nlat, self.nlon = nlat, nlon

1493 self.slat, self.wlon = self.Origin

1494 # note, negative .dlat and .rlat since rows

1495 # are from .slat 90N down in decreasing lat

1496 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon

1497 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0

1498

1499 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0

1500 n = float(self.slat)

1501 s = n + self.dlat * (nlat - 1)

1502 w = self.wlon - self.glon

1503 e = w + self.dlon * nlon

1504 self.crop4 = s, w, n, e

1505

1506 n = self.sizeB - self.skip

1507 if n > 0 and n != (self.knots * self.u2B):

1508 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)

1509

1510 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15

1511 '''Crop the geoid to (south, west, north, east) box.

1512 '''

1513 # flon offset for both west and east

1514 f = 360 if west < 0 else 0

1515 # earth (lat, lon) to grid indices (y, x),

1516 # note y is decreasing, i.e. n < s

1517 s, w = self._lle2yx2(south, west, f)

1518 n, e = self._lle2yx2(north, east, f)

1519 s += 1 # s > n

1520 e += 1 # e > w

1521

1522 hi, wi = self.nlat, self.nlon

1523 # handle special cases

1524 if (s - n) > hi:

1525 n, s = 0, hi # entire lat range

1526 if (e - w) > wi:

1527 w, e, f = 0, wi, 180 # entire lon range

1528 if s == hi and w == n == 0 and e == wi:

1529 return g # use entire geoid as-is

1530

1531 if (e - w) < k1 or (s - n) < (k1 + 1):

1532 raise self._Errorf(_format_, 'swne', (north - south, east - west))

1533

1534 if e > wi > w: # wrap around

1535 # read w..wi and 0..e

1536 r, p = (wi - w), (e - wi)

1537 elif e > w:

1538 r, p = (e - w), 0

1539 else:

1540 raise self._Errorf('%s(%s < %s)', _assert_, w, e)

1541

1542 # convert to bytes

1543 r *= self.u2B

1544 p *= self.u2B

1545 q = wi * self.u2B # stride

1546 # number of rows and cols to skip from

1547 # the original (.slat, .wlon) origin

1548 z = self.skip + (n * wi + w) * self.u2B

1549 # sanity check

1550 if r < 2 or p < 0 or q < 2 or z < self.skip \

1551 or z > self.sizeB:

1552 raise self._Errorf(_format_, _assert_, (r, p, q, z))

1553

1554 # can't use _BytesIO since numpy

1555 # needs .fileno attr in .fromfile

1556 t, c = 0, self._tmpfile()

1557 # reading (s - n) rows, forward

1558 for y in range(n, s): # PYCHOK y unused

1559 g.seek(z, _SEEK_SET)

1560 # Python 2 tmpfile.write returns None

1561 t += c.write(g.read(r)) or r

1562 if p: # wrap around to start of row

1563 g.seek(-q, _SEEK_CUR)

1564 # assert(g.tell() == (z - w * self.u2B))

1565 # Python 2 tmpfile.write returns None

1566 t += c.write(g.read(p)) or p

1567 z += q

1568 c.flush()

1569 g.close()

1570

1571 s -= n # nlat

1572 e -= w # nlon

1573 k = s * e # knots

1574 z = k * self.u2B

1575 if t != z:

1576 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)

1577

1578 # update the _Gpars accordingly, note attributes

1579 # .dlat, .dlon, .rlat and .rlon remain unchanged

1580 self.slat += n * self.dlat

1581 self.wlon += w * self.dlon

1582 self.nlat = s

1583 self.nlon = e

1584 self.flon = self.glon = f

1585

1586 self.crop4 = south, west, north, east

1587 self.knots = k

1588 self.skip = 0 # no header lines in c

1589

1590 c.seek(0, _SEEK_SET)

1591 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-

1592 return c

1593

1594 def _Errorf(self, fmt, *args): # PYCHOK no cover

1595 t = fmt % args

1596 e = self.pgm or NN

1597 if e:

1598 t = _SPACE_(t, _in_, repr(e))

1599 return PGMError(t)

1600

1601 def _lle2yx2(self, lat, lon, flon):

1602 # earth (lat, lon) to grid indices (y, x)

1603 # with .dlat decreasing from 90N .slat

1604 lat -= self.slat

1605 lon += flon - self.wlon

1606 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),

1607 max(0, int(lon * self.rlon)))

1608

1609 def _tmpfile(self):

1610 # create a tmpfile to hold the cropped geoid grid

1611 try:

1612 from tempfile import NamedTemporaryFile as tmpfile

1613 except ImportError: # Python 2.7.16-

1614 from os import tmpfile

1615 t = _os_path.splitext(_os_path.basename(self.pgm))[0]

1616 f = tmpfile(mode='w+b', prefix=t or 'egm')

1617 f.seek(0, _SEEK_SET) # force overwrite

1618 return f

1619

1620 @Property_RO

1621 def pgm(self):

1622 '''Get the geoid file name (C{str}).

1623 '''

1624 return self.name

1625

1626

1627 class PGMError(GeoidError):

1628 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.

1629 '''

1630 pass

1631

1632

1633 def egmGeoidHeights(GeoidHeights_dat):

1634 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1635 html/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat

1636 <https://SourceForge.net/projects/geographiclib/files/testdata/>}

1637 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/

1638 geoid.html#testgeoid>}.

1639

1640 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file

1641 (C{str} or C{file} handle).

1642

1643 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,

1644 egm84, egm96, egm2008)}.

1645

1646 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.

1647

1648 @note: Function L{egmGeoidHeights} is used to test the geoids

1649 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module

1650 C{test/testGeoids.py}.

1651 '''

1652 dat = GeoidHeights_dat

1653 if isinstance(dat, bytes):

1654 dat = _BytesIO(dat)

1655

1656 try:

1657 dat.seek(0, _SEEK_SET) # reset

1658 except AttributeError as x:

1659 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)

1660

1661 for t in dat.readlines():

1662 t = t.strip()

1663 if t and not t.startswith(_bHASH_):

1664 lat, lon, egm84, egm96, egm2008 = map(float, t.split())

1665 while lon > _180_0: # EasternLon to earth lon

1666 lon -= _360_0

1667 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)

1668

1669

1670__all__ += _ALL_DOCS(_GeoidBase)

1671

1672 if __name__ == '__main__':

1673

1674 from pygeodesy.lazily import printf, _sys

1675

1676 _crop = ()

1677 _GeoidEGM = GeoidKarney

1678 _kind = 3

1679

1680 geoids = _sys.argv[1:]

1681 while geoids:

1682 geoid = geoids.pop(0)

1683

1684 if '-crop'.startswith(geoid.lower()):

1685 _crop = 20, -125, 50, -65 # CONUS

1686

1687 elif '-karney'.startswith(geoid.lower()):

1688 _GeoidEGM = GeoidKarney

1689

1690 elif '-kind'.startswith(geoid.lower()):

1691 _kind = int(geoids.pop(0))

1692

1693 elif '-pgm'.startswith(geoid.lower()):

1694 _GeoidEGM = GeoidPGM

1695

1696 elif geoid[-4:].lower() in ('.pgm',):

1697 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)

1698 printf(g.toStr(), nt=1, nl=1)

1699 printf(repr(g.pgm), nt=1)

1700 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:

1701 # The height of the EGM96 geoid at Timbuktu

1702 # echo 16:46:33N 3:00:34W | GeoidEval

1703 # => 28.7068 -0.02e-6 -1.73e-6

1704 # The 1st number is the height of the geoid, the 2nd and

1705 # 3rd are its slopes in northerly and easterly direction

1706 t = 'Timbuktu %s' % (g,)

1707 k = {'egm84-15.pgm': '31.2979',

1708 'egm96-5.pgm': '28.7067',

1709 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')

1710 ll = parseDMS2('16:46:33N', '3:00:34W', sep=':')

1711 for ll in (ll, (16.776, -3.009),):

1712 try:

1713 h, ll = g.height(*ll), fstr(ll, prec=6)

1714 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)

1715 except (GeoidError, RangeError) as x:

1716 printf(_COLONSPACE_(t, str(x)))

1717

1718 elif geoid[-4:].lower() in ('.bin',):

1719 g = GeoidG2012B(geoid, kind=_kind)

1720 print(g.toStr())

1721

1722 else:

1723 raise GeoidError(grid=repr(geoid))

1724

1725_I = int # PYCHOK unused _I

1726 del _intCs # trash ints cache

1727

1728# **) MIT License

1729#

1730# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1731#

1732# Permission is hereby granted, free of charge, to any person obtaining a

1733# copy of this software and associated documentation files (the "Software"),

1734# to deal in the Software without restriction, including without limitation

1735# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1736# and/or sell copies of the Software, and to permit persons to whom the

1737# Software is furnished to do so, subject to the following conditions:

1738#

1739# The above copyright notice and this permission notice shall be included

1740# in all copies or substantial portions of the Software.

1741#

1742# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1743# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1744# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1745# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1746# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1747# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1748# OTHER DEALINGS IN THE SOFTWARE.

1749

1750# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>

1751# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm

1752# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm

1753# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm

1754

1755# _center = 0, 0, 17.2260 # egm2008-1.pgm

1756# _center = 0, 0, 17.1630 # egm96-5.pgm

1757# _center = 0, 0, 18.3296 # egm84-15.pgm

1758

1759# _upperright = 90, 180, 14.8980 # egm2008-1.pgm

1760# _upperright = 90, 180, 13.6050 # egm96-5.pgm

1761# _upperright = 90, 180, 13.0980 # egm84-15.pgm

1762

1763

1764# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm

1765#

1766# 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)

1767#

1768# _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'

1769#

1770# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1771# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1772#

1773# 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)

1774#

1775# _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'

1776#

1777# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1778# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1779#

1780# 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)

1781#

1782# _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'

1783#

1784# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1785# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1786

1787

1788# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm

1789#

1790# 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)

1791#

1792# _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'

1793#

1794# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1795# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1796#

1797# 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)

1798#

1799# _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'

1800#

1801# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1802# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1803#

1804# 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)

1805#

1806# _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'

1807#

1808# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1809# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1810

1811

1812# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm

1813#

1814# 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)

1815#

1816# _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'

1817#

1818# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1819# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1820#

1821# 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)

1822#

1823# _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'

1824#

1825# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979

1826# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979

1827#

1828# 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)

1829#

1830# _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'

1831#

1832# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067

1833# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067