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 # from .heights

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 _as_llis2, _ascalar, _height_called, HeightError, \

91 _HeightsBase, _ellipsoidal_datum, _Wrap

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

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

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

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

96 _SPACE_, _stdev_, _supported_, _tbd_, _W_, _width_

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

98 from pygeodesy.named import _Named, _NamedTuple, notOverloaded

99# from pygeodesy.namedTuples import LatLon3Tuple # _MODS

100 from pygeodesy.props import Property_RO, property_RO

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

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

103# from pygeodesy.utils import _Wrap # from .heights

104

105 from math import floor

106 import os.path as _os_path

107 from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET

108 from struct import calcsize as _calcsize, unpack as _unpack

109

110 try:

111 from StringIO import StringIO as _BytesIO # reads bytes

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

113

114 except ImportError: # Python 3+

115 from io import BytesIO as _BytesIO # PYCHOK expected

116

117__all__ = _ALL_LAZY.geoids

118__version__ = '23.05.26'

119

120_assert_ = 'assert'

121_bHASH_ = b'#'

122_endian_ = 'endian'

123_format_ = '%s %r'

124_header_ = 'header'

125# temporarily hold a single instance for each int value

126_intCs = {}

127_interp2d_ks = {-2: _linear_,

128 -3: _cubic_,

129 -5: 'quintic'}

130_lli_ = 'lli'

131_non_increasing_ = 'non-increasing'

132_rb_ = 'rb'

133

134

135 class _GeoidBase(_HeightsBase):

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

137 '''

138 _cropped = None

139# _datum = _WGS84 # from _HeightsBase

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

141 _endian = _tbd_

142 _geoid = _n_a_

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

144 _interp2d = None # interp2d interpolation

145 _kind = 3 # order for interp2d, RectBivariateSpline

146# _kmin = 2 # min number of knots

147 _knots = 0 # nlat * nlon

148 _mean = None # fixed in GeoidKarney

149# _name = NN # _Named

150 _nBytes = 0 # numpy size in bytes, float64

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

152 _sizeB = 0 # geoid file size in bytes

153 _smooth = 0 # used only for RectBivariateSpline

154 _stdev = None # fixed in GeoidKarney

155 _u2B = 0 # np.itemsize or undefined

156

157 _lat_d = _0_0 # increment, +tive

158 _lat_lo = _0_0 # lower lat, south

159 _lat_hi = _0_0 # upper lat, noth

160 _lon_d = _0_0 # increment, +tive

161 _lon_lo = _0_0 # left lon, west

162 _lon_hi = _0_0 # right lon, east

163 _lon_of = _0_0 # forward lon offset

164 _lon_og = _0_0 # reverse lon offset

165

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

167 _yx_hits = None # cache hits, ala Karney

168

169 def __init__(self, hs, p):

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

171 and several internal geoid attributes.

172

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

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

175 other geoid parameters (C{INTERNAL}).

176

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

178 invalid B{C{kind}}.

179

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

181

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

183 C{-.RectBivariateSpline} issue.

184

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

186 C{-.RectBivariateSpline} warning as

187 exception.

188 '''

189 spi = self.scipy_interpolate

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

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

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

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

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

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

196

197 # both axes and bounding box

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

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

200

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

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

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

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

205 k = self.kind

206 if k in _interp2d_ks:

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

208 elif 1 <= k <= 5:

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

210 s=self._smooth).ev

211 else:

212 raise GeoidError(kind=k)

213

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

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

216 self._knots = p.knots # grid knots

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

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

219 # shrink the box by 1 unit on every side

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

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

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

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

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

225

226 def __call__(self, *llis, **wrap):

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

228

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

230 C{LatLon}s).

231 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{llis}}

232 locations (C{bool}).

233

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

235 a list or tuple of interpolated geoid heights

236 (C{float}s).

237

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

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

240 geoid file is closed.

241

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

243 or longitude range.

244

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

246 C{-.RectBivariateSpline} issue.

247

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

249 C{-.RectBivariateSpline} warning as

250 exception.

251 '''

252 return self._called(llis, True, **wrap)

253

254 def __enter__(self):

255 '''Open context.

256 '''

257 return self

258

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

260 '''Close context.

261 '''

262 self.close()

263 # return None # XXX False

264

265 def __repr__(self):

266 return self.toStr()

267

268 def __str__(self):

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

270

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

272 # handle __call__

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

274 try:

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

276 for i, lli in enumerate(llis):

277 hs.append(self._hGeoid(*_w(lli.lat, lli.lon)))

278 return _as(hs)

279

280 except (GeoidError, RangeError) as x:

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

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

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

284 raise type(x)(t, lli, wrap=wrap, cause=x)

285 except Exception as x:

286 if scipy and self.scipy:

287 raise _SciPyIssue(x)

288 else:

289 raise

290

291 @Property_RO

292 def _center(self):

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

294 '''

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

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

297

298 def center(self, LatLon=None):

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

300

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

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

303

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

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

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

307 center location.

308 '''

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

310

311 def close(self):

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

313 '''

314 if not self.closed:

315 self._egm.close()

316 self._egm = None

317

318 @property_RO

319 def closed(self):

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

321 '''

322 return self._egm is None

323

324 @Property_RO

325 def cropped(self):

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

327 '''

328 return self._cropped

329

330 @Property_RO

331 def dtype(self):

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

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

334 '''

335 return self._hs_y_x.dtype

336

337 @Property_RO

338 def endian(self):

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

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

341 '''

342 return self._endian

343

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

345 # only used for .interpolate.interp2d, but

346 # overwritten for .RectBivariateSpline,

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

348 return self._interp2d(x, y)

349

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

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

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

353 if m != n:

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

355 if d < 0:

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

357 for i in range(1, m):

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

359 if e < EPS: # non-increasing axis

360 i = Fmt.SQUARE(name, i)

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

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

363

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

365 notOverloaded(self, lat, lon)

366

367 def _gyx2g2(self, y, x):

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

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

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

371

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

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

374

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

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

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

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

379

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

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

382

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

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

385

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

387 geoid's lat- or longitude range.

388

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

390 C{-.RectBivariateSpline} issue.

391

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

393 C{-.RectBivariateSpline} warning as

394 exception.

395 '''

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

397

398 def _hGeoid(self, lat, lon):

399 out = self.outside(lat, lon)

400 if out:

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

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

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

404

405 @Property_RO

406 def _highest(self):

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

408 '''

409 return self._llh3minmax(True)

410

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

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

413

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

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

416

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

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

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

420 grid location.

421 '''

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

423

424 @Property_RO

425 def hits(self):

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

427 '''

428 return self._yx_hits

429

430 @Property_RO

431 def kind(self):

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

433 '''

434 return self._kind

435

436 @Property_RO

437 def knots(self):

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

439 '''

440 return self._knots

441

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

443 notOverloaded(self, lat, lon)

444

445 @property_RO

446 def _LL3T(self):

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

448 '''

449 T = _MODS.namedTuples.LatLon3Tuple

450 _GeoidBase._LL3T = T # overwrite poperty_RO

451 return T

452

453 def _llh3(self, lat, lon):

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

455

456 def _llh3LL(self, llh, LatLon):

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

458

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

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

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

462 # numpy.argmin.html#numpy.argmin>

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

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

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

466

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

468 # numpy.fromfile, like .frombuffer

469 g.seek(offset, _SEEK_SET)

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

471

472 @Property_RO

473 def _lowerleft(self):

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

475 '''

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

477

478 def lowerleft(self, LatLon=None):

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

480

481 @kwarg LatLon: Optional class to return the location

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

483

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

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

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

487 SW grid corner.

488 '''

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

490

491 @Property_RO

492 def _loweright(self):

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

494 '''

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

496

497 def loweright(self, LatLon=None):

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

499

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

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

502

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

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

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

506 SE grid corner.

507 '''

508

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

510

511 lowerright = loweright # synonymous

512

513 @Property_RO

514 def _lowest(self):

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

516 '''

517 return self._llh3minmax(False)

518

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

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

521

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

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

524

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

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

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

528 grid location.

529 '''

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

531

532 @Property_RO

533 def mean(self):

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

535 '''

536 if self._mean is None: # see GeoidKarney

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

538 return self._mean

539

540 @property_RO

541 def name(self):

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

543 '''

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

545

546 @Property_RO

547 def nBytes(self):

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

549 '''

550 return self._nBytes

551

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

553 # open the geoid file

554 try:

555 self._geoid = _os_path.basename(geoid)

556 self._sizeB = _os_path.getsize(geoid)

557 g = open(geoid, _rb_)

558 except (IOError, OSError) as x:

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

560

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

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

563 self._kind = int(kind)

564 if name:

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

566 if smooth:

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

568

569 return g

570

571 def outside(self, lat, lon):

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

573 lat-/longitude or crop range.

574

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

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

577

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

579 empty C{str} if inside.

580 '''

581 return (_S_ if lat < self._lat_lo else

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

583 (_W_ if lon < self._lon_lo else

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

585

586 @Property_RO

587 def pgm(self):

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

589 '''

590 return self._pgm

591

592 @Property_RO

593 def sizeB(self):

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

595 '''

596 return self._sizeB

597

598 @Property_RO

599 def smooth(self):

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

601 '''

602 return self._smooth

603

604 @Property_RO

605 def stdev(self):

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

607 '''

608 if self._stdev is None: # see GeoidKarney

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

610 return self._stdev

611

612 def _swne(self, crop):

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

614 try:

615 if len(crop) == 2:

616 try: # sw, ne LatLons

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

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

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

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

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

622 swne = crop

623 if len(swne) == 4:

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

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

626 -180 <= w <= (e - _1_0) <= 179:

627 return s, w, n, e

628 except (IndexError, TypeError, ValueError):

629 pass

630 raise GeoidError(crop=crop)

631

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

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

634

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

636 default). Trailing zero decimals are stripped

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

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

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

640

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

642 '''

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

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

645 (self.lowerleft, self.upperright,

646 self.center,

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

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

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

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

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

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

653

654 @Property_RO

655 def u2B(self):

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

657 '''

658 return self._u2B

659

660 @Property_RO

661 def _upperleft(self):

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

663 '''

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

665

666 def upperleft(self, LatLon=None):

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

668

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

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

671

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

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

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

675 NW grid corner.

676 '''

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

678

679 @Property_RO

680 def _upperright(self):

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

682 '''

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

684

685 def upperright(self, LatLon=None):

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

687

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

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

690

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

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

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

694 NE grid corner.

695 '''

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

697

698

699 class GeoidError(HeightError):

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

701 '''

702 pass

703

704

705 class GeoidG2012B(_GeoidBase):

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

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

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

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

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

711 U{Guam and Northern Mariana Islands

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

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

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

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

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

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

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

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

720

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

722 C{g2012b*.bin} grid files.

723 '''

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

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

726 '''New L{GeoidG2012B} interpolator.

727

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

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

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

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

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

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

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

735 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

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

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

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

739 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

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

741 scipy.interpolate.RectBivariateSpline.html>}

742 only (C{int}).

743

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

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

746

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

748 not installed.

749

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

751

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

753

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

755 warning as exception.

756

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

758 '''

759 if crop is not None:

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

761

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

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

764

765 try:

766 p = _Gpars()

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

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

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

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

771 # skip 4xf8, get 3xi4

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

773 if ien == 1: # correct endian

774 p.knots = p.nlat * p.nlon

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

776 and 1 < p.nlon < n:

777 self._endian = en_+'f4'

778 break

779 else: # couldn't validate endian

780 raise GeoidError(_endian_)

781

782 # get the first 4xf8

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

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

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

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

787 _GeoidBase.__init__(self, hs, p)

788

789 except Exception as x:

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

791 finally:

792 g.close()

793

794 def _g2ll2(self, lat, lon):

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

796 return lat, lon

797

798 def _ll2g2(self, lat, lon):

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

800 return lat, lon

801

802 if _FOR_DOCS:

803 __call__ = _GeoidBase.__call__

804 height = _GeoidBase.height

805

806

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

808 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat

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

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

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

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

813 '''

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

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

816

817

818 def _I(i):

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

820 '''

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

822

823

824 def _T(*cs):

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

826 '''

827 return map1(_I, *cs)

828

829

830 class GeoidKarney(_GeoidBase):

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

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

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

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

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

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

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

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

839

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

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

842 datasets.

843 '''

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

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

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

847 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

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

849 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

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

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

852 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

853 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),

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

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

856

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

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

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

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

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

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

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

864 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),

865 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),

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

867

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

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

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

871 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),

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

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

874 _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),

875 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),

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

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

878

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

880 _T(1, 0),

881 _T(0, 1),

882 _T(1, 1))

883

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

885 _T( 1, -1),

886 _T(-1, 0),

887 _T( 0, 0),

888 _T( 1, 0),

889 _T( 2, 0),

890 _T(-1, 1),

891 _T( 0, 1),

892 _T( 1, 1),

893 _T( 2, 1),

894 _T( 0, 2),

895 _T( 1, 2))

896

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

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

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

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

901# (-8.167, 147.25, 85.422) if egm96-5.pgm else

902# (-4.5, 148.75, 81.33)) # egm84-15.pgm

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

904# (4.667, 78.833, -107.043) if egm96-5.pgm else

905# (4.75, 79.25, -107.34)) # egm84-15.pgm

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

907 _nBytes = None # not applicable

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

909 _smooth = None # not applicable

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

911 _u2B = _calcsize(_endian) # pixelsize_ in bytes

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

913 _Ru2B = 0 # row of pixelsize_s in bytes

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

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

916 _yx_hits = 0 # cache hits

917

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

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

920 '''New L{GeoidKarney} interpolator.

921

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

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

924 note below.

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

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

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

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

929 C{LatLon} instances.

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

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

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

933 for C{cubic}.

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

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

936

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

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

939

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

941

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

943

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

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

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

947 '''

948 if smooth is not None:

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

950

951 if kind in (2,):

952 self._evH = self._ev2H

953 elif kind not in (3,):

954 raise GeoidError(kind=kind)

955

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

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

958

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

960 self._Ru2B = _calcsize(self._Rendian)

961

962 self._knots = p.knots # grid knots

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

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

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

966 self._lat_lo, \

967 self._lon_lo, \

968 self._lat_hi, \

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

970 self._cropped = True if crop else False

971

972 def __call__(self, *llis, **wrap):

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

974

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

976 C{LatLon}s).

977 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{llis}}

978 locations (C{bool}).

979

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

981 a list or tuple of interpolated geoid heights

982 (C{float}s).

983

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

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

986 geoid file is closed.

987

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

989 or longitude range.

990 '''

991 return self._called(llis, False, **wrap)

992

993 def _c0c3v(self, y, x):

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

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

996 p = self._pgm

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

998 # read 4x4 ushorts, drop the 4 corners

999 g = self._egm

1000 e = self._4endian

1001 n = self._4u2B

1002 R = self._Ru2B

1003

1004 b = self._seek(y - 1, x - 1)

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

1006 b += R

1007 g.seek(b, _SEEK_SET)

1008 v += _unpack(e, g.read(n))

1009 b += R

1010 g.seek(b, _SEEK_SET)

1011 v += _unpack(e, g.read(n))

1012 b += R

1013 g.seek(b, _SEEK_SET)

1014 v += _unpack(e, g.read(n))[1:3]

1015 j = 1

1016

1017 else: # likely some wrapped y and/or x's

1018 v = self._raws(y, x, GeoidKarney._CM)

1019 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)

1020

1021 return GeoidKarney._C0[j], GeoidKarney._C3[j], v

1022

1023 @Property_RO

1024 def dtype(self):

1025 '''Get the geoid's grid data type (C{str}).

1026 '''

1027 return 'ushort'

1028

1029 def _ev(self, lat, lon): # PYCHOK expected

1030 # interpolate the geoid height at grid (lat, lon)

1031 fy, fx = self._g2yx2(lat, lon)

1032 y, x = int(floor(fy)), int(floor(fx))

1033 fy -= y

1034 fx -= x

1035 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H

1036 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)

1037 H += self._pgm.Offset # H.fadd(self._pgm.Offset)

1038 return H.fsum()

1039

1040 def _ev2H(self, fy, fx, *yx):

1041 # compute the bilinear 4-tuple and interpolate raw H

1042 if self._yxH == yx:

1043 t = self._yxHt

1044 self._yx_hits += 1

1045 else:

1046 y, x = self._yxH = yx

1047 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)

1048 v = _1_0, -fx, fx

1049 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)

1050 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy

1051 return H

1052

1053 def _ev3H(self, fy, fx, *yx):

1054 # compute the cubic 10-tuple and interpolate raw H

1055 if self._yxH == yx:

1056 t = self._yxHt

1057 self._yx_hits += 1

1058 else:

1059 self._yxH = yx

1060 c0, c3, v = self._c0c3v(*yx)

1061 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]

1062 self._yxHt = t = tuple(t)

1063 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...

1064 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +

1065 # fy * (t[2] + fx * (t[4] + fx * t[7]) +

1066 # fy * (t[5] + fx * t[8] + fy * t[9]));

1067 v = _1_0, fx, fy

1068 H = Fdot(v, t[5], t[8], t[9])

1069 H *= fy

1070 H += Fhorner(fx, t[2], t[4], t[7])

1071 H *= fy

1072 H += Fhorner(fx, t[0], t[1], t[3], t[6])

1073 return H

1074

1075 _evH = _ev3H # overriden for kind == 2

1076

1077 def _g2ll2(self, lat, lon):

1078 # convert grid (lat, lon) to earth (lat, lon), uncropped

1079 while lon > _180_0:

1080 lon -= _360_0

1081 return lat, lon

1082

1083 def _g2yx2(self, lat, lon):

1084 # convert grid (lat, lon) to grid (y, x) indices

1085 p = self._pgm

1086 # note, slat = +90, rlat < 0 makes y >=0

1087 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)

1088

1089 def _gyx2g2(self, y, x):

1090 # convert grid (y, x) indices to grid (lat, lon)

1091 p = self._pgm

1092 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)

1093

1094 def height(self, lats, lons, **wrap):

1095 '''Interpolate the geoid height for one or several lat-/longitudes.

1096

1097 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).

1098 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).

1099 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}

1100 and B{C{lons}} locations (C{bool}).

1101

1102 @return: A single interpolated geoid height (C{float}) or a

1103 list of interpolated geoid heights (C{float}s).

1104

1105 @raise GeoidError: Insufficient or non-matching number of

1106 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}

1107 geoid file is closed.

1108

1109 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this

1110 geoid's lat- or longitude range.

1111 '''

1112 return _height_called(self, lats, lons, Error=GeoidError, **wrap)

1113

1114 @Property_RO

1115 def _highest_ltd(self):

1116 '''(INTERNAL) Cache for L{highest} mesthod.

1117 '''

1118 return self._llh3minmax(True, -12, -4)

1119

1120 def highest(self, LatLon=None, full=False): # PYCHOK full

1121 '''Return the location and largest height of this geoid.

1122

1123 @kwarg LatLon: Optional class to return the location and height

1124 (C{LatLon}) or C{None}.

1125 @kwarg full: Search the full or limited latitude range (C{bool}).

1126

1127 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1128 lon, height)} otherwise a B{C{LatLon}} instance

1129 with the lat-, longitude and height of the highest

1130 grid location.

1131 '''

1132 llh = self._highest if full or self.cropped else self._highest_ltd

1133 return self._llh3LL(llh, LatLon)

1134

1135 def _lat2y2(self, lat2):

1136 # convert earth lat(s) to min and max grid y indices

1137 ys, m = [], self._pgm.nlat - 1

1138 for lat in lat2:

1139 y, _ = self._g2yx2(*self._ll2g2(lat, 0))

1140 ys.append(max(min(int(y), m), 0))

1141 return min(ys), max(ys) + 1

1142

1143 def _ll2g2(self, lat, lon):

1144 # convert earth (lat, lon) to grid (lat, lon), uncropped

1145 while lon < 0:

1146 lon += _360_0

1147 return lat, lon

1148

1149 def _llh3minmax(self, highest=True, *lat2):

1150 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid

1151 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)

1152 y = x = 0

1153 h = self._raw(y, x)

1154 if highest:

1155 for j, r in self._raw2(*lat2):

1156 m = max(r)

1157 if m > h:

1158 h, y, x = m, j, r.index(m)

1159 else: # lowest

1160 for j, r in self._raw2(*lat2):

1161 m = min(r)

1162 if m < h:

1163 h, y, x = m, j, r.index(m)

1164 h *= self._pgm.Scale

1165 h += self._pgm.Offset

1166 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)

1167

1168 @Property_RO

1169 def _lowest_ltd(self):

1170 '''(INTERNAL) Cache for L{lowest}.

1171 '''

1172 return self._llh3minmax(False, 0, 8)

1173

1174 def lowest(self, LatLon=None, full=False): # PYCHOK full

1175 '''Return the location and lowest height of this geoid.

1176

1177 @kwarg LatLon: Optional class to return the location and height

1178 (C{LatLon}) or C{None}.

1179 @kwarg full: Search the full or limited latitude range (C{bool}).

1180

1181 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,

1182 lon, height)} otherwise a B{C{LatLon}} instance

1183 with the lat-, longitude and height of the lowest

1184 grid location.

1185 '''

1186 llh = self._lowest if full or self.cropped else self._lowest_ltd

1187 return self._llh3LL(llh, LatLon)

1188

1189 def _raw(self, y, x):

1190 # get the ushort geoid height at geoid index (y, x),

1191 # like GeographicLib/Geoid.hpp real rawval(is, iy)

1192 p = self._pgm

1193 if x < 0:

1194 x += p.nlon

1195 elif x >= p.nlon:

1196 x -= p.nlon

1197 h = p.nlon // 2

1198 if y < 0:

1199 y = -y

1200 elif y >= p.nlat:

1201 y = (p.nlat - 1) * 2 - y

1202 else:

1203 h = 0

1204 x += h if x < h else -h

1205 self._seek(y, x)

1206 h = _unpack(self._endian, self._egm.read(self._u2B))

1207 return h[0]

1208

1209 def _raws(self, y, x, ijs):

1210 # get bilinear 4-tuple or 10x12 cubic matrix

1211 return tuple(self._raw(y + j, x + i) for i, j in ijs)

1212

1213 def _raw2(self, *lat2):

1214 # yield a 2-tuple (y, ushorts) for each row or for

1215 # the rows between two (or more) earth lat values

1216 p = self._pgm

1217 g = self._egm

1218 e = self._Rendian

1219 n = self._Ru2B

1220 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat

1221 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)

1222 self._seek(s, 0) # to start of row s

1223 for y in range(s, t):

1224 yield y, _unpack(e, g.read(n))

1225

1226 def _seek(self, y, x):

1227 # position geoid to grid index (y, x)

1228 p, g = self._pgm, self._egm

1229 if g:

1230 b = p.skip + (y * p.nlon + x) * self._u2B

1231 g.seek(b, _SEEK_SET)

1232 return b # position

1233 raise GeoidError('closed file: %r' % (p.egm,)) # IOError

1234

1235

1236 class GeoidPGM(_GeoidBase):

1237 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth

1238 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/

1239 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1240 html/geoid.html#geoidinst>} datasets but based on C{SciPy}

1241 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/

1242 generated/scipy.interpolate.RectBivariateSpline.html>} or

1243 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1244 scipy.interpolate.interp2d.html>} interpolation.

1245

1246 Use any of the U{egm84-, egm96- or egm2008-*.pgm

1247 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}

1248 datasets. However, unless cropped, an entire C{egm*.pgm} dataset

1249 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/

1250 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}

1251 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/

1252 scipy.interpolate.interp2d.html>} interpolator and converted from

1253 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory

1254 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/

1255 geoid.html#geoidinst>} file size and may exceed the available memory,

1256 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.

1257 '''

1258 _endian = '>u2'

1259

1260 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84

1261 kind=3, name=NN, smooth=0):

1262 '''New L{GeoidPGM} interpolator.

1263

1264 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/

1265 html/geoid.html#geoidinst>} file name (C{egm*.pgm}).

1266 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,

1267 north, east}) or 2-tuple (C{(south, west), (north, east)}),

1268 in C{degrees90} lat- and C{degrees180} longitudes or a

1269 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.

1270 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

1271 or L{a_f2Tuple}), default C{WGS84}.

1272 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for

1273 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/

1274 reference/generated/scipy.interpolate.RectBivariateSpline.html>},

1275 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/

1276 reference/generated/scipy.interpolate.interp2d.html>}, -3

1277 for C{interp2d cubic} or -5 for C{interp2d quintic}.

1278 @kwarg name: Optional geoid name (C{str}).

1279 @kwarg smooth: Smoothing factor for U{RectBivariateSpline

1280 <https://docs.SciPy.org/doc/scipy/reference/generated/

1281 scipy.interpolate.RectBivariateSpline.html>}

1282 only (C{int}).

1283

1284 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},

1285 B{C{kind}} or B{C{smooth}}.

1286

1287 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.

1288

1289 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.

1290

1291 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.

1292

1293 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}

1294 warning as exception.

1295

1296 @raise TypeError: Invalid B{C{datum}}.

1297

1298 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/

1299 html/geoid.html#geoidinst>} file sizes are based on a 2-byte

1300 C{int} height converted to 8-byte C{dtype float64} for C{scipy}

1301 interpolators. Therefore, internal memory usage is 4 times the

1302 C{egm*.pgm} file size and may exceed the available memory,

1303 especially with 32-bit Python. To reduce memory usage, set

1304 keyword argument B{C{crop}} to the region of interest. For example

1305 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://

1306 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}

1307 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.

1308

1309 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.

1310 '''

1311 np = self.numpy

1312 self._u2B = np.dtype(self.endian).itemsize

1313

1314 g = self._open(egm_pgm, datum, kind, name, smooth)

1315 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)

1316 if crop:

1317 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))

1318 self._g2ll2 = self._g2ll2_cropped

1319 self._ll2g2 = self._ll2g2_cropped

1320 if map2(int, np.__version__.split(_DOT_)[:2]) < (1, 9):

1321 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-

1322 self._cropped = True

1323 else:

1324 self._cropped = False

1325

1326 try:

1327 # U{numpy dtype formats are different from Python struct formats

1328 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}

1329 # read all heights, skipping the PGM header lines, converted to float

1330 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale

1331 if p.Offset: # offset

1332 hs = p.Offset + hs

1333 if p.dlat < 0: # flip the rows

1334 hs = np.flipud(hs)

1335 _GeoidBase.__init__(self, hs, p)

1336 except Exception as x:

1337 raise _SciPyIssue(x, _in_, repr(egm_pgm))

1338 finally:

1339 g.close()

1340

1341 def _g2ll2(self, lat, lon):

1342 # convert grid (lat, lon) to earth (lat, lon), uncropped

1343 while lon > _180_0:

1344 lon -= _360_0

1345 return lat, lon

1346

1347 def _g2ll2_cropped(self, lat, lon):

1348 # convert cropped grid (lat, lon) to earth (lat, lon)

1349 return lat, lon - self._lon_og

1350

1351 def _ll2g2(self, lat, lon):

1352 # convert earth (lat, lon) to grid (lat, lon), uncropped

1353 while lon < 0:

1354 lon += _360_0

1355 return lat, lon

1356

1357 def _ll2g2_cropped(self, lat, lon):

1358 # convert earth (lat, lon) to cropped grid (lat, lon)

1359 return lat, lon + self._lon_of

1360

1361 if _FOR_DOCS:

1362 __call__ = _GeoidBase.__call__

1363 height = _GeoidBase.height

1364

1365

1366 class _Gpars(_Named):

1367 '''(INTERNAL) Basic geoid parameters.

1368 '''

1369 # interpolator parameters

1370 dlat = 0 # +/- latitude resolution in C{degrees}

1371 dlon = 0 # longitude resolution in C{degrees}

1372 nlat = 1 # number of latitude knots (C{int})

1373 nlon = 0 # number of longitude knots (C{int})

1374 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat

1375 rlon = 0 # longitude resolution in C{float}, 1 / .dlon

1376 slat = 0 # nothern- or southern most latitude (C{degrees90})

1377 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})

1378

1379 flon = 0 # forward, earth to grid longitude offset

1380 glon = 0 # reverse, grid to earth longitude offset

1381

1382 knots = 0 # number of knots, nlat * nlon (C{int})

1383 skip = 0 # header bytes to skip (C{int})

1384

1385 def __repr__(self):

1386 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for

1387 a in dir(self.__class__)

1388 if a[:1].isupper()))

1389 return _COLONSPACE_(self, t)

1390

1391 def __str__(self):

1392 return Fmt.PAREN(self.classname, repr(self.name))

1393

1394

1395 class _PGM(_Gpars):

1396 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.

1397

1398 # Geoid file in PGM format for the GeographicLib::Geoid class

1399 # Description WGS84 EGM96, 5-minute grid

1400 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html

1401 # DateTime 2009-08-29 18:45:03

1402 # MaxBilinearError 0.140

1403 # RMSBilinearError 0.005

1404 # MaxCubicError 0.003

1405 # RMSCubicError 0.001

1406 # Offset -108

1407 # Scale 0.003

1408 # Origin 90N 0E

1409 # AREA_OR_POINT Point

1410 # Vertical_Datum WGS84

1411 <width> <height>

1412 <pixel>

1413 ...

1414 '''

1415 crop4 = () # 4-tuple (C{south, west, north, east}).

1416 egm = None

1417 glon = 180 # reverse offset, uncropped

1418# pgm = NN # name

1419 sizeB = 0

1420 u2B = 2 # item size of grid height (C{int}).

1421

1422 @staticmethod

1423 def _llstr2floats(latlon):

1424 # llstr to (lat, lon) floats

1425 lat, lon = latlon.split()

1426 return parseDMS2(lat, lon)

1427

1428 # PGM file attributes, CamelCase but not .istitle()

1429 AREA_OR_POINT = str

1430 DateTime = str

1431 Description = str # 'WGS84 EGM96, 5-minute grid'

1432 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'

1433 MaxBilinearError = float

1434 MaxCubicError = float

1435 Offset = float

1436 Origin = _llstr2floats

1437 Pixel = 0

1438 RMSBilinearError = float

1439 RMSCubicError = float

1440 Scale = float

1441 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'

1442 Vertical_Datum = str

1443

1444 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22

1445 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.

1446 '''

1447 self.name = pgm # geoid file name

1448 if itemsize:

1449 self._u2B = itemsize

1450 if sizeB:

1451 self.sizeB = sizeB

1452

1453 t = g.readline() # make sure newline == '\n'

1454 if t != b'P5\n' and t.strip() != b'P5':

1455 raise self._Errorf(_format_, _header_, t)

1456

1457 while True: # read all # Attr ... lines,

1458 try: # ignore empty ones or comments

1459 t = g.readline().strip()

1460 if t.startswith(_bHASH_):

1461 t = t.lstrip(_bHASH_).lstrip()

1462 a, v = map(_ub2str, t.split(None, 1))

1463 f = getattr(_PGM, a, None)

1464 if callable(f) and a[:1].isupper():

1465 setattr(self, a, f(v))

1466 elif t:

1467 break

1468 except (TypeError, ValueError):

1469 raise self._Errorf(_format_, 'Attr', t)

1470 else: # should never get here

1471 raise self._Errorf(_format_, _header_, g.tell())

1472

1473 try: # must be (even) width and (odd) height

1474 nlon, nlat = map(int, t.split())

1475 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \

1476 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):

1477 raise ValueError

1478 except (TypeError, ValueError):

1479 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)

1480

1481 try: # must be 16 bit pixel height

1482 t = g.readline().strip()

1483 self.Pixel = int(t)

1484 if not 255 < self.Pixel < 65536: # >u2 or >H only

1485 raise ValueError

1486 except (TypeError, ValueError):

1487 raise self._Errorf(_format_, 'pixel', t)

1488

1489 for a in dir(_PGM): # set undefined # Attr ... to None

1490 if a[:1].isupper() and callable(getattr(self, a)):

1491 setattr(self, a, None)

1492

1493 if self.Origin is None:

1494 raise self._Errorf(_format_, 'Origin', self.Origin)

1495 if self.Offset is None or self.Offset > 0:

1496 raise self._Errorf(_format_, 'Offset', self.Offset)

1497 if self.Scale is None or self.Scale < EPS:

1498 raise self._Errorf(_format_, 'Scale', self.Scale)

1499

1500 self.skip = g.tell()

1501 self.knots = nlat * nlon

1502

1503 self.nlat, self.nlon = nlat, nlon

1504 self.slat, self.wlon = self.Origin

1505 # note, negative .dlat and .rlat since rows

1506 # are from .slat 90N down in decreasing lat

1507 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon

1508 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0

1509

1510 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0

1511 n = float(self.slat)

1512 s = n + self.dlat * (nlat - 1)

1513 w = self.wlon - self.glon

1514 e = w + self.dlon * nlon

1515 self.crop4 = s, w, n, e

1516

1517 n = self.sizeB - self.skip

1518 if n > 0 and n != (self.knots * self.u2B):

1519 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)

1520

1521 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15

1522 '''Crop the geoid to (south, west, north, east) box.

1523 '''

1524 # flon offset for both west and east

1525 f = 360 if west < 0 else 0

1526 # earth (lat, lon) to grid indices (y, x),

1527 # note y is decreasing, i.e. n < s

1528 s, w = self._lle2yx2(south, west, f)

1529 n, e = self._lle2yx2(north, east, f)

1530 s += 1 # s > n

1531 e += 1 # e > w

1532

1533 hi, wi = self.nlat, self.nlon

1534 # handle special cases

1535 if (s - n) > hi:

1536 n, s = 0, hi # entire lat range

1537 if (e - w) > wi:

1538 w, e, f = 0, wi, 180 # entire lon range

1539 if s == hi and w == n == 0 and e == wi:

1540 return g # use entire geoid as-is

1541

1542 if (e - w) < k1 or (s - n) < (k1 + 1):

1543 raise self._Errorf(_format_, 'swne', (north - south, east - west))

1544

1545 if e > wi > w: # wrap around

1546 # read w..wi and 0..e

1547 r, p = (wi - w), (e - wi)

1548 elif e > w:

1549 r, p = (e - w), 0

1550 else:

1551 raise self._Errorf('%s(%s < %s)', _assert_, w, e)

1552

1553 # convert to bytes

1554 r *= self.u2B

1555 p *= self.u2B

1556 q = wi * self.u2B # stride

1557 # number of rows and cols to skip from

1558 # the original (.slat, .wlon) origin

1559 z = self.skip + (n * wi + w) * self.u2B

1560 # sanity check

1561 if r < 2 or p < 0 or q < 2 or z < self.skip \

1562 or z > self.sizeB:

1563 raise self._Errorf(_format_, _assert_, (r, p, q, z))

1564

1565 # can't use _BytesIO since numpy

1566 # needs .fileno attr in .fromfile

1567 t, c = 0, self._tmpfile()

1568 # reading (s - n) rows, forward

1569 for y in range(n, s): # PYCHOK y unused

1570 g.seek(z, _SEEK_SET)

1571 # Python 2 tmpfile.write returns None

1572 t += c.write(g.read(r)) or r

1573 if p: # wrap around to start of row

1574 g.seek(-q, _SEEK_CUR)

1575 # assert(g.tell() == (z - w * self.u2B))

1576 # Python 2 tmpfile.write returns None

1577 t += c.write(g.read(p)) or p

1578 z += q

1579 c.flush()

1580 g.close()

1581

1582 s -= n # nlat

1583 e -= w # nlon

1584 k = s * e # knots

1585 z = k * self.u2B

1586 if t != z:

1587 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)

1588

1589 # update the _Gpars accordingly, note attributes

1590 # .dlat, .dlon, .rlat and .rlon remain unchanged

1591 self.slat += n * self.dlat

1592 self.wlon += w * self.dlon

1593 self.nlat = s

1594 self.nlon = e

1595 self.flon = self.glon = f

1596

1597 self.crop4 = south, west, north, east

1598 self.knots = k

1599 self.skip = 0 # no header lines in c

1600

1601 c.seek(0, _SEEK_SET)

1602 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-

1603 return c

1604

1605 def _Errorf(self, fmt, *args): # PYCHOK no cover

1606 t = fmt % args

1607 e = self.pgm or NN

1608 if e:

1609 t = _SPACE_(t, _in_, repr(e))

1610 return PGMError(t)

1611

1612 def _lle2yx2(self, lat, lon, flon):

1613 # earth (lat, lon) to grid indices (y, x)

1614 # with .dlat decreasing from 90N .slat

1615 lat -= self.slat

1616 lon += flon - self.wlon

1617 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),

1618 max(0, int(lon * self.rlon)))

1619

1620 def _tmpfile(self):

1621 # create a tmpfile to hold the cropped geoid grid

1622 try:

1623 from tempfile import NamedTemporaryFile as tmpfile

1624 except ImportError: # Python 2.7.16-

1625 from os import tmpfile

1626 t = _os_path.splitext(_os_path.basename(self.pgm))[0]

1627 f = tmpfile(mode='w+b', prefix=t or 'egm')

1628 f.seek(0, _SEEK_SET) # force overwrite

1629 return f

1630

1631 @Property_RO

1632 def pgm(self):

1633 '''Get the geoid file name (C{str}).

1634 '''

1635 return self.name

1636

1637

1638 class PGMError(GeoidError):

1639 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.

1640 '''

1641 pass

1642

1643

1644 def egmGeoidHeights(GeoidHeights_dat):

1645 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/

1646 html/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat

1647 <https://SourceForge.net/projects/geographiclib/files/testdata/>}

1648 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/

1649 geoid.html#testgeoid>}.

1650

1651 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file

1652 (C{str} or C{file} handle).

1653

1654 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,

1655 egm84, egm96, egm2008)}.

1656

1657 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.

1658

1659 @note: Function L{egmGeoidHeights} is used to test the geoids

1660 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module

1661 C{test/testGeoids.py}.

1662 '''

1663 dat = GeoidHeights_dat

1664 if isinstance(dat, bytes):

1665 dat = _BytesIO(dat)

1666

1667 try:

1668 dat.seek(0, _SEEK_SET) # reset

1669 except AttributeError as x:

1670 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)

1671

1672 for t in dat.readlines():

1673 t = t.strip()

1674 if t and not t.startswith(_bHASH_):

1675 lat, lon, egm84, egm96, egm2008 = map(float, t.split())

1676 while lon > _180_0: # EasternLon to earth lon

1677 lon -= _360_0

1678 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)

1679

1680

1681__all__ += _ALL_DOCS(_GeoidBase)

1682

1683 if __name__ == '__main__':

1684

1685 from pygeodesy.lazily import printf, _sys

1686

1687 _crop = ()

1688 _GeoidEGM = GeoidKarney

1689 _kind = 3

1690

1691 geoids = _sys.argv[1:]

1692 while geoids:

1693 geoid = geoids.pop(0)

1694

1695 if '-crop'.startswith(geoid.lower()):

1696 _crop = 20, -125, 50, -65 # CONUS

1697

1698 elif '-karney'.startswith(geoid.lower()):

1699 _GeoidEGM = GeoidKarney

1700

1701 elif '-kind'.startswith(geoid.lower()):

1702 _kind = int(geoids.pop(0))

1703

1704 elif '-pgm'.startswith(geoid.lower()):

1705 _GeoidEGM = GeoidPGM

1706

1707 elif geoid[-4:].lower() in ('.pgm',):

1708 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)

1709 printf(g.toStr(), nt=1, nl=1)

1710 printf(repr(g.pgm), nt=1)

1711 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:

1712 # The height of the EGM96 geoid at Timbuktu

1713 # echo 16:46:33N 3:00:34W | GeoidEval

1714 # => 28.7068 -0.02e-6 -1.73e-6

1715 # The 1st number is the height of the geoid, the 2nd and

1716 # 3rd are its slopes in northerly and easterly direction

1717 t = 'Timbuktu %s' % (g,)

1718 k = {'egm84-15.pgm': '31.2979',

1719 'egm96-5.pgm': '28.7067',

1720 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')

1721 ll = parseDMS2('16:46:33N', '3:00:34W', sep=':')

1722 for ll in (ll, (16.776, -3.009),):

1723 try:

1724 h, ll = g.height(*ll), fstr(ll, prec=6)

1725 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)

1726 except (GeoidError, RangeError) as x:

1727 printf(_COLONSPACE_(t, str(x)))

1728

1729 elif geoid[-4:].lower() in ('.bin',):

1730 g = GeoidG2012B(geoid, kind=_kind)

1731 printf(g.toStr())

1732

1733 else:

1734 raise GeoidError(grid=repr(geoid))

1735

1736_I = int # PYCHOK unused _I

1737 del _intCs # trash ints cache

1738

1739# **) MIT License

1740#

1741# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1742#

1743# Permission is hereby granted, free of charge, to any person obtaining a

1744# copy of this software and associated documentation files (the "Software"),

1745# to deal in the Software without restriction, including without limitation

1746# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1747# and/or sell copies of the Software, and to permit persons to whom the

1748# Software is furnished to do so, subject to the following conditions:

1749#

1750# The above copyright notice and this permission notice shall be included

1751# in all copies or substantial portions of the Software.

1752#

1753# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1754# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1755# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1756# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1757# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1758# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1759# OTHER DEALINGS IN THE SOFTWARE.

1760

1761# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>

1762# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm

1763# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm

1764# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm

1765

1766# _center = 0, 0, 17.2260 # egm2008-1.pgm

1767# _center = 0, 0, 17.1630 # egm96-5.pgm

1768# _center = 0, 0, 18.3296 # egm84-15.pgm

1769

1770# _upperright = 90, 180, 14.8980 # egm2008-1.pgm

1771# _upperright = 90, 180, 13.6050 # egm96-5.pgm

1772# _upperright = 90, 180, 13.0980 # egm84-15.pgm

1773

1774

1775# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm

1776#

1777# 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)

1778#

1779# _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'

1780#

1781# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1782# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1783#

1784# 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)

1785#

1786# _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'

1787#

1788# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1789# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1790#

1791# 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)

1792#

1793# _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'

1794#

1795# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1796# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1797

1798

1799# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm

1800#

1801# 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)

1802#

1803# _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'

1804#

1805# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1806# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1807#

1808# 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)

1809#

1810# _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'

1811#

1812# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979

1813# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979

1814#

1815# 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)

1816#

1817# _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'

1818#

1819# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067

1820# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067

1821

1822

1823# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm

1824#

1825# 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)

1826#

1827# _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'

1828#

1829# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880

1830# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880

1831#

1832# 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)

1833#

1834# _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'

1835#

1836# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979

1837# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979

1838#

1839# 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)

1840#

1841# _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'

1842#

1843# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067

1844# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067