Coverage for pygeodesy/trf.py: 89%
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2# -*- coding: utf-8 -*-
4u'''I{Veness}' Terrestrial Reference Frames (TRF).
6Classes L{RefFrame}, registry L{RefFrames} and L{TRFError}.
8Transcoded from I{Chris Veness'} (C) 2006-2022 JavaScript originals
9U{latlon-ellipsoidal-referenceframe.js<https://GitHub.com/ChrisVeness/geodesy/blob/master/
10latlon-ellipsoidal-referenceframe.js>} and U{latlon-ellipsoidal-referenceframe-txparams.js
11<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}.
13Following 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>}.
16Modern geodetic reference frames: a latitude/longitude point defines a geographic location on,
17above or below the earth’s surface, measured in degrees from the equator and the U{International
18Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above
19the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}.
21This is scratching the surface of complexities involved in high precision geodesy, but may
22be 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>}.
26Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian
27coordinates. The GRS80 ellipsoid is recommended for transformations to geographical coordinates.
29Note 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
31to agree at the centimeter level"}, see also U{QPS/Qinsy<https://Confluence.QPS.NL/qinsy/
32en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}.
34@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -14)
35@var RefFrames.ETRF2005: RefFrame(name='ETRF2005', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -1)
36@var RefFrames.ETRF2008: RefFrame(name='ETRF2008', epoch=2008, datum=Datums.GRS80) .Xforms=(0, 0)
37@var RefFrames.ETRF2014: RefFrame(name='ETRF2014', epoch=2014, datum=Datums.GRS80) .Xforms=(0, -14)
38@var RefFrames.ETRF2020: RefFrame(name='ETRF2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -14)
39@var RefFrames.ETRF88: RefFrame(name='ETRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(0, 0)
40@var RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(0, -1)
41@var RefFrames.ETRF90: RefFrame(name='ETRF90', epoch=1990, datum=Datums.GRS80) .Xforms=(0, -1)
42@var RefFrames.ETRF91: RefFrame(name='ETRF91', epoch=1991, datum=Datums.GRS80) .Xforms=(0, -1)
43@var RefFrames.ETRF92: RefFrame(name='ETRF92', epoch=1992, datum=Datums.GRS80) .Xforms=(0, -1)
44@var RefFrames.ETRF93: RefFrame(name='ETRF93', epoch=1993, datum=Datums.GRS80) .Xforms=(0, -1)
45@var RefFrames.ETRF94: RefFrame(name='ETRF94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -1)
46@var RefFrames.ETRF96: RefFrame(name='ETRF96', epoch=1996, datum=Datums.GRS80) .Xforms=(0, -1)
47@var RefFrames.ETRF97: RefFrame(name='ETRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -1)
48@var RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -4)
49@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -3)
50@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, datum=Datums.GRS80) .Xforms=(15, -5)
51@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, datum=Datums.GRS80) .Xforms=(8, -3)
52@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005, datum=Datums.GRS80) .Xforms=(17, -2)
53@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010, datum=Datums.GRS80) .Xforms=(16, -1)
54@var RefFrames.ITRF2020: RefFrame(name='ITRF2020', epoch=2015, datum=Datums.GRS80) .Xforms=(16, 0)
55@var RefFrames.ITRF88: RefFrame(name='ITRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(3, -4)
56@var RefFrames.ITRF89: RefFrame(name='ITRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(4, -4)
57@var RefFrames.ITRF90: RefFrame(name='ITRF90', epoch=1988, datum=Datums.GRS80) .Xforms=(6, -4)
58@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
59@var RefFrames.ITRF92: RefFrame(name='ITRF92', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
60@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
61@var RefFrames.ITRF94: RefFrame(name='ITRF94', epoch=1993, datum=Datums.GRS80) .Xforms=(4, -4)
62@var RefFrames.ITRF96: RefFrame(name='ITRF96', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -5)
63@var RefFrames.ITRF97: RefFrame(name='ITRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -4)
64@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -6)
65@var RefFrames.NAD83cors96: RefFrame(name='NAD83cors96', epoch=1997, datum=Datums.GRS80) .Xforms=(1, 0)
66@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, datum=Datums.GRS80) .Xforms=(0, -1)
67@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, datum=Datums.GRS80) .Xforms=(1, 0)
68@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
69@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
70'''
72from pygeodesy.basics import map1, neg, isstr, _xinstanceof, _xisscalar, _zip
73from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0, _N_1_0
74from pygeodesy.datums import Datums, _earth_datum, _GDA2020_, _minus, _Names7, \
75 Transform, _S1_S, _WGS84
76from pygeodesy.errors import TRFError, _xattr, _xellipsoidall, _xkwds
77from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, \
78 _datum_, _DOT_, _exists_, _invalid_, _MINUS_, \
79 _NAD83_, _no_, _PLUS_, _reframe_, _s_, _SPACE_, \
80 _STAR_, _to_, _WGS84_, _x_, _intern as _i
81from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
82from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \
83 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
84from pygeodesy.props import deprecated_method, property_doc_, Property_RO, property_RO
85# from pygeodesy.streprs import Fmt, unstr # from .named
86from pygeodesy.units import Epoch, Float
88from math import ceil as _ceil
90__all__ = _ALL_LAZY.trf
91__version__ = '24.02.24'
93_EP0CH = Epoch(0, low=0)
94_Es = {_EP0CH: _EP0CH} # L{Epoch}s, deleted below
95_GRS80 = Datums.GRS80
96_inverse_ = 'inverse'
97_MAS = _MM = _PPB = Float # Units
98_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as
99_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
100_366_0 = _F(sum(_mDays))
101_rates_ = 'rates' # PYCHOK used!
102_Rs = {} # L{TRFXform7Tuple}s de-dup, deleted below
103_S_S1 = _N_1_0 / _S1_S # Transform.s for .s1 == 0
104_v_ = 'v'
105_xform_ = 'xform' # PYCHOK used!
106_Xs = {} # L{TRFXform7Tuple}s de-dup, deleted below
108_ETRF88_ = _i('ETRF88')
109_ETRF89_ = _i('ETRF89')
110_ETRF90_ = _i('ETRF90')
111_ETRF91_ = _i('ETRF91')
112_ETRF92_ = _i('ETRF92')
113_ETRF93_ = _i('ETRF93')
114_ETRF94_ = _i('ETRF94')
115_ETRF96_ = _i('ETRF96')
116_ETRF97_ = _i('ETRF97')
117_ETRF2000_ = _i('ETRF2000')
118_ETRF2005_ = _i('ETRF2005')
119_ETRF2008_ = _i('ETRF2008')
120_ETRF2014_ = _i('ETRF2014')
121_ETRF2020_ = _i('ETRF2020')
122_GDA94_ = _i('GDA94')
123_ITRF_ = _i('ITRF')
124_ITRF88_ = _i('ITRF88')
125_ITRF89_ = _i('ITRF89')
126_ITRF90_ = _i('ITRF90')
127_ITRF91_ = _i('ITRF91')
128_ITRF92_ = _i('ITRF92')
129_ITRF93_ = _i('ITRF93')
130_ITRF94_ = _i('ITRF94')
131_ITRF96_ = _i('ITRF96')
132_ITRF97_ = _i('ITRF97')
133_ITRF2000_ = _i('ITRF2000')
134_ITRF2005_ = _i('ITRF2005')
135_ITRF2008_ = _i('ITRF2008')
136_ITRF2014_ = _i('ITRF2014')
137_ITRF2020_ = _i('ITRF2020')
138_NAD83cors96_ = _i('NAD83cors96')
139_WGS84g1150_ = _i('WGS84g1150')
140_WGS84g1674_ = _i('WGS84g1674')
141_WGS84g1762_ = _i('WGS84g1762')
144def _E(epoch): # deleted below
145 '''(INTERNAL) De-dup L{Epochs}s.
146 '''
147 e = Epoch(_F(epoch))
148 return _Es.setdefault(e, e) # PYCHOK del
151def _P(ps, name, _Ps): # deleted below
152 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
153 '''
154 t = TRFXform7Tuple(map(_F, ps), name=name)
155 return _Ps.setdefault(t, t)
158class RefFrame(_NamedEnumItem):
159 '''Terrestrial Reference Frame (TRF) parameters.
160 '''
161 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
162 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
164 def __init__(self, epoch, datum, name=NN):
165 '''New L{RefFrame}.
167 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
168 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
169 or L{a_f2Tuple}).
170 @kwarg name: Unique, non-empty name (C{str}).
172 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
174 @raise TRFError: Invalid B{C{epoch}}.
176 @raise TypeError: Invalid B{C{datum}}.
177 '''
178 if datum is not _GRS80:
179 _earth_datum(self, datum, raiser=_datum_)
180 self._epoch = _Epoch(epoch)
181 self._Xto = {} # dict of Xforms
182 if name:
183 self._register(RefFrames, name)
185 def __eq__(self, other):
186 return isinstance(other, RefFrame) and other.epoch == self.epoch \
187 and other.datum == self.datum
189 def __lt__(self, other): # for sorting
190 return isinstance(other, RefFrame) and (self.name < other.name
191 or self.epoch < other.epoch)
193 @deprecated_method # PYCHOK Python 3.5+
194 def __matmul__(self, point):
195 '''DEPRECATED on 2024.02.16, use method C{B{point}.toRefFrame}.'''
196 return _toRefFrame(point, self)
198 @property_RO
199 def datum(self):
200 '''Get this reference frame's datum (L{Datum}).
201 '''
202 return self._datum
204 @property_RO
205 def ellipsoid(self):
206 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
207 '''
208 return self._datum.ellipsoid
210 @Property_RO
211 def epoch(self):
212 '''Get this reference frame's epoch (C{Epoch}).
213 '''
214 return self._epoch
216 def toRefFrame(self, point, reframe2, **epoch2_epoch_name):
217 '''Convert an ellipsoidal point from this reframe and from C{epoch} to
218 an other C{reframe2} and C{epoch2 or epoch}.
220 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
221 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
222 @kwarg epoch2_epoch_name: Optional keyword arguments C{B{epoch2}=None},
223 C{B{epoch}=None} and C{B{name}=NN}.
225 @return: A copy of the B{C{point}}, converted or renamed.
227 @raise TypeError: Invalid B{C{point}}.
229 @note: The B{C{point}}'s C{reframe} and C{epoch} are overridden by
230 this reframe respectively B{C{epoch}} or this reframe's epoch.
232 @see: Ellipsoidal methods L{toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
233 and L{toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
234 for more details.
235 '''
236 return _toRefFrame(point, reframe2, reframe=self,
237 **_xkwds(epoch2_epoch_name, name=self.name))
239 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected
240 '''Return this reference frame as a string.
242 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
243 @kwarg name: Override name (C{str}) or C{None} to exclude the
244 reframe's name.
246 @return: This L{RefFrame}'s attributes (C{str}).
247 '''
248 D = self.datum
249 e = self.epoch if epoch is None else _Epoch(epoch)
250 t = (Fmt.EQUAL(name=repr(name or self.name)),
251 Fmt.EQUAL(epoch=e),
252 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
253 return _COMMASPACE_.join(t[int(name is None):])
255 def Xform(self, reframe2):
256 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
258 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
260 @return: The L{TRFXform} instance or C{None} if not available.
262 @raise TypeError: Invalid B{C{reframe2}}.
263 '''
264 _xinstanceof(RefFrame, str, reframe2=reframe2)
265 n2 = reframe2 if isstr(reframe2) else reframe2.name
266 return self._Xto.get(n2, None)
268 def Xforms(self, inverse=False):
269 '''Return all Xforms converting I{from} or I{to} this reference frame or both.
271 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}) or if
272 C{B{inverse}=2} (C{int}) get all I{to} Xforms I{inverted}
273 plus all I{from} Xforms.
275 @return: An L{ADict} of C{name=}L{TRFXform}s I{from} this reframe or if
276 C{B{inverse}=True} I{to} this reframe or if C{B{inverse}=2} both.
277 '''
278 def _Xi(n2, i):
279 for n1, r in RefFrames.items():
280 X = r._Xto.get(n2, None)
281 if X:
282 yield n1, (X.inverse() if i else X)
284 i = inverse == 2
285 d = ADict(_Xi(self.name, i) if inverse else self._Xto)
286 if i:
287 d.update(self._Xto) # from overrides inverted to
288 return d
291class RefFrames(_NamedEnum):
292 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
293 to accommodate the L{_LazyNamedEnumItem} properties.
294 '''
295 def _Lazy(self, epoch, datum=_GRS80, name=NN):
296 '''(INTERNAL) Instantiate the L{RefFrame}.
297 '''
298 return RefFrame(epoch, datum, name=name)
300RefFrames = RefFrames(RefFrame) # PYCHOK singleton
301'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
302# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
303RefFrames._assert(
304 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
305 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
306 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
307 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
308 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
309 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
310 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
311 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
312 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
313 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
314 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
315 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
316 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
317 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
318 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
319 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
320 ITRF88 = _lazy(_ITRF88_, _E(1988)),
321 ITRF89 = _lazy(_ITRF89_, _E(1989)),
322 ITRF90 = _lazy(_ITRF90_, _E(1988)),
323 ITRF91 = _lazy(_ITRF91_, _E(1988)),
324 ITRF92 = _lazy(_ITRF92_, _E(1988)),
325 ITRF93 = _lazy(_ITRF93_, _E(1988)),
326 ITRF94 = _lazy(_ITRF94_, _E(1993)),
327 ITRF96 = _lazy(_ITRF96_, _E(1997)),
328 ITRF97 = _lazy(_ITRF97_, _E(1997)),
329 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
330 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
331 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
332 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
333 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
334 NAD83 = _lazy(_NAD83_, _E(1997)),
335 NAD83cors96 = _lazy(_NAD83cors96_, _E(1997)),
336 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
337 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
338 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
339 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
342class TransformXform(Transform):
343 '''Helmert transformation, extended with an C{Xform} converter.
345 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
346 '''
347 _Xform = None
349 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
350 '''New L{TransformXform}.
352 @kwarg name: Optional name (C{str}), I{not registered}.
354 @see: L{Transform<datums.Transform>} for details.
356 @note: This L{TransformXform}'s name starts with C{"-"} iff
357 I{inversed}.
358 '''
359 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
360 if name:
361 self.name = name
363 def __eq__(self, other):
364 return isinstance(other, TransformXform) and Transform.__eq__(self, other)
366 def __hash__(self):
367 return Transform.__hash__(self)
369 def rename(self, name=NN):
370 '''Change this transform's name.
372 @arg name: New name (C{str}), overriding this transform's Xform's name.
374 @return: The previous name (C{str}).
375 '''
376 X = self.Xform
377 n = name or (X.toStr() if X else NN)
378 return Transform.rename(self, n)
380 def toRefFrame(self, point, name=NN): # PYCHOK signature
381 '''Convert an ellipsoidal point using this transform and Xform.
383 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
385 @return: A copy of the B{C{point}}, converted I{directly} to
386 this transform's Xform's C{refName2} and C{epoch}.
388 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
389 I{ignored}, its C{datum} and C{height} are preserved
390 but I{not} taken into account.
391 '''
392 _ = _xellipsoidall(point)
393 p = point.dup() if self.isunity else point.toTransform(self)
394 X = self.Xform
395 if X: # see _toRefFrame below
396 p._reframe = X.reframe2
397 p._epoch = X.epoch
398 p.rename(name or self.name)
399 return p
401 def toTransform(self, epoch1, **epoch2_inverse):
402 '''Return this transform observed at B{C{epoch1}} as a Helmert
403 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
405 @arg epoch1: Epoch to observe I{from} (C{scalar}).
406 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe
407 I{to} and C{B{inverse}=False}, see method
408 L{toTransform<TRFXform.toTransform>} from
409 L{TRFXform}.
411 @return: The Helmert transform (L{TransformXform}).
413 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
414 missing Xform.
415 '''
416 X = self.Xform
417 if X is None:
418 raise TRFError(Xform=X, txt=MISSING)
419 return X.toTransform(epoch1, **epoch2_inverse)
421 def velocities(self, factor=_MM2M, **Vector_and_kwds):
422 '''Compute the X, Y and Z I{velocities} of this transform.
424 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
425 default from C{milli-meter-} to C{meter-per-year}.
426 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
427 cartesian class and additional C{B{Vector}}
428 keyword arguments to return the I{velocities}.
430 @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}}
431 is specified or C{None} if this transform's Xform is missing.
433 @raise TypeError: Non-scalar B{C{factor}}.
435 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
436 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}.
437 '''
438 v = X = self.Xform
439 if X is not None:
440 r = X.rates * factor # eq (3) ...
441 H = Transform(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot
442 s=_S_S1, name=NN(self.name, _v_))
443 H.s1, H.rx, H.ry, H.rz = 0, self.rx, self.ry, self.rz
444 v = H.transform(r.tx, r.ty, r.tz, inverse=False, # Xyy
445 **Vector_and_kwds)
446 return v
448 @property_doc_(''' the Xform (L{TRFXform}).''')
449 def Xform(self):
450 '''Get this Helmert transform's Xform (L{TRFXform} or C{None}).
451 '''
452 return self._Xform
454 @Xform.setter # PYCHOK setter!
455 def Xform(self, Xform):
456 '''Set this Helmert transform's Xform (L{TRFXform}).
458 @raise TypeError: Invalid B{C{Xform}}.
459 '''
460 _xinstanceof(TRFXform, Xform=Xform)
461 self._Xform = Xform
464class TRFXform7Tuple(_NamedTuple):
465 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
466 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
467 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}.
469 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
470 or C{(T1, T2, T3, D, R1, R2, R3)}.
472 @see: Class L{TransformXform}'s matching keyword argument names.
473 '''
474 _Names_ = _Names7 # ('tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz') == Transform.__init__
475 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
477 def __add__(self, other):
478 _xinstanceof(TRFXform7Tuple, other=other)
479 return type(self)(((a + b) for a, b in _zip(self, other)), name=_PLUS_) # .fsums._add_op
481 def __eq__(self, other):
482 return isinstance(other, TRFXform7Tuple) and all(a == b for a, b in _zip(self, other))
483 # PYCHOK and self.name == other.name
485 def __hash__(self):
486 return self._hash # memoized
488 def __mul__(self, factor):
489 _xisscalar(factor=factor)
490 return type(self)((s * factor for s in self), name=_STAR_) # .fsums._mul_op
492 def __neg__(self):
493 return self.inverse()
495 def __sub__(self, other):
496 _xinstanceof(TRFXform7Tuple, other=other)
497 return type(self)(((a - b) for a, b in _zip(self, other)), name=_MINUS_) # .fsums._sub_op
499 @Property_RO
500 def _hash(self):
501 return hash(s for s in self)
503 def inverse(self, name=NN):
504 '''Return the inverse of this transform.
506 @kwarg name: Optional name (C{str}).
508 @return: Inverse (L{TransformXform}).
509 '''
510 n = name or _minus(self.name)
511 return type(self)(map(neg, self), name=n)
513 @Property_RO
514 def isunity(self):
515 '''Is this a C{unity, identidy} transform (C{bool}).
516 '''
517 return not any(self)
520class TRFXform(_Named):
521 '''A Terrestrial Reference Frame (TRF) converter between two
522 reference frames observed at an C{epoch}.
523 '''
524 _epoch = _EP0CH
525 _epoch_d = _0_0
526 _indir_d = NN # refName
527 _inver_d = False
528 refName1 = \
529 refName2 = NN
530 rates = \
531 xform = None
533 def __init__(self, refName1, refName2, epoch=None, xform=None,
534 rates=None, name=NN):
535 '''New L{trfXform}.
537 @arg refName1: Source reframe (C{str}), converting I{from}.
538 @arg refName2: Destination reframe (C{str}), converting I{to}.
539 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
540 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
541 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}},
542 but in C{units-per-year}.
543 @kwarg name: Optional name (C{str}), overriding the default from
544 method L{toStr<TRFXform.toStr>}.
546 @return: The TRF converter (L{TRFXform}).
548 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}.
549 '''
550 self.refName1 = str(refName1)
551 self.refName2 = str(refName2)
552 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
553 self.epoch = epoch
554 self.xform = xform
555 self.rates = rates
556 self.rename(name or self.toStr())
558 def __add__(self, other):
559 _xinstanceof(TRFXform, other=other)
560 assert self.epoch == other.epoch
561 n = other.name
562 n = NN(self.name, (NN if n.startswith(_MINUS_) else _PLUS_), n)
563 return type(self)(self.refName1, other.refName2, epoch=self.epoch,
564 xform=self.xform + other.xform,
565 rates=self.rates + other.rates,
566 name=n)
568 def __eq__(self, other):
569 return isinstance(other, TRFXform) and self.epoch == other.epoch and \
570 self.xform == other.xform and self.rates == other.rates
572# def __hash__(self):
573# return hash((self.xform._hash * 1e18 + self.rates._hash) * 1e5 + self.epoch)
575 def __lt__(self, other): # for sorting
576 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
577 or self.refName2 < other.refName2
578 or self.epoch < other.epoch)
580 def __neg__(self):
581 return self.inverse()
583 def __repr__(self):
584 return self.toRepr()
586 def __str__(self):
587 return self.toStr()
589 def _at(self, epoch):
590 '''(INTERNAL) Return C{"self.nameB{@}epoch"}.
591 '''
592 n = self.name
593 if epoch != self.epoch:
594 _e = _AT_(NN, epoch)
595 if not n.endswith(_e):
596 n = NN(n, _e)
597 return n
599 @property_doc_(''' the epoch, fractional year (L{Epoch}).''')
600 def epoch(self):
601 '''Get the epoch (L{Epoch}).
602 '''
603 return self._epoch
605 @epoch.setter # PYCHOK setter!
606 def epoch(self, epoch):
607 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
609 @raise TRFError: Invalid B{C{epoch}}.
610 '''
611 e = _Epoch(epoch)
612 if self._epoch != e:
613 self.rename(self._at(e))
614 self._epoch = e
616 @property_RO
617 def epoched(self):
618 '''Get this Xform's I{epoch} deltas (C{float}).
619 '''
620 return self._epoch_d
622 @property_RO
623 def indirected(self):
624 '''Is this an I{indirected} Xform? (C{str}) or C{NN}.
625 '''
626 return self._indir_d
628 def inverse(self, name=NN):
629 '''Get an I{inverse} of this Xform, C{refName1} and C{-2} swapped.
631 @return: Inverse (L{TRFXform}).
632 '''
633 return self.dup(refName1=self.refName2, xform=-self.xform,
634 refName2=self.refName1, rates=-self.rates,
635 name=name or _minus(self.name),
636 _inver_d=not self.inversed)
638 @property_RO
639 def inversed(self):
640 '''Is this an I{inversed} Xform? (C{bool}).
641 '''
642 return self._inver_d
644 def _reframe(self, name, datum=_GRS80):
645 '''(INTERNAL) Get an un-/registered frame.
646 '''
647 r = RefFrames.get(name)
648 if r is None or r.datum != datum:
649 r = RefFrame(self.epoch, datum)
650 r.name = name # unregistered
651 return r
653 @property_RO
654 def reframe1(self):
655 '''Get the un-/registered I{from} frame (C{RefFrame}).
656 '''
657 return self._reframe(self.refName1)
659 @property_RO
660 def reframe2(self):
661 '''Get the un-/registered I{to} frame (C{RefFrame}).
662 '''
663 return self._reframe(self.refName2)
665 def rename(self, name=NN):
666 '''Change this Xform's name.
668 @arg name: New name (C{str}), overriding the base
669 name C{"refName1B{@}epochB{x}refName2"}.
671 @return: The old name (C{str}).
672 '''
673 return _Named.rename(self, name or self.toStr())
675 def toEpoch(self, epoch):
676 '''Convert this Xform to B{C{epoch}}, if needed.
678 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
679 or C{str}).
681 @return: This Xform or a copy converted to B{C{epoch}}.
683 @raise TRFError: Invalid B{C{epoch}}.
684 '''
685 e = _Epoch(epoch)
686 X, d = self, e - self.epoch
687 if d:
688 t = X.xform + X.rates * d
689 X = X.dup(epoch=e, xform=t, name=X._at(e))
690 X._epoch_d += d # abs(d)?
691 return X
693 def toHelmert(self, factor=_MM2M):
694 '''Return the Helmert transform from this Xform scaled accordingly.
696 @kwarg factor: Scale to convert C{milli-meter} (C{scalar}).
698 @return: The Helmert transform (L{TransformXform}).
700 @note: By defaut, Translations are converted from C{milli-meter} to
701 C{meter}, rates from C{milli-arc-seconds} to C{arc-seconds}
702 and scale from C{ppb} to C{ppM}.
703 '''
704 h = self.xform * factor
705 H = TransformXform(name=self.name, **dict(h.items()))
706 H.Xform = self
707 return H
709 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name):
710 '''Convert an ellipsoidal point from this Xform's C{refName1} and
711 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.
713 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
714 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})),
715 overriding this Xform's C{epoch}.
716 @kwarg datum: Optional datum to define a temporary L{RefFrame} from
717 this Xform's C{refName1} or C{refName2} (C{datum}).
718 @kwarg epoch2_name: Optional keyword arguments B{C{epoch2}=None}
719 and C{B{name}=refName1}.
721 @return: A copy of the B{C{point}}, converted or renamed.
723 @see: Method L{RefFrame.toRefFrame} for more details.
724 '''
725 def _r(name):
726 r = RefFrames.get(name)
727 if r is None or r.datum != datum:
728 r = RefFrame(epoch or self.epoch, datum)
729 r.name = name # unregistered
730 return r
732 return _r(self.refName1).toRefFrame(point,
733 _r(self.refName2), epoch=epoch, **epoch2_name)
735 def toRepr(self, **unused): # PYCHOK signature
736 '''Return the represention of this Xform (C{str}).
737 '''
738 return unstr(self.classname, name=self.name, epoch=self.epoch)
740 def toStr(self, epoch=None, **unused): # PYCHOK signature
741 '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}).
743 @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding
744 this Xform's epoch.
745 '''
746 e = self.epoch if epoch is None else _Epoch(epoch)
747 return NN(_AT_(self.refName1, e), _x_, self.refName2)
749 def toTransform(self, epoch, epoch2=None, inverse=False):
750 '''Combine this Xform observed at B{C{epoch}} into a Helmert
751 L{TransformXform}, optionally at B{C{epoch2 or epoch}}.
753 @arg epoch: Epoch to observe I{from} (C{scalar}).
754 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
755 @kwarg inverse: Use the Xform's inverse (C{bool}).
757 @return: The Helmert transform (L{TransformXform}).
759 @raise TRFError: Invalid B{C{epoch}} or B{C{epoch2}}.
761 @see: Method L{toHelmert}.
762 '''
763 # X=self.toEpoch(epoch); if epoch2: X=X.toEpoch(epoch2)
764 e = epoch if epoch2 is None else Epoch(epoch2=epoch2)
765 X = self.toEpoch(e)
766 if inverse:
767 X = X.inverse()
768 return X.toHelmert()
771def date2epoch(year, month, day):
772 '''Return the C{epoch} for a calendar day.
774 @arg year: Year of the date (C{scalar}).
775 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
776 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
778 @return: Epoch, the fractional year (C{float}).
780 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
782 @note: Any B{C{year}} is considered a leap year, i.e. having
783 29 days in February.
784 '''
785 try:
786 y, m, d = map1(int, year, month, day)
787 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
788 e = y + float(sum(_mDays[:m]) + d) / _366_0
789 return Epoch(e, low=0)
791 raise ValueError # _invalid_
792 except (TRFError, TypeError, ValueError) as x:
793 raise TRFError(year=year, month=month, day=day, cause=x)
796def _direct(n1, n2):
797 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
798 '''
799 r = RefFrames.get(n1)
800 return r._Xto.get(n2, None) if r else None
803def _Epoch(e, **kwds):
804 '''(INTERNAL) Get the C{Epoch(B{e})}.
805 '''
806 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)
809def epoch2date(epoch):
810 '''Return the date for a reference frame C{epoch}.
812 @arg epoch: Fractional year (C{scalar}).
814 @return: 3-Tuple C{(year, month, day)}.
816 @raise TRFError: Invalid B{C{epoch}}.
818 @note: Any B{C{year}} is considered a leap year, i.e. having
819 29 days in February.
820 '''
821 e = Epoch(epoch, low=0)
822 y = int(e)
823 d = int(_ceil((e - y) * _366_0))
824 for m, n in enumerate(_mDays[1:]):
825 if d > n:
826 d -= n
827 else:
828 break
829 return y, (m + 1), max(1, d)
832def _eXhaust(n1, n2):
833 '''(INTERNAL) Yield all possible Xforms C{n1} to {n2} via
834 any number of intermediate reframes.
835 '''
836 R = dict(RefFrames)
837 r = R.pop(n1, None)
838 if r:
839 Xs = list(r.Xforms(inverse=2).items())
840 while Xs:
841 n, X = Xs.pop(0)
842 if n == n2:
843 yield X
844 else:
845 r = R.pop(n, None)
846 if r:
847 for n, x in r.Xforms(inverse=2).items():
848 x = x.toEpoch(X.epoch)
849 Xs.append((n, X + x))
852def _indirects(n1, n2):
853 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via
854 I{one} intermediate reframe C{n}.
855 '''
856 def _X4(_Xto, n2):
857 _d = _direct
858 for n, X1 in _Xto.items():
859 X2 = _d(n, n2)
860 if X2:
861 yield X1, X2, n, True # +
862 X2 = _d(n2, n)
863 if X2:
864 yield X1, X2, n, False # -
866 r1 = RefFrames.get(n1)
867 if r1:
868 for X1, X2, n, f in _X4(r1._Xto, n2):
869 e1, e2 = X1.epoch, X2.epoch
870 if e1 < e2: # X1 to e2
871 X1 = X1.toEpoch(e2)
872 e1 = e2
873 elif e1 > e2: # X2 to e1
874 X2 = X2.toEpoch(e1)
875 # U{Appendix, Table 7, last column "Sum of the previous ..."
876 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
877 X = TRFXform(n1, n2, epoch=e1,
878 xform=X1.xform + (X2.xform if f else -X2.xform),
879 rates=X1.rates + (X2.rates if f else -X2.rates),
880 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_,
881 X2._at(e1)))
882 X._epoch_d = X1.epoched + X2.epoched # max, abs?
883 X._indir_d = n # reframe?
884 yield X
887def _reframe(**name_reframe):
888 '''(INTERNAL) Get a C{reframe}.
889 '''
890 if len(name_reframe) == 1:
891 for r in name_reframe.values():
892 break
893 if isstr(r) and r: # not NN
894 r = RefFrames.get(r)
895 if r and isinstance(r, RefFrame):
896 return r
897 raise TRFError(**name_reframe) # _invalid_
900def _toRefFrame(point, reframe2, reframe=None, epoch=None,
901 epoch2=None, name=NN, **LatLon_kwds):
902 '''(INTERNAL) Convert an ellipsoidal point to C{reframe2}
903 and C{epoch2 or epoch or pont.epoch or reframe.epoch}.
904 '''
905 ll = _xellipsoidall(point)
906 r1 = reframe or point.reframe
907 if not r1:
908 t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING)
909 raise TRFError(_no_(_conversion_), txt=t)
911 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r1)
913 e1 = _Epoch(epoch or point.epoch or r1.epoch)
914 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
915 t0 = _toTransform0(r1.name, e1, reframe2.name, e2)
916 if t0 is None:
917 t = _SPACE_(RefFrame.__name__, _AT_(r1.name, e1),
918 _to_, _AT_(reframe2.name, e2))
919 raise TRFError(_no_(_conversion_), txt=t)
921 if t0: # is not ()
922 if t0.isunity:
923 p = point.dup()
924 elif point.datum:
925 p = point.toCartesian() if ll else point
926 p = p.toDatum( r1.datum).toTransform(t0) \
927 .toDatum(reframe2.datum).toDatum(point.datum)
928 if ll:
929 p = p.toLatLon(LatLon=point.classof, **LatLon_kwds)
930 elif ll: # and LatLon_kwds
931 p = point.toTransform(t0, **LatLon_kwds)
932 else:
933 p = point.toTransform(t0)
934 p._reframe = reframe2 # see TRFXform.toRefFrame above
935 p._epoch = _xattr(t0.Xform, epoch=e2)
936 p.rename(name or reframe2.name)
937 else:
938 p = point.dup(name=name) if name else point
939 return p
942def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
943 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
944 '''
945 if n1 == n2 and e1 == e2:
946 return () # unity?
948 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
949 return X # first OK?
951 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
952 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):
953 return () # unity?
955 return None
958def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True, exhaust=False): # MCCABE 16
959 '''(INTERNAL) Yield all possible Helmert transforms, if any.
960 '''
961 class Ts(list): # L{TransformXform}s de-dup
962 def __call__(self, Xs, e1=e1, e2=e2, inverse=False):
963 for X in Xs:
964 if X:
965 T = X.toTransform(e1, epoch2=e2, inverse=inverse)
966 if T not in self:
967 self.append(T)
968 yield T
970 def _k(X):
971 return -X.epoch
973 _Ts = Ts()
975 for T in _Ts((_direct(n1, n2),)):
976 yield T
977 if inverse:
978 for T in _Ts((_direct(n2, n1),), inverse=True):
979 yield T
981 if indirect:
982 for T in _Ts(sorted(_indirects(n1, n2), key=_k)):
983 yield T
984 if inverse:
985 for T in _Ts(sorted(_indirects(n2, n1), key=_k), inverse=True):
986 yield T
988 if exhaust:
989 for T in _Ts(sorted(_eXhaust(n1, n2), key=_k)):
990 yield T
991 for T in _Ts(sorted(_eXhaust(n2, n1), key=_k), inverse=True):
992 yield T
995def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
996 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
997 to an other C{reframe2} at observed at C{epoch2 or epoch}.
999 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
1000 C{None} if no conversion exists.
1002 @see: Function L{trfTransforms} for futher details.
1003 '''
1004 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
1005 indirect=indirect, inverse=inverse, exhaust=exhaust)
1008def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
1009 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
1010 to an other C{reframe2} at observed at C{epoch2 or epoch}.
1012 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
1013 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
1014 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
1015 otherwise C{B{reframe}}'s C{epoch}.
1016 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar}
1017 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}.
1018 @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe,
1019 otherwise only I{direct} B{C{reframe}} to B{C{reframe2}}
1020 transforms (C{bool}).
1021 @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms
1022 (C{bool}).
1023 @kwarg exhaust: If C{True}, exhaustively search for all aggregate, concatenated
1024 transforms, forward and inverse (C{bool}).
1026 @return: A L{TransformXform} instance for each available conversion.
1028 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or
1029 B{C{epoch2}}.
1031 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
1032 '''
1033 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
1034 indirect=indirect, inverse=inverse, exhaust=exhaust)
1037def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse_exhaust):
1038 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
1039 '''
1040 r1 = _reframe(reframe=reframe)
1041 e1 = r1.epoch if epoch is None else _Epoch(epoch)
1042 r2 = _reframe(reframe2=reframe2)
1043 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
1044 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse_exhaust)
1047def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True):
1048 '''Define a new Terrestrial Reference Frame (TRF) converter or get an
1049 existing one.
1051 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
1052 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
1053 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
1054 or C{None} for C{B{reframe2}}'s epoch.
1055 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
1056 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
1057 but in C{units-per-year}.
1058 @kwarg raiser: If C{False}, do not raise an error if the converter
1059 exists, replace it (C{bool}).
1061 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}},
1062 B{C{xform}} and B{C{rates}} are given, return the existing
1063 one (L{TRFXform}) or C{None} if not available.
1065 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
1066 B{C{xform}} or B{C{rates}} or the TRF converter
1067 already exists.
1068 '''
1069 try:
1070 r1 = _reframe(reframe1=reframe1)
1071 r2 = _reframe(reframe2=reframe2)
1072 if epoch is None:
1073 if xform is rates is None:
1074 return r1._Xto.get(r2.name, None)
1075 e = r2.epoch
1076 else:
1077 e = _Epoch(epoch)
1078 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e,
1079 xform=xform, rates=rates)
1080 except (TypeError, ValueError) as x:
1081 t = unstr(trfXform, reframe1, reframe2, epoch=epoch)
1082 raise TRFError(t, cause=x)
1085def _trfX(n1, n2, raiser=True, **epoch_xform_rates):
1086 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
1087 '''
1088 r1 = RefFrames.get(n1)
1089 if r1 is None:
1090 raise ValueError(_invalid_)
1091 r2 = RefFrames.get(n2)
1092 if r2 is None:
1093 raise ValueError(_invalid_)
1094 if raiser:
1095 if n2 in r1._Xto:
1096 raise ValueError(_exists_)
1097 if n1 in r2._Xto:
1098 raise ValueError(_SPACE_(_inverse_, _exists_))
1099 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
1100 return X
1103def _X(*ps): # deleted below
1104 return _P(ps, _xform_, _Xs) # PYCHOK del
1107def _R(*ps): # deleted below
1108 return _P(ps, _rates_, _Rs) # PYCHOK del
1111_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity')
1113# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical
1114# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
1115# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
1116# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
1117# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
1118# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
1119_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
1120 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
1121 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
1122_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
1123 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
1124 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1125_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
1126 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
1127 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1128_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
1129 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
1130 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
1131_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
1132 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1133 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1134_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
1135 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1136 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1137_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
1138 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1139 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1140_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
1141 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
1142 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
1143_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
1144 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
1145 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1146_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1147 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1148 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1149_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1150 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1151 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1152_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1153 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1154 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1155_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1156 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1157 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1159# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1160# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1161# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1162_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1163 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1164 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1165_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1166 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1167 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1168_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1169 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1170 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1171_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1172 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1173 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1174_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1175 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1176 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1177_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1178 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1179 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1180_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1181 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1182 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1183_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1184 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1185 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1186_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1187 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1188 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1189_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1190 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1191 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1192_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1193 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1194 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1195_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1196 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1197 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1199# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1200# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1201_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1202 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1203 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1204# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1205# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1206# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1207# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1208# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1209# xform=_X( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1210# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1211_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1212 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1213 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1214_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1215 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1216 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1217_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1218 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1219 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1220_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1221 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1222 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1223_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1224 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1225 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1226_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1227 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1228 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1229_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1230 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1231 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1232_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1233 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1234 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1235_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1236 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1237 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1238_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1239 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1240 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1242# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1243# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1244# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1245# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1246# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1247_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1248 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1249 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1251_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1252 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1253 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1254_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1255 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1256 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1257_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1258 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1259 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1260_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1261 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1262 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1263_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1264 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1265 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1266_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1267 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1268 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1269_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1270 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1271 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1272_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1273 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1274 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1275_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1276 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1277 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1279# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1280# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1281# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1282# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1283_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1284 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1285 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1286_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1287 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1288 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1290# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1291# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1292# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1293# xform=_P_0_0s,
1294# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1295# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1296# xform=_P_0_0s,
1297# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1298_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1299 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1300 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1301# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1302# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1303# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1304_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1305 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1306 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1307_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1308 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1309 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1310_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1311 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1312 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1313_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1314 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1315 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1316_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1317 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1318 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1319_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1320 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1321 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1322_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1323 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1324 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1325_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1326 xform=_P_0_0s,
1327 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1329# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1330# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1331_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1332 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1333 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1334_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1335 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1336 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1337_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1338 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1339 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1340_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1341 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1342 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1343_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1344 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1345 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1346_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1347 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1348 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1349_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1350 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1351 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1352_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1353 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1354 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1355_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1356 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1357 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1358_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1359 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1360 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1361_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1362 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1363 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1364_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1365 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1366 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1367_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1368 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1369 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1370_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1371 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1372 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1374# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1375# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1376_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1377 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1378 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1379_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1380 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1381 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1382_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1383 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1384 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1385_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1386 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1387 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1388_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1389 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1390 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1391_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1392 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1393 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1394_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1395 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1396 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1397_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1398 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1399 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1400_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1401 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1402 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1403_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1404 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1405 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1406_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1407 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1408 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1409_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1410 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1411 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1412_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1413 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1414 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1415_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1416 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1417 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1419# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1420# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1421# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1422# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1423# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1424_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1425 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1426 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1427# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1428# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1429# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1430_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1431 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1432 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1433# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1434# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1435# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1436_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1437 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1438 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1439# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1440# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1441# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1442_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1443 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1444 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1445# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1446# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1447# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1448_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1449 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1450 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1451_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1452 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1453 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1454_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1455 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1456 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1457_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1458 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1459 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1460_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1461 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1462 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1463_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1464 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1465 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1466_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1467 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1468 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1469_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1470 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1471 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1472_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1473 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1474 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1475_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1476 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1477 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1479# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1480# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1481# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1482_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1483 xform=_P_0_0s,
1484 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1485_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1486 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1487 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1488_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1489 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1490 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1491_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1492 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1493 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1495# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1496# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1497# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1498# rather than the more conventional "position around the coordinate axes")
1499_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1500 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1501 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1502_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1503 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1504 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1505_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1506 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1507 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1509# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1510# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1511# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1512# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1513_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1514 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1515 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1516# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1517# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1518_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1519 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1520 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1521# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
1522# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1523_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1524 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1525 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1526_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1527 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1528 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1529_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage
1530 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1531 rates=_P_0_0s)
1533# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>}
1534trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s)
1535trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s)
1537del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs
1539if __name__ == '__main__':
1541 def _main():
1542 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_
1543 from pygeodesy.lazily import printf
1544 from time import localtime
1546 D = date2epoch.__name__
1547 E = epoch2date.__name__
1548 y = localtime()[0]
1549 for m in range(1, 13):
1550 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1551 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1552 e = date2epoch(y, m, d)
1553 t = epoch2date(e)
1554 x = NN if t == (y, m, d) else _STAR_
1555 e = '%.3f' % (e,)
1556 e = '%s, %s(%s)' % (e, E, e)
1557 t = '%d,%3d,%3d' % t
1558 printf('# %s = %s = %s %s', f, e, t, x)
1560 # __doc__ of this file, force all into registery
1561 def _RFs():
1562 yield NN
1563 for t in RefFrames.toRepr(all=True).split(_NL_):
1564 t = t.strip(_COMMA_)
1565 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1566 r = RefFrames.get(n)
1567 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1568 yield '%s .Xforms=%s' % (t, x)
1570 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1572 X, t = (), 0 # all form
1573 for r in RefFrames.values():
1574 X += tuple(r._Xto.values())
1575 for X in sorted(X):
1576 t += 1
1577 printf('#%4d %-24s xform=%r', t, X.name, X.xform)
1578 printf('#%29s rates=%r', _SPACE_, X.rates)
1580 t = _MODS.basics._args_kwds_names(Transform.__init__)
1581 for n in TRFXform7Tuple._Names_:
1582 if n not in t:
1583 raise AssertionError(_SPACE_(n, _vs_, t))
1585 _main()
1586 del _main
1588# **) MIT License
1589#
1590# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1591#
1592# Permission is hereby granted, free of charge, to any person obtaining a
1593# copy of this software and associated documentation files (the "Software"),
1594# to deal in the Software without restriction, including without limitation
1595# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1596# and/or sell copies of the Software, and to permit persons to whom the
1597# Software is furnished to do so, subject to the following conditions:
1598#
1599# The above copyright notice and this permission notice shall be included
1600# in all copies or substantial portions of the Software.
1601#
1602# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1603# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1604# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1605# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1606# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1607# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1608# OTHER DEALINGS IN THE SOFTWARE.
1610# % python -m pygeodesy.trf
1611#
1612# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1613# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1614# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1615# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1616# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1617# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1618# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1619# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1620# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1621# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1622# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1623# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1624# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1625# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1626# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1627# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1628# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1629# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1630# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1631# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1632# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1633# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1634# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1635# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1636# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1637# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1638# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1639# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1640# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1641# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1642# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1643# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1644# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1645# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1646# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1647# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1648# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1649# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1650# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1651# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1652# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1653# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1654# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1655# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1656# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1657# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1658# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1659# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1661# 1 WGS84g1150@2004xITRF2000 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1662# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1663# 2 NAD83cors96@1997xNAD83 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1664# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1665# 3 ITRF88@2015xETRF2014 xform=xform(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
1666# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1667# 4 ITRF89@2015xETRF2000 xform=xform(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
1668# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1669# 5 ITRF89@2015xETRF2014 xform=xform(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
1670# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1671# 6 ITRF89@2015xETRF2020 xform=xform(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
1672# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1673# 7 ITRF89@1989xETRF89 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1674# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1675# 8 ITRF90@1984xWGS84 xform=xform(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
1676# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1677# 9 ITRF90@2015xETRF2000 xform=xform(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
1678# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1679# 10 ITRF90@1989xETRF90 xform=xform(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1680# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1681# 11 ITRF90@1997xNAD83 xform=xform(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
1682# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1683# 12 ITRF91@2015xETRF2000 xform=xform(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
1684# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1685# 13 ITRF91@1989xETRF91 xform=xform(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1686# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1687# 14 ITRF92@2015xETRF2000 xform=xform(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
1688# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1689# 15 ITRF92@2015xETRF2014 xform=xform(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
1690# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1691# 16 ITRF92@2015xETRF2020 xform=xform(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
1692# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1693# 17 ITRF92@1989xETRF92 xform=xform(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1694# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1695# 18 ITRF93@2015xETRF2000 xform=xform(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
1696# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1697# 19 ITRF93@2015xETRF2014 xform=xform(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
1698# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1699# 20 ITRF93@2015xETRF2020 xform=xform(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
1700# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1701# 21 ITRF93@1989xETRF93 xform=xform(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1702# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1703# 22 ITRF94@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1704# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1705# 23 ITRF94@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1706# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1707# 24 ITRF94@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1708# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1709# 25 ITRF94@1989xETRF94 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1710# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1711# 26 ITRF96@1989xETRF96 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1712# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1713# 27 ITRF97@1989xETRF97 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1714# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1715# 28 ITRF2000@1994xGDA94 xform=xform(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
1716# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1717# 29 ITRF2000@2015xETRF2000 xform=xform(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
1718# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1719# 30 ITRF88@2015xETRF2000 xform=xform(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
1720# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1721# 31 ITRF88@2015xETRF2020 xform=xform(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
1722# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1723# 32 ITRF96@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1724# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1725# 33 ITRF97@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1726# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1727# 34 ITRF2000@2015xETRF2014 xform=xform(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
1728# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1729# 35 ITRF90@2015xETRF2014 xform=xform(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
1730# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1731# 36 ITRF90@2015xETRF2020 xform=xform(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
1732# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1733# 37 ITRF91@2015xETRF2014 xform=xform(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
1734# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1735# 38 ITRF96@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1736# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1737# 39 ITRF97@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1738# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1739# 40 ITRF2000@2015xETRF2020 xform=xform(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
1740# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1741# 41 ITRF91@2015xETRF2020 xform=xform(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
1742# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1743# 42 ITRF96@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1744# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1745# 43 ITRF97@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1746# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1747# 44 ITRF2000@2020xGDA2020 xform=xform(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
1748# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1749# 45 ITRF2000@1988xITRF88 xform=xform(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
1750# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1751# 46 ITRF2000@1988xITRF89 xform=xform(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
1752# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1753# 47 ITRF2000@1988xITRF90 xform=xform(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
1754# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1755# 48 ITRF2000@1988xITRF91 xform=xform(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
1756# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1757# 49 ITRF2000@1988xITRF92 xform=xform(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
1758# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1759# 50 ITRF2000@1988xITRF93 xform=xform(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
1760# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1761# 51 ITRF2000@1997xITRF94 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1762# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1763# 52 ITRF2000@1997xITRF96 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1764# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1765# 53 ITRF97@1997xITRF96 xform=xform(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
1766# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1767# 54 ITRF2000@1997xITRF97 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1768# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1769# 55 ITRF2000@1997xNAD83 xform=xform(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
1770# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1771# 56 ITRF2005@2015xETRF2000 xform=xform(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
1772# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1773# 57 ITRF2005@1989xETRF2005 xform=xform(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1774# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1775# 58 ITRF2005@1994xGDA94 xform=xform(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
1776# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1777# 59 ITRF2005@1997xNAD83 xform=xform(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
1778# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1779# 60 ITRF2005@2015xETRF2014 xform=xform(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
1780# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1781# 61 ITRF2005@2015xETRF2020 xform=xform(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
1782# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1783# 62 ITRF2005@2020xGDA2020 xform=xform(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
1784# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1785# 63 ITRF2005@2000xITRF2000 xform=xform(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
1786# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1787# 64 ITRF2008@1994xGDA94 xform=xform(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
1788# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1789# 65 ITRF2008@1997xNAD83 xform=xform(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
1790# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1791# 66 ITRF96@1997xNAD83 xform=xform(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
1792# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1793# 67 ITRF2008@2015xETRF2000 xform=xform(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
1794# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1795# 68 ITRF2008@2015xETRF2014 xform=xform(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
1796# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1797# 69 ITRF2008@2015xETRF2020 xform=xform(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
1798# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1799# 70 ITRF2008@2020xGDA2020 xform=xform(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
1800# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1801# 71 ITRF2008@2000xITRF2000 xform=xform(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
1802# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1803# 72 ITRF2008@2000xITRF88 xform=xform(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
1804# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1805# 73 ITRF2008@2000xITRF89 xform=xform(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
1806# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1807# 74 ITRF2008@2000xITRF90 xform=xform(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
1808# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1809# 75 ITRF2008@2000xITRF91 xform=xform(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
1810# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1811# 76 ITRF2008@2000xITRF92 xform=xform(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
1812# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1813# 77 ITRF2008@2000xITRF93 xform=xform(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
1814# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
1815# 78 ITRF2008@2000xITRF94 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1816# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1817# 79 ITRF2008@2000xITRF96 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1818# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1819# 80 ITRF2008@2000xITRF97 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1820# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1821# 81 ITRF2008@2005xITRF2005 xform=xform(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
1822# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1823# 82 ITRF2014@2015xETRF2000 xform=xform(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
1824# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1825# 83 ITRF2014@2015xETRF2014 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
1826# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1827# 84 ITRF2014@2015xETRF2020 xform=xform(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
1828# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1829# 85 ITRF2014@2020xGDA2020 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1830# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
1831# 86 ITRF2014@2010xITRF2000 xform=xform(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
1832# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1833# 87 ITRF2014@2010xITRF2005 xform=xform(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
1834# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1835# 88 ITRF2014@2010xITRF2008 xform=xform(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
1836# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1837# 89 ITRF2014@2010xITRF88 xform=xform(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
1838# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1839# 90 ITRF2014@2010xITRF89 xform=xform(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
1840# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1841# 91 ITRF2014@2010xITRF90 xform=xform(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
1842# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1843# 92 ITRF2014@2010xITRF91 xform=xform(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
1844# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1845# 93 ITRF2014@2010xITRF92 xform=xform(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
1846# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1847# 94 ITRF2014@2010xITRF93 xform=xform(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
1848# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1849# 95 ITRF2014@2010xITRF94 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1850# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1851# 96 ITRF2014@2010xITRF96 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1852# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1853# 97 ITRF2014@2010xITRF97 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1854# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1855# 98 ITRF2020@2015xETRF2000 xform=xform(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
1856# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1857# 99 ITRF2020@2015xETRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
1858# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1859# 100 ITRF2020@2015xETRF2020 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
1860# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1861# 101 ITRF2020@2015xITRF2000 xform=xform(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
1862# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1863# 102 ITRF2020@2015xITRF2005 xform=xform(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
1864# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1865# 103 ITRF2020@2015xITRF2008 xform=xform(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
1866# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1867# 104 ITRF2020@2015xITRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
1868# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1869# 105 ITRF2020@2015xITRF88 xform=xform(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
1870# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1871# 106 ITRF2020@2015xITRF89 xform=xform(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
1872# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1873# 107 ITRF2020@2015xITRF90 xform=xform(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
1874# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1875# 108 ITRF2020@2015xITRF91 xform=xform(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
1876# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1877# 109 ITRF2020@2015xITRF92 xform=xform(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
1878# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1879# 110 ITRF2020@2015xITRF93 xform=xform(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
1880# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1881# 111 ITRF2020@2015xITRF94 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1882# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1883# 112 ITRF2020@2015xITRF96 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1884# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1885# 113 ITRF2020@2015xITRF97 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1886# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)