1

2# -*- coding: utf-8 -*-

3

4 u'''I{Veness}' Terrestrial Reference Frames (TRF).

5

6 Classes L{RefFrame}, registry L{RefFrames} and L{TRFError}.

7

8 Transcoded from I{Chris Veness'} (C) 2006-2022 JavaScript originals

9 U{latlon-ellipsoidal-referenceframe.js<https://GitHub.com/ChrisVeness/geodesy/blob/master/

10 latlon-ellipsoidal-referenceframe.js>} and U{latlon-ellipsoidal-referenceframe-txparams.js

11<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}.

12

13 Following is a copy of the comments in I{Veness}' U{latlon-ellipsoidal-referenceframe.js

14<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>}.

15

16 Modern geodetic reference frames: a latitude/longitude point defines a geographic location on,

17 above or below the earth’s surface, measured in degrees from the equator and the U{International

18 Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above

19 the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}.

20

21 This is scratching the surface of complexities involved in high precision geodesy, but may

22 be of interest and/or value to those with less demanding requirements. More information U{here

23<https://www.Movable-Type.co.UK/scripts/geodesy-library.html>} and U{here

24<https://www.Movable-Type.co.UK/scripts/geodesy-library.html#latlon-ellipsoidal-referenceframe>}.

25

26 Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian

27 coordinates. The GRS80 ellipsoid is recommended for transformations to geographical coordinates.

28

29 Note WGS84(G730/G873/G1150) are coincident with ITRF at 10-centimetre level, see also U{here

30<ftp://ITRF.ENSG.IGN.Fr/pub/itrf/WGS84.TXT>}. WGS84(G1674) and ITRF20014 / ITRF2008 I{"are likely

31 to agree at the centimeter level"}, see also U{QPS/Qinsy<https://Confluence.QPS.NL/qinsy/

32 en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}.

33

34@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, ellipsoid=Ellipsoid(name='GRS80')

35@var RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, ellipsoid=Ellipsoid(name='GRS80')

36@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, ellipsoid=Ellipsoid(name='GRS80')

37@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, ellipsoid=Ellipsoid(name='GRS80')

38@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, ellipsoid=Ellipsoid(name='GRS80')

39@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005, ellipsoid=Ellipsoid(name='GRS80')

40@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010, ellipsoid=Ellipsoid(name='GRS80')

41@var RefFrames.ITRF90: RefFrame(name='ITRF90', epoch=1988, ellipsoid=Ellipsoid(name='GRS80')

42@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988, ellipsoid=Ellipsoid(name='GRS80')

43@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988, ellipsoid=Ellipsoid(name='GRS80')

44@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997, ellipsoid=Ellipsoid(name='GRS80')

45@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, ellipsoid=Ellipsoid(name='WGS84')

46@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, ellipsoid=Ellipsoid(name='WGS84')

47@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, ellipsoid=Ellipsoid(name='WGS84')

48@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, ellipsoid=Ellipsoid(name='WGS84')

49'''

50

51 from pygeodesy.basics import map1, _xinstanceof, _zip

52 from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, \

53 _0_01, _0_1, _0_26, _0_5, _N_0_5, _1_0

54 from pygeodesy.datums import _a_ellipsoid, Transform

55 from pygeodesy.ellipsoids import Ellipsoids, Fmt, Property_RO

56 from pygeodesy.errors import _ALL_LAZY, _IsnotError, TRFError

57 from pygeodesy.interns import NN, _COMMASPACE_, _cartesian_, _conversion_, \

58 _ellipsoid_, _ellipsoidal_, _epoch_, _exists_, \

59 _GRS80_, _NAD83_, _name_, _no_, _s_, _SPACE_, \

60 _sx_, _sy_, _sz_, _to_, _tx_, _ty_, _tz_, _WGS84_

61# from pygeodesy.lazily import _ALL_LAZY # from .errors

62 from pygeodesy.named import classname, _lazyNamedEnumItem as _lazy, _NamedEnum, \

63 _NamedEnumItem, _NamedDict as _XD, _NamedTuple

64# from pygeodesy.props import Property_RO # from .ellipsoids

65# from pygeodesy.streprs import Fmt # from .ellipsoids

66 from pygeodesy.units import Epoch, Float

67

68 from math import ceil

69

70__all__ = _ALL_LAZY.trf

71__version__ = '23.05.26'

72

73_0_02 = 0.02

74_0_06 = 0.06

75_0_09 = 0.09

76_0_12 = 0.12

77_366_0 = 366.0

78

79_Forward = _0_001 # mm2m, ppb2ppM, mas2as

80_Inverse = -_0_001 # same, inverse transforms

81_mas = _mm = _ppb = Float # as == arcseconds

82_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)

83_N_0_06 = -_0_06

84_N_0_1 = -_0_1

85

86_ETRF2000_ = 'ETRF2000'

87_GDA2020_ = 'GDA2020'

88_GDA94_ = 'GDA94'

89_ITRF_ = 'ITRF'

90_ITRF88_ = 'ITRF88'

91_ITRF89_ = 'ITRF89'

92_ITRF90_ = 'ITRF90'

93_ITRF91_ = 'ITRF91'

94_ITRF92_ = 'ITRF92'

95_ITRF93_ = 'ITRF93'

96_ITRF94_ = 'ITRF94'

97_ITRF96_ = 'ITRF96'

98_ITRF97_ = 'ITRF97'

99_ITRF2000_ = 'ITRF2000'

100_ITRF2005_ = 'ITRF2005'

101_ITRF2008_ = 'ITRF2008'

102_ITRF2014_ = 'ITRF2014'

103_WGS84g1150_ = 'WGS84g1150'

104_WGS84g1674_ = 'WGS84g1674'

105_WGS84g1762_ = 'WGS84g1762'

106

107

108 class Helmert7Tuple(_NamedTuple):

109 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of Helmert transform

110 parameters with translations C{tx}, C{ty} and C{tz} in

111 C{millimeter}, scale C{s} in C{ppb} and rotations C{sx},

112 C{sy} and C{sz} in C{milliarcseconds}.

113

114 @see: L{Datum} L{Transform}.

115 '''

116 _Names_ = (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_)

117 _Units_ = (_mm, _mm, _mm, _ppb, _mas, _mas, _mas)

118

119 def __new__(cls, tx, ty, tz, s, sx, sy, sz, name=NN):

120 '''New L{Helmert7Tuple}.

121 '''

122 t = map1(_F, tx, ty, tz, s, sx, sy, sz)

123 return _NamedTuple.__new__(cls, *t, name=name)

124

125

126 class RefFrame(_NamedEnumItem):

127 '''Terrestrial Reference Frame (TRF) parameters.

128 '''

129 _ellipsoid = None # ellipsoid GRS80 or WGS84 (L{Ellipsoid} or L{Ellipsoid2})

130 _epoch = _0_0 # epoch, calendar year (L{Epoch} or C{float})

131

132 def __init__(self, epoch, ellipsoid, name=NN):

133 '''New L{RefFrame}.

134

135 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).

136 @arg ellipsoid: The ellipsoid (L{Ellipsoid}, L{Ellipsoid2},

137 L{Datum} or L{a_f2Tuple}).

138 @kwarg name: Optional, unique name (C{str}).

139

140 @raise NameError: A L{RefFrame} with that B{C{name}}

141 already exists.

142

143 @raise TRFError: Invalid B{C{epoch}}.

144

145 @raise TypeError: Invalid B{C{ellipsoid}}.

146 '''

147 self._ellipsoid = _a_ellipsoid(ellipsoid, name=name, raiser=_ellipsoid_)

148 self._epoch = Epoch(epoch)

149 self._register(RefFrames, name)

150

151 def __matmul__(self, other): # PYCHOK Python 3.5+

152 '''Convert cartesian or ellipsoidal B{C{other}} to this reframe.

153

154 @raise TypeError: Invalid B{C{other}}.

155 '''

156 try: # only Cartesian- and LatLonEllipsoidalBase

157 return other.toRefFrame(self)

158 except AttributeError:

159 pass

160 raise _IsnotError(_cartesian_, _ellipsoidal_, other=other)

161

162 @Property_RO

163 def ellipsoid(self):

164 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).

165 '''

166 return self._ellipsoid

167

168 @Property_RO

169 def epoch(self):

170 '''Get this reference frame's epoch (C{Epoch}).

171 '''

172 return self._epoch

173

174 def toStr(self, name=NN, **unused): # PYCHOK expected

175 '''Return this reference frame as a text string.

176

177 @kwarg name: Override name (C{str}) or C{None} to exclude the

178 reframe's name.

179

180 @return: This L{RefFrame}'s attributes (C{str}).

181 '''

182 e = self.ellipsoid

183 t = (Fmt.EQUAL(_name_, repr(name or self.name)),

184 Fmt.EQUAL(_epoch_, self.epoch),

185 Fmt.PAREN(Fmt.EQUAL(_ellipsoid_, classname(e)),

186 Fmt.EQUAL(_name_, repr(e.name))))

187 return _COMMASPACE_.join(t[1:] if name is None else t)

188

189

190 class RefFrames(_NamedEnum):

191 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class

192 to accommodate the L{_LazyNamedEnumItem} properties.

193 '''

194 def _Lazy(self, epoch, ellipsoid_name, name=NN):

195 '''(INTERNAL) Instantiate the L{RefFrame}.

196 '''

197 return RefFrame(epoch, Ellipsoids.get(ellipsoid_name), name=name)

198

199 RefFrames = RefFrames(RefFrame) # PYCHOK singleton

200'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''

201# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>

202 RefFrames._assert(

203 ETRF2000 = _lazy(_ETRF2000_, _F(2005), _GRS80_), # ETRF2000(R08)

204 GDA2020 = _lazy(_GDA2020_, _F(2020), _GRS80_), # Australia

205 GDA94 = _lazy(_GDA94_, _F(1994), _GRS80_), # Australia

206 ITRF2000 = _lazy(_ITRF2000_, _F(1997), _GRS80_),

207 ITRF2005 = _lazy(_ITRF2005_, _F(2000), _GRS80_),

208 ITRF2008 = _lazy(_ITRF2008_, _F(2005), _GRS80_), # aka ITRF08

209 ITRF2014 = _lazy(_ITRF2014_, _F(2010), _GRS80_),

210 ITRF90 = _lazy(_ITRF90_, _F(1988), _GRS80_),

211 ITRF91 = _lazy(_ITRF91_, _F(1988), _GRS80_),

212 ITRF93 = _lazy(_ITRF93_, _F(1988), _GRS80_),

213 NAD83 = _lazy(_NAD83_, _F(1997), _GRS80_), # CORS96

214 WGS84 = _lazy(_WGS84_, _F(1984), _WGS84_),

215 WGS84g1150 = _lazy(_WGS84g1150_, _F(2001), _WGS84_),

216 WGS84g1674 = _lazy(_WGS84g1674_, _F(2005), _WGS84_),

217 WGS84g1762 = _lazy(_WGS84g1762_, _F(2005), _WGS84_)) # same epoch

218

219

220 def date2epoch(year, month, day):

221 '''Return the reference frame C{epoch} for a calendar day.

222

223 @arg year: Year of the date (C{scalar}).

224 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).

225 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).

226

227 @return: Epoch, the fractional year (C{float}).

228

229 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.

230

231 @note: Any B{C{year}} is considered a leap year, i.e. having

232 29 days in February.

233 '''

234 try:

235 y, m, d = map1(int, year, month, day)

236 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:

237 return Epoch(y + float(sum(_mDays[:m]) + d) / _366_0, low=0)

238

239 raise ValueError # _invalid_

240 except (TRFError, TypeError, ValueError) as x:

241 raise TRFError(year=year, month=month, day=day, cause=x)

242

243

244 def epoch2date(epoch):

245 '''Return the date for a reference frame C{epoch}.

246

247 @arg epoch: Fractional year (C{scalar}).

248

249 @return: 3-Tuple C{(year, month, day)}.

250

251 @raise TRFError: Invalid B{C{epoch}}.

252

253 @note: Any B{C{year}} is considered a leap year, i.e. having

254 29 days in February.

255 '''

256 e = Epoch(epoch, Error=TRFError, low=0)

257 y = int(e)

258 d = int(ceil(_366_0 * (e - y)))

259 for m, n in enumerate(_mDays[1:]):

260 if d > n:

261 d -= n

262 else:

263 break

264 return y, (m + 1), max(1, d)

265

266

267 def _intermediate(n1, n2):

268 '''(INTERNAL) Find a trf* "in between" C{n1} and C{n2}.

269 '''

270 f1 = set(m for n, m in _trfXs.keys() if n == n1) # from trf1

271 t2 = set(n for n, m in _trfXs.keys() if m == n2) # to trf2

272 n = f1.intersection(t2)

273 return n.pop() if n else NN

274

275

276 def _reframeTransforms2(rf2, rf, epoch):

277 '''(INTERNAL) Get 0, 1 or 2 Helmert L{Transform}s to convert

278 reference frame B{C{rf}} observed at B{C{epoch}} into B{C{rf2}}.

279 '''

280 e = rf.epoch if epoch is None else Epoch(epoch)

281

282 n2 = rf2.name # .upper()

283 n1 = rf.name # .upper()

284 if n1 == n2 or (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) \

285 or (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):

286 return e, () # PYCHOK returns

287

288 if (n1, n2) in _trfXs:

289 return e, (_2Transform((n1, n2), e, _Forward),) # PYCHOK returns

290

291 if (n2, n1) in _trfXs:

292 return e, (_2Transform((n2, n1), e, _Inverse),) # PYCHOK returns

293

294 n = _intermediate(n1, n2)

295 if n:

296 return e, (_2Transform((n1, n), e, _Forward), # PYCHOK returns

297 _2Transform((n, n2), e, _Forward))

298

299 n = _intermediate(n2, n1)

300 if n:

301 return e, (_2Transform((n, n1), e, _Inverse), # PYCHOK returns

302 _2Transform((n2, n), e, _Inverse))

303

304 t = _SPACE_(RefFrame.__name__, repr(n1), _to_, repr(n2))

305 raise TRFError(_no_(_conversion_), txt=t)

306

307

308 def _2Transform(n1_n2, epoch, _Forward_Inverse):

309 '''(INTERNAL) Combine two Helmert transforms from TRF

310 conversion C{_trfXs[n1_n2]} observed at B{C{epoch}}

311 into a single datum L{Transform}.

312

313 @note: Translations are converted from C{millimeter}

314 to C{meter}, rotations from C{milliarcseconds}

315 to C{arcseconds} and scale from C{ppb} to C{ppM}.

316 '''

317 X = _trfXs[n1_n2]

318 e = epoch - X.epoch # fractional delta years

319 d = dict((n, (p + r * e) * _Forward_Inverse) for n, p, r in

320 _zip(Helmert7Tuple._Names_, X.xform, X.rates)) # strict=True

321 return Transform(**d)

322

323

324 def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None):

325 '''Define a new Terrestrial Reference Frame (TRF) conversion.

326

327 @arg reframe1: Source reframe (L{RefFrame}), converting I{from}.

328 @arg reframe2: Destination reframe (L{RefFrame}), converting I{to}.

329 @kwarg epoch: Epoch, a fractional calendar year (C{scalar} or C{str})

330 or C{None} for C{B{reframe2}.epoch}.

331 @kwarg xform: Helmert transform parameters (C{Helmert7Tuple}).

332 @kwarg rates: Helmert rate parameters (C{Helmert7Tuple}).

333

334 @raise TRFError: Invalid B{C{epoch}} or TRF conversion already exists.

335 '''

336 _xinstanceof(RefFrame, reframe1=reframe1, reframe2=reframe2)

337 e = reframe2.epoch if epoch is None else Epoch(epoch=epoch, Error=TRFError)

338 _xinstanceof(Helmert7Tuple, xform=xform, rates=rates)

339 _trfX(reframe1.name, reframe2.name, epoch=e, xform=xform, rates=rates)

340

341

342 def _trfX(n1, n2, **epoch_xform_rates):

343 '''(INTERNAL) New C{_trfXs} entry.

344 '''

345 n1_n2 = n1, n2

346 if n1_n2 in _trfXs:

347 raise TRFError(trfX=n1_n2, txt=_exists_) # _NameError

348 _trfXs[n1_n2] = _XD(X=n1_n2, **epoch_xform_rates)

349

350

351_H = Helmert7Tuple

352_H_0_0s = _H(*_0_0s(len(_H._Names_)))

353# TRF conversions specified as an epoch and dual 7-parameter Helmert transforms. Most from U{Transformation

354# Parameters<http://ITRF.IGN.Fr/trans_para.php>}, more at U{Quinsy QPS<https://confluence.QPS.NL/qinsy/

355# files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}. See also

356# U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/

357# latest/en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.

358_trfXs = dict() # key is [(from_TRF, to_TRF)] 2-tuple

359# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>}

360_trfX(_ITRF2014_, _ITRF2008_, epoch=_F(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>

361 xform=_H( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),

362 rates=_H( _0_0, _0_0, _N_0_1, 0.03, _0_0, _0_0, _0_0))

363_trfX(_ITRF2014_, _ITRF2005_, epoch=_F(2010),

364 xform=_H( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),

365 rates=_H( 0.3, _0_0, _N_0_1, 0.03, _0_0, _0_0, _0_0))

366_trfX(_ITRF2014_, _ITRF2000_, epoch=_F(2010),

367 xform=_H( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),

368 rates=_H( _0_1, _0_1, -1.9, 0.11, _0_0, _0_0, _0_0))

369_trfX(_ITRF2014_, _ITRF97_, epoch=_F(2010),

370 xform=_H( 7.4, _N_0_5, -62.8, 3.8, _0_0, _0_0, _0_26),

371 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

372_trfX(_ITRF2014_, _ITRF96_, epoch=_F(2010),

373 xform=_H( 7.4, _N_0_5, -62.8, 3.8, _0_0, _0_0, _0_26),

374 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

375_trfX(_ITRF2014_, _ITRF94_, epoch=_F(2010),

376 xform=_H( 7.4, _N_0_5, -62.8, 3.8, _0_0, _0_0, _0_26),

377 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

378_trfX(_ITRF2014_, _ITRF93_, epoch=_F(2010),

379 xform=_H( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),

380 rates=_H( -2.8, _N_0_1, -2.5, _0_12, -0.11, -0.19, 0.07))

381_trfX(_ITRF2014_, _ITRF92_, epoch=_F(2010),

382 xform=_H( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, _0_26),

383 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

384_trfX(_ITRF2014_, _ITRF91_, epoch=_F(2010),

385 xform=_H( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, _0_26),

386 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

387_trfX(_ITRF2014_, _ITRF90_, epoch=_F(2010),

388 xform=_H( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, _0_26),

389 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

390_trfX(_ITRF2014_, _ITRF89_, epoch=_F(2010),

391 xform=_H( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, _0_26),

392 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

393_trfX(_ITRF2014_, _ITRF88_, epoch=_F(2010),

394 xform=_H( 25.4, _N_0_5, -154.8, 11.29, _0_1, _0_0, _0_26),

395 rates=_H( _0_1, _N_0_5, -3.3, _0_12, _0_0, _0_0, _0_02))

396

397# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}

398# _trfX(_ITRF2008_, _ITRF2005_, epoch=_F(2005), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>

399# xform=_H(_N_0_5, s -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),

400# rates=_H( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))

401_trfX(_ITRF2008_, _ITRF2005_, epoch=_F(2000),

402 xform=_H( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),

403 rates=_H( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))

404_trfX(_ITRF2008_, _ITRF2000_, epoch=_F(2000),

405 xform=_H( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),

406 rates=_H( _0_1, _0_1, -1.8, 0.08, _0_0, _0_0, _0_0))

407_trfX(_ITRF2008_, _ITRF97_, epoch=_F(2000),

408 xform=_H( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, _0_06),

409 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

410_trfX(_ITRF2008_, _ITRF96_, epoch=_F(2000),

411 xform=_H( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, _0_06),

412 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

413_trfX(_ITRF2008_, _ITRF94_, epoch=_F(2000),

414 xform=_H( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, _0_06),

415 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

416_trfX(_ITRF2008_, _ITRF93_, epoch=_F(2000),

417 xform=_H( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),

418 rates=_H( -2.8, _N_0_1, -2.4, _0_09, -0.11, -0.19, 0.07))

419_trfX(_ITRF2008_, _ITRF92_, epoch=_F(2000),

420 xform=_H( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, _0_06),

421 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

422_trfX(_ITRF2008_, _ITRF91_, epoch=_F(2000),

423 xform=_H( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, _0_06),

424 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

425_trfX(_ITRF2008_, _ITRF90_, epoch=_F(2000),

426 xform=_H( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, _0_06),

427 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

428_trfX(_ITRF2008_, _ITRF89_, epoch=_F(2000),

429 xform=_H( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, _0_06),

430 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

431_trfX(_ITRF2008_, _ITRF88_, epoch=_F(2000),

432 xform=_H( 22.8, 2.6, -125.2, 10.41, _0_1, _0_0, _0_06),

433 rates=_H( _0_1, _N_0_5, -3.2, _0_09, _0_0, _0_0, _0_02))

434

435_trfX(_ITRF2005_, _ITRF2000_, epoch=_F(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>

436 xform=_H( _0_1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),

437 rates=_H( -0.2, _0_1, -1.8, 0.08, _0_0, _0_0, _0_0))

438

439_trfX(_ITRF2000_, _ITRF97_, epoch=_F(1997),

440 xform=_H( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),

441 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

442_trfX(_ITRF2000_, _ITRF96_, epoch=_F(1997),

443 xform=_H( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),

444 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

445_trfX(_ITRF2000_, _ITRF94_, epoch=_F(1997),

446 xform=_H( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),

447 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

448_trfX(_ITRF2000_, _ITRF93_, epoch=_F(1988),

449 xform=_H( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),

450 rates=_H( -2.9, -0.2, -0.6, _0_01, -0.11, -0.19, 0.07))

451_trfX(_ITRF2000_, _ITRF92_, epoch=_F(1988),

452 xform=_H( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),

453 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

454_trfX(_ITRF2000_, _ITRF91_, epoch=_F(1988),

455 xform=_H( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),

456 rates=_H( _0_0, -0.6, -1.4, _0_01, _0_0, _0_0, _0_02))

457_trfX(_ITRF2000_, _ITRF90_, epoch=_F(1988),

458 xform=_H( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),

459 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

460_trfX(_ITRF2000_, _ITRF89_, epoch=_F(1988),

461 xform=_H( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),

462 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

463_trfX(_ITRF2000_, _ITRF88_, epoch=_F(1988),

464 xform=_H( 2.47, 1.15, -9.79, 8.95, _0_1, _0_0, -0.18),

465 rates=_H( _0_0, _N_0_06, -0.14, _0_01, _0_0, _0_0, _0_02))

466

467# see U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the

468# analysis of a EUREF GPS campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and

469# Altamimi, Z. U{"Key results of ITRF2014 and implication to ETRS89 realization", EUREF2016

470# <https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.

471_trfX(_ITRF2014_, _ETRF2000_, epoch=_F(2000),

472 xform=_H( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),

473 rates=_H( _0_1, _0_1, -1.9, 0.11, 0.081, 0.49, -0.792))

474_trfX(_ITRF2008_, _ETRF2000_, epoch=_F(2000),

475 xform=_H( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),

476 rates=_H( _0_1, _0_1, -1.8, 0.08, 0.081, 0.49, -0.792))

477_trfX(_ITRF2005_, _ETRF2000_, epoch=_F(2000),

478 xform=_H( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),

479 rates=_H( -0.2, _0_1, -1.8, 0.08, 0.081, 0.49, -0.792))

480_trfX(_ITRF2000_, _ETRF2000_, epoch=_F(2000),

481 xform=_H( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),

482 rates=_H( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))

483

484# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4

485# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>

486# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)

487_trfX(_ITRF2014_, _GDA2020_, epoch=_F(2020),

488 xform=_H_0_0s,

489 rates=_H( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))

490_trfX(_ITRF2008_, _GDA2020_, epoch=_F(2020),

491 xform=_H( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),

492 rates=_H( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))

493_trfX(_ITRF2005_, _GDA2020_, epoch=_F(2020),

494 xform=_H( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),

495 rates=_H( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))

496_trfX(_ITRF2000_, _GDA2020_, epoch=_F(2020),

497 xform=_H(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),

498 rates=_H( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))

499

500# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied

501# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}

502# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",

503# rather than the more conventional "position around the coordinate axes")

504_trfX(_ITRF2008_, _GDA94_, epoch=_F(1994),

505 xform=_H( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),

506 rates=_H( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))

507_trfX(_ITRF2005_, _GDA94_, epoch=_F(1994),

508 xform=_H( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),

509 rates=_H( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))

510_trfX(_ITRF2000_, _GDA94_, epoch=_F(1994),

511 xform=_H( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),

512 rates=_H( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))

513

514# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the

515# International Terrestrial Reference Frame of 2000 and North American Datum of 1983"

516# (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}

517_trfX(_ITRF2000_, _NAD83_, epoch=_F(1997), # note NAD83(CORS96)

518 xform=_H( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),

519 rates=_H( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))

520

521# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/

522# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83

523_trfX(_ITRF2008_, _NAD83_, epoch=_F(1997),

524 xform=_H( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),

525 rates=_H( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))

526_trfX(_ITRF2005_, _NAD83_, epoch=_F(1997),

527 xform=_H( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),

528 rates=_H( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))

529_trfX(_ITRF90_, _NAD83_, epoch=_F(1997),

530 xform=_H( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),

531 rates=_H( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))

532_trfX(_ITRF90_, _WGS84_, epoch=_F(1984),

533 xform=_H( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),

534 rates=_H_0_0s)

535# del _H, _H_0_0s

536

537 if __name__ == '__main__':

538

539 from pygeodesy.interns import _COMMA_, _NL_, _NLATvar_, _STAR_

540 from pygeodesy.lazily import printf

541 from time import localtime

542

543 D = date2epoch.__name__

544 E = epoch2date.__name__

545 y = localtime()[0]

546 for m in range(1, 13):

547 for d in (1, 15, _mDays[m] - 1, _mDays[m]):

548 f = '%s(%d,%3d,%3d)' % (D, y, m, d)

549 e = date2epoch(y, m, d)

550 t = epoch2date(e)

551 x = NN if t == (y, m, d) else _STAR_

552 e = '%.3f' % (e,)

553 e = '%s, %s(%s)' % (e, E, e)

554 t = '%d,%3d,%3d' % t

555 printf('# %s = %s = %s %s', f, e, t, x)

556

557 # __doc__ of this file, force all into registery

558 t = [NN] + RefFrames.toRepr(all=True).split(_NL_)

559 printf(_NLATvar_.join(i.strip(_COMMA_) for i in t))

560

561# **) MIT License

562#

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

564#

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

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

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

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

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

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

571#

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

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

574#

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

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

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

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

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

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

581# OTHER DEALINGS IN THE SOFTWARE.

582

583# % python -m pygeodesy.trf

584#

585# date2epoch(2022, 1, 1) = 2022.003, epoch2date(2022.003) = 2022, 1, 1

586# date2epoch(2022, 1, 15) = 2022.041, epoch2date(2022.041) = 2022, 1, 15

587# date2epoch(2022, 1, 30) = 2022.082, epoch2date(2022.082) = 2022, 1, 30

588# date2epoch(2022, 1, 31) = 2022.085, epoch2date(2022.085) = 2022, 1, 31

589# date2epoch(2022, 2, 1) = 2022.087, epoch2date(2022.087) = 2022, 2, 2 *

590# date2epoch(2022, 2, 15) = 2022.126, epoch2date(2022.126) = 2022, 2, 16 *

591# date2epoch(2022, 2, 28) = 2022.161, epoch2date(2022.161) = 2022, 2, 28

592# date2epoch(2022, 2, 29) = 2022.164, epoch2date(2022.164) = 2022, 3, 1 *

593# date2epoch(2022, 3, 1) = 2022.167, epoch2date(2022.167) = 2022, 3, 2 *

594# date2epoch(2022, 3, 15) = 2022.205, epoch2date(2022.205) = 2022, 3, 16 *

595# date2epoch(2022, 3, 30) = 2022.246, epoch2date(2022.246) = 2022, 3, 31 *

596# date2epoch(2022, 3, 31) = 2022.249, epoch2date(2022.249) = 2022, 4, 1 *

597# date2epoch(2022, 4, 1) = 2022.251, epoch2date(2022.251) = 2022, 4, 1

598# date2epoch(2022, 4, 15) = 2022.290, epoch2date(2022.290) = 2022, 4, 15

599# date2epoch(2022, 4, 29) = 2022.328, epoch2date(2022.328) = 2022, 4, 29

600# date2epoch(2022, 4, 30) = 2022.331, epoch2date(2022.331) = 2022, 4, 30

601# date2epoch(2022, 5, 1) = 2022.333, epoch2date(2022.333) = 2022, 5, 1

602# date2epoch(2022, 5, 15) = 2022.372, epoch2date(2022.372) = 2022, 5, 15

603# date2epoch(2022, 5, 30) = 2022.413, epoch2date(2022.413) = 2022, 5, 30

604# date2epoch(2022, 5, 31) = 2022.415, epoch2date(2022.415) = 2022, 6, 1 *

605# date2epoch(2022, 6, 1) = 2022.418, epoch2date(2022.418) = 2022, 6, 2 *

606# date2epoch(2022, 6, 15) = 2022.456, epoch2date(2022.456) = 2022, 6, 16 *

607# date2epoch(2022, 6, 29) = 2022.495, epoch2date(2022.495) = 2022, 6, 30 *

608# date2epoch(2022, 6, 30) = 2022.497, epoch2date(2022.497) = 2022, 7, 1 *

609# date2epoch(2022, 7, 1) = 2022.500, epoch2date(2022.500) = 2022, 7, 1

610# date2epoch(2022, 7, 15) = 2022.538, epoch2date(2022.538) = 2022, 7, 16 *

611# date2epoch(2022, 7, 30) = 2022.579, epoch2date(2022.579) = 2022, 7, 30

612# date2epoch(2022, 7, 31) = 2022.582, epoch2date(2022.582) = 2022, 7, 31

613# date2epoch(2022, 8, 1) = 2022.585, epoch2date(2022.585) = 2022, 8, 1

614# date2epoch(2022, 8, 15) = 2022.623, epoch2date(2022.623) = 2022, 8, 15

615# date2epoch(2022, 8, 30) = 2022.664, epoch2date(2022.664) = 2022, 8, 31 *

616# date2epoch(2022, 8, 31) = 2022.667, epoch2date(2022.667) = 2022, 9, 1 *

617# date2epoch(2022, 9, 1) = 2022.669, epoch2date(2022.669) = 2022, 9, 2 *

618# date2epoch(2022, 9, 15) = 2022.708, epoch2date(2022.708) = 2022, 9, 16 *

619# date2epoch(2022, 9, 29) = 2022.746, epoch2date(2022.746) = 2022, 9, 30 *

620# date2epoch(2022, 9, 30) = 2022.749, epoch2date(2022.749) = 2022, 10, 1 *

621# date2epoch(2022, 10, 1) = 2022.751, epoch2date(2022.751) = 2022, 10, 1

622# date2epoch(2022, 10, 15) = 2022.790, epoch2date(2022.790) = 2022, 10, 15

623# date2epoch(2022, 10, 30) = 2022.831, epoch2date(2022.831) = 2022, 10, 30

624# date2epoch(2022, 10, 31) = 2022.833, epoch2date(2022.833) = 2022, 10, 31

625# date2epoch(2022, 11, 1) = 2022.836, epoch2date(2022.836) = 2022, 11, 1

626# date2epoch(2022, 11, 15) = 2022.874, epoch2date(2022.874) = 2022, 11, 15

627# date2epoch(2022, 11, 29) = 2022.913, epoch2date(2022.913) = 2022, 11, 29

628# date2epoch(2022, 11, 30) = 2022.915, epoch2date(2022.915) = 2022, 12, 1 *

629# date2epoch(2022, 12, 1) = 2022.918, epoch2date(2022.918) = 2022, 12, 2 *

630# date2epoch(2022, 12, 15) = 2022.956, epoch2date(2022.956) = 2022, 12, 16 *

631# date2epoch(2022, 12, 30) = 2022.997, epoch2date(2022.997) = 2022, 12, 31 *

632# date2epoch(2022, 12, 31) = 2023.000, epoch2date(2023.000) = 2023, 1, 1 *