Coverage for pygeodesy/trf.py: 95%
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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, -4)
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, -5)
65@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, datum=Datums.GRS80) .Xforms=(0, -1)
66@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, datum=Datums.GRS80) .Xforms=(0, 0)
67@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
68@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
69'''
71from pygeodesy.basics import map1, neg, isstr, _xinstanceof, _xisscalar, _zip
72from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0
73from pygeodesy.datums import Datums, _earth_datum, _minus, Transform, _WGS84
74from pygeodesy.errors import TRFError, _xkwds
75from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, _datum_, \
76 _DOT_, _exists_, _invalid_, _MINUS_, _NAD83_, _no_, \
77 _PLUS_, _reframe_, _s_, _SPACE_, _sx_, _sy_, _sz_, _to_, \
78 _tx_, _ty_, _tz_, _WGS84_, _x_, _intern as _i
79from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
80from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \
81 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
82from pygeodesy.props import Property, Property_RO, property_RO
83# from pygeodesy.streprs import Fmt, unstr # from .named
84from pygeodesy.units import Epoch, Float
86from math import ceil
88__all__ = _ALL_LAZY.trf
89__version__ = '24.02.09'
91_EP0CH = Epoch(0, low=0)
92_Es = {_EP0CH: _EP0CH} # L{Epoch}s de_dup, deleted below
93_GRS80 = Datums.GRS80
94_inverse_ = 'inverse'
95_MAS = _MM = _PPB = Float # Units
96_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as
97_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
98_366_0 = _F(sum(_mDays))
99_Ps = {} # L{TRFXform7Tuple}s de-dup, deleted below
100_v_ = 'v'
102_ETRF88_ = _i('ETRF88')
103_ETRF89_ = _i('ETRF89')
104_ETRF90_ = _i('ETRF90')
105_ETRF91_ = _i('ETRF91')
106_ETRF92_ = _i('ETRF92')
107_ETRF93_ = _i('ETRF93')
108_ETRF94_ = _i('ETRF94')
109_ETRF96_ = _i('ETRF96')
110_ETRF97_ = _i('ETRF97')
111_ETRF2000_ = _i('ETRF2000')
112_ETRF2005_ = _i('ETRF2005')
113_ETRF2008_ = _i('ETRF2008')
114_ETRF2014_ = _i('ETRF2014')
115_ETRF2020_ = _i('ETRF2020')
116_GDA94_ = _i('GDA94')
117_GDA2020_ = _i('GDA2020')
118_ITRF_ = _i('ITRF')
119_ITRF88_ = _i('ITRF88')
120_ITRF89_ = _i('ITRF89')
121_ITRF90_ = _i('ITRF90')
122_ITRF91_ = _i('ITRF91')
123_ITRF92_ = _i('ITRF92')
124_ITRF93_ = _i('ITRF93')
125_ITRF94_ = _i('ITRF94')
126_ITRF96_ = _i('ITRF96')
127_ITRF97_ = _i('ITRF97')
128_ITRF2000_ = _i('ITRF2000')
129_ITRF2005_ = _i('ITRF2005')
130_ITRF2008_ = _i('ITRF2008')
131_ITRF2014_ = _i('ITRF2014')
132_ITRF2020_ = _i('ITRF2020')
133_WGS84g1150_ = _i('WGS84g1150')
134_WGS84g1674_ = _i('WGS84g1674')
135_WGS84g1762_ = _i('WGS84g1762')
136# del _i
139def _E(epoch): # deleted below
140 '''(INTERNAL) De-dup L{Epochs}s.
141 '''
142 e = Epoch(_F(epoch))
143 return _Es.setdefault(e, e) # PYCHOK deleted
146def _xellipsoidal(point):
147 '''(INTERNAL) Check an ellipsoidal position.
148 '''
149 m = _MODS.ellipsoidalBase
150 _xinstanceof(m.CartesianEllipsoidalBase,
151 m.LatLonEllipsoidalBase, point=point)
152 return isinstance(point, m.CartesianEllipsoidalBase)
155class RefFrame(_NamedEnumItem):
156 '''Terrestrial Reference Frame (TRF) parameters.
157 '''
158 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
159 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
161 def __init__(self, epoch, datum, name=NN):
162 '''New L{RefFrame}.
164 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
165 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
166 or L{a_f2Tuple}).
167 @kwarg name: Unique, non-empty name (C{str}).
169 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
171 @raise TRFError: Invalid B{C{epoch}}.
173 @raise TypeError: Invalid B{C{datum}}.
174 '''
175 if datum is not _GRS80:
176 _earth_datum(self, datum, raiser=_datum_)
177 self._epoch = _Epoch(epoch)
178 self._Xs = {} # dict of Xforms
179 if name:
180 self._register(RefFrames, name)
182 def __eq__(self, other):
183 return isinstance(other, RefFrame) and other.epoch == self.epoch \
184 and other.datum == self.datum
186 def __lt__(self, other): # for sorting
187 return isinstance(other, RefFrame) and (self.name < other.name
188 or self.epoch < other.epoch)
190 def __matmul__(self, point): # PYCHOK Python 3.5+
191 '''Convert an ellipsoidal B{C{point}} to this reframe and epoch.
193 @see: Method C{toRefFrame}.
194 '''
195 _xellipsoidal(point)
196 return point.toRefFrame(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}
218 to 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 and B{C{epoch}} or this reframe's epoch.
232 @see: Ellipsoidal methods L{LatLon.toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
233 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
234 for more details.
235 '''
236 _xellipsoidal(point)
237 kwds = _xkwds(epoch2_epoch_name, name=self.name)
238 p = point.dup(reframe=self) if point.reframe != self else point
239 return p.toRefFrame(reframe2, reframe=self, **kwds)
241 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected
242 '''Return this reference frame as a text string.
244 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
245 @kwarg name: Override name (C{str}) or C{None} to exclude the
246 reframe's name.
248 @return: This L{RefFrame}'s attributes (C{str}).
249 '''
250 D = self.datum
251 e = self.epoch if epoch is None else _Epoch(epoch)
252 t = (Fmt.EQUAL(name=repr(name or self.name)),
253 Fmt.EQUAL(epoch=e),
254 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
255 return _COMMASPACE_.join(t[1:] if name is None else t)
257 def Xform(self, reframe2):
258 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
260 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
262 @return: The L{TRFXform} instance or C{None} if not available.
264 @raise TypeError: Invalid B{C{reframe2}}.
265 '''
266 _xinstanceof(RefFrame, str, reframe2=reframe2)
267 n2 = reframe2 if isstr(reframe2) else reframe2.name
268 return self._Xs.get(n2, None)
270 def Xforms(self, inverse=False):
271 '''Return all Xforms converting I{from} or I{to} this reference frame.
273 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}).
275 @return: An L{ADict} of I{from} C{[refName2]=}L{TRFXform}s) or if
276 C{B{inverse}=True} of I{to} C{[refName1]=}L{TRFXform}s).
277 '''
278 def _Xi(n2):
279 for n1, r in RefFrames.items():
280 if n2 in r._Xs:
281 yield n1, r
283 return ADict(_Xi(self.name)) if inverse else ADict(self._Xs)
286class RefFrames(_NamedEnum):
287 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
288 to accommodate the L{_LazyNamedEnumItem} properties.
289 '''
290 def _Lazy(self, epoch, datum=_GRS80, name=NN):
291 '''(INTERNAL) Instantiate the L{RefFrame}.
292 '''
293 return RefFrame(epoch, datum, name=name)
295RefFrames = RefFrames(RefFrame) # PYCHOK singleton
296'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
297# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
298RefFrames._assert(
299 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
300 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
301 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
302 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
303 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
304 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
305 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
306 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
307 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
308 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
309 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
310 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
311 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
312 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
313 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
314 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
315 ITRF88 = _lazy(_ITRF88_, _E(1988)),
316 ITRF89 = _lazy(_ITRF89_, _E(1989)),
317 ITRF90 = _lazy(_ITRF90_, _E(1988)),
318 ITRF91 = _lazy(_ITRF91_, _E(1988)),
319 ITRF92 = _lazy(_ITRF92_, _E(1988)),
320 ITRF93 = _lazy(_ITRF93_, _E(1988)),
321 ITRF94 = _lazy(_ITRF94_, _E(1993)),
322 ITRF96 = _lazy(_ITRF96_, _E(1997)),
323 ITRF97 = _lazy(_ITRF97_, _E(1997)),
324 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
325 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
326 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
327 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
328 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
329 NAD83 = _lazy(_NAD83_, _E(1997)), # aka CORS96
330 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
331 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
332 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
333 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
336class TransformXform(Transform):
337 '''Helmert transformation, extended with an C{Xform} converter.
339 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
340 '''
341 _Xform = None
343 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
344 '''New L{TransformXform}.
346 @kwarg name: Optional name (C{str}), I{not registered}.
348 @see: L{Transform<datums.Transform>} for details.
350 @note: The name of this L{TransformXform} starts with C{"-"}
351 if its C{Xform} was I{inversed}.
352 '''
353 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
354 if name:
355 self.name = name
357 def __eq__(self, other):
358 return isinstance(other, TransformXform) and Transform.__eq__(self, other)
360 def rename(self, name=NN):
361 '''Change this transform and its Xform's name.
363 @arg name: The new name (C{str}), overriding
364 the base name.
366 @return: The old name (C{str}).
367 '''
368 X = self.Xform
369 return Transform.rename(self, name or (X.toStr() if X else NN))
371 def toRefFrame(self, point, name=NN): # PYCHOK signature
372 '''Convert an ellipsoidal point using this transform and Xform.
374 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
376 @return: A copy of the B{C{point}}, converted I{directly} to
377 this transform's Xform's C{refName2} and C{epoch}.
379 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
380 I{ignored}, its C{datum} and C{height} are preserved
381 but I{not} taken into account.
382 '''
383 C = _xellipsoidal(point)
384 c = point.dup() if C else point.toCartesian()
385 r = c.toTransforms_(self)
386 if not C: # i.e. back to LatLon
387 r = r.toLatLon(datum=point.datum, height=point.height,
388 LatLon=point.classof)
389 X = self.Xform
390 if X:
391 r.reframe = X.reframe2
392 r.epoch = X.epoch
394 r.rename(name or self.name)
395 return r
397 def toTransform(self, epoch1, **epoch2_inverse):
398 '''Return this transform observed at B{C{epoch1}} as a Helmert
399 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
401 @arg epoch1: Epoch to observe I{from} (C{scalar}).
402 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
403 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} and
404 C{B{inverse}=False}, see class Xform's method
405 L{toTransform<TRFXform.toTransform>}.
407 @return: The Helmert transform (L{TransformXform}).
409 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
410 missing Xform.
411 '''
412 X = self.Xform
413 if not X:
414 raise TRFError(Xform=X, txt=MISSING)
415 X = X.dup(epoch=epoch1)
416 _ = X.rename()
417 return X.toTransform(epoch1, **epoch2_inverse)
419 def velocities(self, factor=_MM2M):
420 '''Compute the X, Y and Z I{velocities} of this transform.
422 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}), default
423 from C{milli-meter-} to C{meter-per-year}.
425 @return: A L{Vector3Tuple}C{(x, y, z)} or C{None}.
427 @raise TypeError: Non-scalar B{C{factor}}.
429 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
430 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}.
431 '''
432 v = self.Xform
433 if v is not None:
434 r = v.rates * factor # eq (3) ...
435 t = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot
436 s1=0, name=NN(self.name, _v_))
437 v = t.transform(r.tx, r.ty, r.tz) # Xyy
438 return v
440 @Property
441 def Xform(self):
442 '''Get the Xform of this Helmert (L{TRFXform} or C{None}).
443 '''
444 return self._Xform
446 @Xform.setter # PYCHOK setter!
447 def Xform(self, Xform):
448 '''Set the Xform of this Helmert (L{TRFXform}).
450 @raise TypeError: Invalid B{C{Xform}}.
451 '''
452 _xinstanceof(TRFXform, Xform=Xform)
453 self._Xform = Xform
456class TRFXform7Tuple(_NamedTuple):
457 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
458 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
459 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}.
461 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
462 or C{(T1, T2, T3, D, R1, R2, R3)}.
464 @see: Class L{TransformXform}'s matching keyword argument names.
465 '''
466 _Names_ = (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_) # == kwds
467 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
469 def __add__(self, other):
470 '''Return the sum of this and an other L{TRFXform7Tuple}.
471 '''
472 _xinstanceof(TRFXform7Tuple, other=other)
473 return type(self)(((s + t) for s, t in _zip(self, other)),
474 name=_PLUS_) # .fsums._add_op_
476 def __eq__(self, other):
477 return isinstance(other, TRFXform7Tuple) and all(s == t for s, t in
478 _zip(self, other))
480 def __hash__(self):
481 return self._hash # memoized
483 def __mul__(self, factor):
484 _xisscalar(factor=factor)
485 return type(self)(s * factor for s in self)
487 def __neg__(self):
488 return self.inverse()
490 @Property_RO
491 def _hash(self):
492 return hash(s for s in self)
494 def inverse(self, name=NN):
495 '''Return the inverse of this transform.
497 @kwarg name: Optional name (C{str}).
499 @return: Inverse (L{TransformXform}).
500 '''
501 n = name or _minus(self.name)
502 return type(self)(map(neg, self), name=n)
504 @Property_RO
505 def isunity(self):
506 '''Is this a C{unity, identidy} transform (C{bool}).
507 '''
508 return not any(self)
511class TRFXform(_Named):
512 '''A Terrestrial Reference Frame (TRF) converter between two
513 reference frames observed at an C{epoch}.
514 '''
515 _epoch = _EP0CH
516 _epoch_d = _0_0
517 _indir_d = \
518 _inver_d = False
519 refName1 = \
520 refName2 = NN
521 rates = \
522 xform = TRFXform7Tuple(_0_0s(len(
523 TRFXform7Tuple._Names_)))
525 def __init__(self, refName1, refName2, epoch=None,
526 xform=None, rates=None, name=NN):
527 '''New L{trfXform}.
529 @arg refName1: Source reframe (C{str}), converting I{from}.
530 @arg refName2: Destination reframe (C{str}), converting I{to}.
531 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
532 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
533 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
534 but in C{units-per-year}.
535 @kwarg name: Optional name (C{str})
537 @return: The TRF converter (L{TRFXform}).
539 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}.
540 '''
541 self.refName1 = str(refName1)
542 self.refName2 = str(refName2)
543 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
544 self.epoch = epoch
545 self.xform = xform
546 self.rates = rates
547 self.rename(name or self.toStr())
549 def __eq__(self, other):
550 return isinstance(other, TRFXform) and self.epoch == other.epoch and \
551 self.xform == other.xform and self.rates == other.rates
553 def __lt__(self, other): # for sorting
554 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
555 or self.refName2 < other.refName2
556 or self.epoch < other.epoch)
558 def __neg__(self):
559 return self.inverse()
561 def __repr__(self):
562 return self.toRepr()
564 def _at(self, epoch):
565 '''(INTERNAL) Return C{self.name@epoch}.
566 '''
567 n = self.name
568 if epoch != self.epoch:
569 _e = _AT_(NN, epoch)
570 if not n.endswith(_e):
571 n = NN(n, _e)
572 return n
574 @Property
575 def epoch(self):
576 '''Get the epoch (L{Epoch}).
577 '''
578 return self._epoch
580 @epoch.setter # PYCHOK setter!
581 def epoch(self, epoch):
582 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
584 @raise TRFError: Invalid B{C{epoch}}.
585 '''
586 e = _Epoch(epoch)
587 if self._epoch != e:
588 self._epoch = e
589 self.rename(self._at(e))
591 @property_RO
592 def epoched(self):
593 '''Get this Xform's I{epoch} deltas (C{float}).
594 '''
595 return self._epoch_d
597 def _7Helmert(self, epoch, factor=_MM2M):
598 '''(INTERNAL) Get the Helmert parameters observed at C{epoch}
599 and converted by I{signed} factor C{factor} (C{dict}).
600 '''
601 e = epoch - self.epoch # delta in fractional years
602 # dict((self.toEpoch(epoch).xform * factor).items())
603 return dict((n, (x + r * e) * factor) for n, x, r in
604 _zip(TRFXform7Tuple._Names_, self.xform, self.rates))
606 def inverse(self, name=NN):
607 '''Return the inverse of this Xform.
609 @return: Inverse (L{TRFXform}).
610 '''
611 return self.dup(refName1=self.refName2, xform=-self.xform,
612 refName2=self.refName1, rates=-self.rates,
613 name=name or _minus(self.name),
614 _inver_d=not self.inversed)
616 @property_RO
617 def indirected(self):
618 '''Is this an I{indirected} Xform? (C{bool}).
619 '''
620 return self._indir_d
622 @property_RO
623 def inversed(self):
624 '''Is this an I{inversed} Xform? (C{bool}).
625 '''
626 return self._inver_d
628 def _reframe(self, name, datum=_GRS80):
629 '''(INTERNAL) Get an un-/registered frame.
630 '''
631 r = RefFrames.get(name)
632 if r is None or r.datum != datum:
633 r = RefFrame(self.epoch, datum)
634 r.name = name # unregistered
635 return r
637 @property_RO
638 def reframe1(self):
639 '''Get the un-/registered I{from} frame (C{RefFrame}).
640 '''
641 return self._reframe(self.refName1)
643 @property_RO
644 def reframe2(self):
645 '''Get the un-/registered I{to} frame (C{RefFrame}).
646 '''
647 return self._reframe(self.refName2)
649 def rename(self, name=NN):
650 '''Change this Xform's name.
652 @arg name: The new name (C{str}), overriding the
653 base name C{"refName1@epochxrefName2"}.
655 @return: The old name (C{str}).
656 '''
657 return _Named.rename(self, name or self.toStr())
659 def toEpoch(self, epoch):
660 '''Convert this Xform to B{C{epoch}}, if needed.
662 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
663 or C{str}).
665 @return: This Xform or a copy converted to B{C{epoch}}.
667 @raise TRFError: Invalid B{C{epoch}}.
668 '''
669 e = _Epoch(epoch) - self.epoch
670 if e:
671 t = self.xform + self.rates * e
672 X = self.dup(epoch=epoch, xform=t,
673 name=self._at(epoch))
674 X._epoch_d += e
675 else:
676 X = self
677 return X
679 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name):
680 '''Convert an ellipsoidal point from this Xform's C{refName1} and
681 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.
683 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
684 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})), overriding
685 this Xform's C{epoch}.
686 @kwarg datum: Optional datum to define a temporary L{RefFrame} from this
687 Xform's C{refName1} or C{refName2} (C{datum}).
688 @kwarg epoch2_name: Optional keyword arguments B{C{epoch2}=None} and
689 C{B{name}=NN}.
691 @return: A copy of the B{C{point}}, converted or renamed.
693 @see: Method L{RefFrame.toRefFrame} for more details.
694 '''
695 def _r(name):
696 r = RefFrames.get(name)
697 if r is None or r.datum != datum:
698 r = RefFrame(self.epoch, datum)
699 r.name = name # unregistered
700 return r
702 return _r(self.refName1).toRefFrame(point,
703 _r(self.refName2), epoch=epoch, **epoch2_name)
705 def toRepr(self, **unused): # PYCHOK signature
706 '''Return the represention of this Xform (C{str}).
707 '''
708 return unstr(self.classname, epoch=self.epoch, name=self.name)
710 def toStr(self, epoch=None, **unused): # PYCHOK signature
711 '''Return this Xform as C{"refName1@epochxrefName2"} (C{str}).
713 @kwarg epoch: Epoch (C{scalar}), overriding this Xform's epoch.
714 '''
715 e = epoch or self.epoch
716 return NN(_AT_(self.refName1, e), _x_, self.refName2)
718 def toTransform(self, epoch1, epoch2=None, inverse=False):
719 '''Combine this Xform observed at B{C{epoch1}} into a Helmert
720 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
722 @arg epoch1: Epoch to observe I{from} (C{scalar}).
723 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
724 @kwarg inverse: Invert the Helmert tranform (C{bool}).
726 @return: The Helmert transform (L{TransformXform}).
728 @raise TRFError: Invalid B{C{epoch1}} or B{C{epoch2}}.
730 @note: Translations are converted from C{milli-meter} to
731 C{meter}, shift rates from C{milli-arc-seconds} to
732 C{arc-seconds} and scale from C{ppb} to C{ppM}.
733 '''
734 e = Epoch(epoch2=epoch1 if epoch2 is None else epoch2)
735 X = self.dup() if e == epoch1 else self.toEpoch(epoch1)
736 if inverse:
737 X = X.inverse()
738 H = TransformXform(name=X._at(e), **X._7Helmert(e))
739 H.Xform = X
740 X.epoch = e
741 return H
744def date2epoch(year, month, day):
745 '''Return the C{epoch} for a calendar day.
747 @arg year: Year of the date (C{scalar}).
748 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
749 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
751 @return: Epoch, the fractional year (C{float}).
753 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
755 @note: Any B{C{year}} is considered a leap year, i.e. having
756 29 days in February.
757 '''
758 try:
759 y, m, d = map1(int, year, month, day)
760 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
761 e = y + float(sum(_mDays[:m]) + d) / _366_0
762 return Epoch(e, low=0)
764 raise ValueError # _invalid_
765 except (TRFError, TypeError, ValueError) as x:
766 raise TRFError(year=year, month=month, day=day, cause=x)
769def epoch2date(epoch):
770 '''Return the date for a reference frame C{epoch}.
772 @arg epoch: Fractional year (C{scalar}).
774 @return: 3-Tuple C{(year, month, day)}.
776 @raise TRFError: Invalid B{C{epoch}}.
778 @note: Any B{C{year}} is considered a leap year, i.e. having
779 29 days in February.
780 '''
781 e = _Epoch(epoch, low=0)
782 y = int(e)
783 d = int(ceil(_366_0 * (e - y)))
784 for m, n in enumerate(_mDays[1:]):
785 if d > n:
786 d -= n
787 else:
788 break
789 return y, (m + 1), max(1, d)
792def _Epoch(e, **kwds):
793 '''(INTERNAL) Get the C{Epoch(B{e})}.
794 '''
795 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)
798def _eT0Ds4(inst, reframe, epoch, reframe2, epoch2):
799 '''(INTERNAL) Get epoch, a Helmert L{Transform}s or 0-tuple, datum
800 and datum2 to convert B{C{refFrame}} observed at B{C{epoch}}
801 into B{C{refFrame2}} observed at C{epoch2 or epoch}.
802 '''
803 r = reframe or inst.reframe
804 if not r:
805 t = _SPACE_(_DOT_(repr(inst), _reframe_), MISSING)
806 raise TRFError(_no_(_conversion_), txt=t)
808 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r)
810 e1 = _Epoch(epoch or inst.epoch or r.epoch)
811 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
813 t0 = _toTransform0(r.name, e1, reframe2.name, e2)
814 if t0 is None:
815 t = _SPACE_(RefFrame.__name__, _AT_(r.name, e1),
816 _to_, _AT_(reframe2.name, e2))
817 raise TRFError(_no_(_conversion_), txt=t)
819 if t0: # not ()
820 e2 = t0.Xform.epoch
821 return e2, t0, r.datum, reframe2.datum
824def _direct(n1, n2):
825 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
826 '''
827 X = RefFrames.get(n1)
828 if X:
829 X = X._Xs.get(n2, None)
830 return X
833def _indirects(n1, n2):
834 '''(INTERNAL) Yield all Xforms "between" C{n1} and C{n2}.
835 '''
836 def _X3(_Xs, n2):
837 for n, X1 in _Xs.items():
838 X2 = _direct(n, n2)
839 if X2:
840 yield X1, X2, True # +
841 X2 = _direct(n2, n)
842 if X2:
843 yield X1, X2, False # -
845 r = RefFrames.get(n1)
846 if r:
847 for X1, X2, f in _X3(r._Xs, n2):
848 e1, e2 = X1.epoch, X2.epoch
849 if e1 < e2: # X1 to e2
850 X1 = X1.toEpoch(e2)
851 e1 = e2
852 elif e1 > e2: # X2 to e1
853 X2 = X2.toEpoch(e1)
854 # U{Appendix, Table 7, last column "Sum of the previous ..."
855 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
856 X = TRFXform(n1, n2, epoch=e1,
857 xform=X1.xform + (X2.xform if f else -X2.xform),
858 rates=X1.rates + (X2.rates if f else -X2.rates),
859 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_,
860 X2._at(e1)))
861 X._epoch_d = X1.epoched + X2.epoched # max, abs?
862 X._indir_d = True # reframe?
863 yield X
866def _P(*ps): # deleted below
867 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
868 '''
869 t = TRFXform7Tuple(map(_F, ps))
870 return _Ps.setdefault(t, t) # PYCHOK del
873def _reframe(**name_reframe):
874 '''(INTERNAL) Get a C{reframe}.
875 '''
876 if len(name_reframe) == 1:
877 for n, r in name_reframe.items():
878 break
879 if isstr(r):
880 r = RefFrames.get(r)
881 if r and isinstance(r, RefFrame):
882 return r
883 raise TRFError(**name_reframe) # _invalid_
886def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
887 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
888 '''
889 if (n1 == n2 and e1 == e2):
890 return () # unity?
892 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
893 return X # first OK?
895 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
896 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):
897 return () # unity?
899 return None
902def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True):
903 '''(INTERNAL) Yield all possible Helmert transforms, if any.
904 '''
905 def _k(X):
906 return -X.epoch
908 X = _direct(n1, n2)
909 if X:
910 yield X.toTransform(e1, epoch2=e2)
912 if inverse:
913 X = _direct(n2, n1)
914 if X:
915 yield X.toTransform(e1, epoch2=e2, inverse=True)
917 if indirect:
918 for X in sorted(_indirects(n1, n2), key=_k):
919 yield X.toTransform(e1, epoch2=e2)
921 if inverse:
922 for X in sorted(_indirects(n2, n1), key=_k):
923 yield X.toTransform(e1, epoch2=e2, inverse=True)
926def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True):
927 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
928 to an other C{reframe2} at observed at C{epoch2 or epoch}.
930 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
931 C{None} if no conversion exists.
933 @see: Function L{trfTransforms} for futher details.
934 '''
935 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
936 indirect=indirect, inverse=inverse)
939def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True):
940 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
941 to an other C{reframe2} at observed at C{epoch2 or epoch}.
943 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
944 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
945 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
946 otherwise C{B{reframe}}'s C{epoch}.
947 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar}
948 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}.
949 @kwarg indirect: If C{True}, include double transforms via I{one} intermediate
950 reframe, otherwise only direct transforms between B{C{reframe1}
951 and B{C{reframe2}} (C{bool}).
952 @kwarg inverse: If C{True}, include inverse, otherwise only foward transforms
953 (C{bool}).
955 @return: A L{TransformXform} instance for each conversion.
957 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or
958 B{C{epoch2}}.
960 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
961 '''
962 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
963 indirect=indirect, inverse=inverse)
966def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse):
967 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
968 '''
969 r1 = _reframe(reframe=reframe)
970 e1 = r1.epoch if epoch is None else _Epoch(epoch)
971 r2 = _reframe(reframe2=reframe2)
972 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
973 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse)
976def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None):
977 '''Define a new Terrestrial Reference Frame (TRF) converter.
979 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
980 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
981 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
982 or C{None} for C{B{reframe2}}'s epoch.
983 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
984 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
985 but in C{units-per-year}.
987 @return: The new TRF converter (L{TRFXform}).
989 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
990 B{C{xform}} or B{C{rates}} or the TRF converter
991 already exists.
992 '''
993 r1 = _reframe(reframe1=reframe1)
994 r2 = _reframe(reframe2=reframe2)
995 e = r2.epoch if epoch is None else _Epoch(epoch)
996 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
997 return _trfX(r1.name, r2.name, epoch=e, xform=xform, rates=rates)
1000def _trfX(n1, n2, **epoch_xform_rates):
1001 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
1002 '''
1003 r1 = RefFrames.get(n1)
1004 r2 = RefFrames.get(n2)
1005 if r1 and r2:
1006 if n2 in r1._Xs:
1007 t = _exists_
1008 elif n1 in r2._Xs:
1009 t = _SPACE_(_inverse_, _exists_)
1010 else:
1011 r1._Xs[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
1012 return X
1013 else:
1014 t = _invalid_
1015 raise TRFError(TRFXform=_SPACE_(n1, _to_, n2), txt=t) # _NameError
1018# TRF conversions specified as an epoch and 2 sets of 7-parameters. Most from Altamimi, Z. U{"EUREF Technical
1019# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
1020# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
1021# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
1022# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
1023# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
1024_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
1025 xform=_P( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
1026 rates=_P( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
1027_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
1028 xform=_P( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
1029 rates=_P( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1030_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
1031 xform=_P( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
1032 rates=_P( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
1033_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
1034 xform=_P( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
1035 rates=_P( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
1036_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
1037 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1038 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1039_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
1040 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1041 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1042_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
1043 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
1044 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1045_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
1046 xform=_P( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
1047 rates=_P( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
1048_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
1049 xform=_P( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
1050 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1051_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1052 xform=_P( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1053 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1054_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1055 xform=_P( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1056 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1057_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1058 xform=_P( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1059 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1060_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1061 xform=_P( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1062 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1064# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1065# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1066# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1067_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1068 xform=_P( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1069 rates=_P( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1070_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1071 xform=_P( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1072 rates=_P( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1073_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1074 xform=_P( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1075 rates=_P( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1076_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1077 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1078 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1079_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1080 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1081 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1082_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1083 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1084 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1085_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1086 xform=_P( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1087 rates=_P( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1088_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1089 xform=_P( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1090 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1091_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1092 xform=_P( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1093 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1094_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1095 xform=_P( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1096 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1097_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1098 xform=_P( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1099 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1100_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1101 xform=_P( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1102 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1104# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1105# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1106_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1107 xform=_P( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1108 rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1109# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1110# xform=_P( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1111# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1112# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1113# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1114# xform=_P( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1115# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1116_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1117 xform=_P( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1118 rates=_P( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1119_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1120 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1121 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1122_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1123 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1124 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1125_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1126 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1127 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1128_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1129 xform=_P( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1130 rates=_P( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1131_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1132 xform=_P( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1133 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1134_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1135 xform=_P( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1136 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1137_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1138 xform=_P( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1139 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1140_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1141 xform=_P( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1142 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1143_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1144 xform=_P( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1145 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1147# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1148# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1149# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1150# xform=_P( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1151# rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1152_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1153 xform=_P( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1154 rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1156_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1157 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1158 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1159_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1160 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1161 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1162_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1163 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1164 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1165_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1166 xform=_P( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1167 rates=_P( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1168_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1169 xform=_P( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1170 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1171_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1172 xform=_P( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1173 rates=_P( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1174_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1175 xform=_P( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1176 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1177_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1178 xform=_P( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1179 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1180_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1181 xform=_P( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1182 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1184# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1185# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1186# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1187# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1188_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1189 xform=_P( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1190 rates=_P( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1191_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1192 xform=_P( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1193 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1195# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1196# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1197# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1198# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1199# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1200# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1201# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1202# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1203_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1204 xform=_P( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1205 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1206# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1207# xform=_P( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1208# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1209_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1210 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1211 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1212_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1213 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1214 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1215_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1216 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1217 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1218_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1219 xform=_P( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1220 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1221_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1222 xform=_P( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1223 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1224_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1225 xform=_P( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1226 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1227_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1228 xform=_P( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1229 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1230_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1231 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1232 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1234# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1235# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1236_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1237 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1238 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1239_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1240 xform=_P( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1241 rates=_P( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1242_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1243 xform=_P( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1244 rates=_P( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1245_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1246 xform=_P( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1247 rates=_P( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1248_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1249 xform=_P( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1250 rates=_P( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1251_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1252 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1253 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1254_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1255 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1256 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1257_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1258 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1259 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1260_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1261 xform=_P( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1262 rates=_P( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1263_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1264 xform=_P( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1265 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1266_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1267 xform=_P( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1268 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1269_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1270 xform=_P( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1271 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1272_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1273 xform=_P( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1274 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1275_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1276 xform=_P( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1277 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1279# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1280# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1281_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1282 xform=_P( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1283 rates=_P( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1284_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1285 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1286 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1287_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1288 xform=_P( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1289 rates=_P( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1290_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1291 xform=_P( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1292 rates=_P( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1293_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1294 xform=_P( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1295 rates=_P( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1296_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1297 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1298 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1299_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1300 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1301 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1302_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1303 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1304 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1305_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1306 xform=_P( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1307 rates=_P( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1308_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1309 xform=_P( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1310 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1311_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1312 xform=_P( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1313 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1314_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1315 xform=_P( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1316 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1317_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1318 xform=_P( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1319 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1320_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1321 xform=_P( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1322 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1324# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1325# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1326# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1327# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1328# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1329_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1330 xform=_P( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1331 rates=_P( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1332# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1333# xform=_P( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1334# rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1335_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1336 xform=_P( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1337 rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1338# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1339# xform=_P( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1340# rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1341_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1342 xform=_P( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1343 rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1344# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1345# xform=_P( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1346# rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1347_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1348 xform=_P( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1349 rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1350# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1351# xform=_P( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1352# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1353_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1354 xform=_P( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1355 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1356_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1357 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1358 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1359_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1360 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1361 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1362_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1363 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1364 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1365_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1366 xform=_P( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1367 rates=_P( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1368_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1369 xform=_P( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1370 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1371_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1372 xform=_P( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1373 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1374_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1375 xform=_P( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1376 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1377_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1378 xform=_P( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1379 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1380_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1381 xform=_P( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1382 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1384# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1385# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1386# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1387_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1388 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1389 rates=_P( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1390_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1391 xform=_P( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1392 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1393_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1394 xform=_P( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1395 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1396_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1397 xform=_P(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1398 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1400# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1401# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1402# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1403# rather than the more conventional "position around the coordinate axes")
1404_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1405 xform=_P( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1406 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1407_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1408 xform=_P( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1409 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1410_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1411 xform=_P( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1412 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1414# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
1415# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1416_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1417 xform=_P( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1418 rates=_P( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1420# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1421# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1422# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1423# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1424trfXform(_ITRF2008_, _NAD83_, epoch=_E(1997), # coverage
1425 xform=_P( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1426 rates=_P( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1427# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1428# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1429_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1430 xform=_P( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1431 rates=_P( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1432_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1433 xform=_P( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1434 rates=_P( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1435_trfX(_ITRF90_, _WGS84_, epoch=_E(1984),
1436 xform=_P( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1437 rates=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1439del _E, _Es, _P, _Ps
1441if __name__ == '__main__':
1443 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _STAR_
1444 from pygeodesy.lazily import printf
1445 from time import localtime
1447 D = date2epoch.__name__
1448 E = epoch2date.__name__
1449 y = localtime()[0]
1450 for m in range(1, 13):
1451 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1452 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1453 e = date2epoch(y, m, d)
1454 t = epoch2date(e)
1455 x = NN if t == (y, m, d) else _STAR_
1456 e = '%.3f' % (e,)
1457 e = '%s, %s(%s)' % (e, E, e)
1458 t = '%d,%3d,%3d' % t
1459 printf('# %s = %s = %s %s', f, e, t, x)
1461 # __doc__ of this file, force all into registery
1462 def _RFs():
1463 yield NN
1464 for t in RefFrames.toRepr(all=True).split(_NL_):
1465 t = t.strip(_COMMA_)
1466 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1467 r = RefFrames.get(n)
1468 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1469 yield '%s .Xforms=%s' % (t, x)
1471 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1473 X, t = (), 0 # all form
1474 for r in RefFrames.values():
1475 X += tuple(r._Xs.values())
1476 for X in sorted(X):
1477 t += 1
1478 printf('#%4d %-22s xform=%r', t, X.name, X.xform)
1479 printf('#%27s rates=%r', _SPACE_, X.rates)
1481# **) MIT License
1482#
1483# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1484#
1485# Permission is hereby granted, free of charge, to any person obtaining a
1486# copy of this software and associated documentation files (the "Software"),
1487# to deal in the Software without restriction, including without limitation
1488# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1489# and/or sell copies of the Software, and to permit persons to whom the
1490# Software is furnished to do so, subject to the following conditions:
1491#
1492# The above copyright notice and this permission notice shall be included
1493# in all copies or substantial portions of the Software.
1494#
1495# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1496# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1497# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1498# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1499# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1500# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1501# OTHER DEALINGS IN THE SOFTWARE.
1503# % python -m pygeodesy.trf
1504#
1505# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1506# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1507# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1508# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1509# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1510# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1511# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1512# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1513# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1514# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1515# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1516# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1517# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1518# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1519# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1520# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1521# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1522# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1523# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1524# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1525# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1526# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1527# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1528# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1529# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1530# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1531# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1532# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1533# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1534# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1535# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1536# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1537# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1538# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1539# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1540# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1541# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1542# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1543# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1544# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1545# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1546# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1547# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1548# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1549# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1550# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1551# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1552# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1554# 1 ITRF2005@2015xETRF2000 xform=TRFXform7Tuple(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
1555# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1556# 2 ITRF88@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
1557# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1558# 3 ITRF2005@1989xETRF2005 xform=TRFXform7Tuple(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1559# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1560# 4 ITRF88@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
1561# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1562# 5 ITRF88@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
1563# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1564# 6 ITRF89@2015xETRF2000 xform=TRFXform7Tuple(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
1565# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1566# 7 ITRF89@2015xETRF2014 xform=TRFXform7Tuple(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
1567# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1568# 8 ITRF89@2015xETRF2020 xform=TRFXform7Tuple(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
1569# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1570# 9 ITRF89@1989xETRF89 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1571# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1572# 10 ITRF90@1984xWGS84 xform=TRFXform7Tuple(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
1573# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1574# 11 ITRF2005@1994xGDA94 xform=TRFXform7Tuple(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
1575# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1576# 12 ITRF90@1997xNAD83 xform=TRFXform7Tuple(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
1577# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1578# 13 ITRF90@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
1579# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1580# 14 ITRF2005@2015xETRF2014 xform=TRFXform7Tuple(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
1581# rates=TRFXform7Tuple(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1582# 15 ITRF90@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
1583# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1584# 16 ITRF2005@2015xETRF2020 xform=TRFXform7Tuple(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
1585# rates=TRFXform7Tuple(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1586# 17 ITRF90@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
1587# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1588# 18 ITRF90@1989xETRF90 xform=TRFXform7Tuple(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1589# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1590# 19 ITRF91@2015xETRF2000 xform=TRFXform7Tuple(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
1591# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1592# 20 ITRF91@2015xETRF2014 xform=TRFXform7Tuple(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
1593# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1594# 21 ITRF91@1989xETRF91 xform=TRFXform7Tuple(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1595# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1596# 22 ITRF92@2015xETRF2000 xform=TRFXform7Tuple(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
1597# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1598# 23 ITRF92@2015xETRF2014 xform=TRFXform7Tuple(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
1599# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1600# 24 ITRF92@2015xETRF2020 xform=TRFXform7Tuple(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
1601# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1602# 25 ITRF92@1989xETRF92 xform=TRFXform7Tuple(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1603# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1604# 26 ITRF93@2015xETRF2000 xform=TRFXform7Tuple(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
1605# rates=TRFXform7Tuple(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1606# 27 ITRF93@2015xETRF2014 xform=TRFXform7Tuple(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
1607# rates=TRFXform7Tuple(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1608# 28 ITRF93@2015xETRF2020 xform=TRFXform7Tuple(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
1609# rates=TRFXform7Tuple(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1610# 29 ITRF93@1989xETRF93 xform=TRFXform7Tuple(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1611# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1612# 30 ITRF94@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1613# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1614# 31 ITRF94@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1615# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1616# 32 ITRF94@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1617# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1618# 33 ITRF94@1989xETRF94 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1619# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1620# 34 ITRF96@1989xETRF96 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1621# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1622# 35 ITRF97@1989xETRF97 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1623# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1624# 36 ITRF2000@1994xGDA94 xform=TRFXform7Tuple(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
1625# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1626# 37 ITRF2000@2015xETRF2000 xform=TRFXform7Tuple(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
1627# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1628# 38 ITRF96@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1629# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1630# 39 ITRF97@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1631# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1632# 40 ITRF2000@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
1633# rates=TRFXform7Tuple(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1634# 41 ITRF96@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1635# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1636# 42 ITRF97@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1637# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1638# 43 ITRF2000@2015xETRF2020 xform=TRFXform7Tuple(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
1639# rates=TRFXform7Tuple(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1640# 44 ITRF91@2015xETRF2020 xform=TRFXform7Tuple(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
1641# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1642# 45 ITRF96@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1643# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1644# 46 ITRF97@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1645# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1646# 47 ITRF2000@2020xGDA2020 xform=TRFXform7Tuple(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
1647# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1648# 48 ITRF2000@1988xITRF88 xform=TRFXform7Tuple(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
1649# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1650# 49 ITRF2000@1988xITRF89 xform=TRFXform7Tuple(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
1651# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1652# 50 ITRF2000@1988xITRF90 xform=TRFXform7Tuple(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
1653# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1654# 51 ITRF2000@1988xITRF91 xform=TRFXform7Tuple(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
1655# rates=TRFXform7Tuple(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1656# 52 ITRF2000@1988xITRF92 xform=TRFXform7Tuple(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
1657# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1658# 53 ITRF2000@1988xITRF93 xform=TRFXform7Tuple(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
1659# rates=TRFXform7Tuple(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1660# 54 ITRF2000@1997xITRF94 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1661# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1662# 55 ITRF2000@1997xITRF96 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1663# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1664# 56 ITRF97@1997xITRF96 xform=TRFXform7Tuple(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
1665# rates=TRFXform7Tuple(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1666# 57 ITRF2000@1997xITRF97 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1667# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1668# 58 ITRF2000@1997xNAD83 xform=TRFXform7Tuple(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
1669# rates=TRFXform7Tuple(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1670# 59 ITRF2005@1997xNAD83 xform=TRFXform7Tuple(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
1671# rates=TRFXform7Tuple(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1672# 60 ITRF96@1997xNAD83 xform=TRFXform7Tuple(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
1673# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1674# 61 ITRF2005@2020xGDA2020 xform=TRFXform7Tuple(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
1675# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1676# 62 ITRF2005@2000xITRF2000 xform=TRFXform7Tuple(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
1677# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1678# 63 ITRF2008@1994xGDA94 xform=TRFXform7Tuple(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
1679# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1680# 64 ITRF2008@1997xNAD83 xform=TRFXform7Tuple(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
1681# rates=TRFXform7Tuple(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1682# 65 ITRF2008@2015xETRF2000 xform=TRFXform7Tuple(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
1683# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1684# 66 ITRF2008@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
1685# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1686# 67 ITRF2008@2015xETRF2020 xform=TRFXform7Tuple(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
1687# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1688# 68 ITRF2008@2020xGDA2020 xform=TRFXform7Tuple(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
1689# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1690# 69 ITRF2008@2000xITRF2000 xform=TRFXform7Tuple(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
1691# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1692# 70 ITRF2008@2000xITRF88 xform=TRFXform7Tuple(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
1693# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1694# 71 ITRF2008@2000xITRF89 xform=TRFXform7Tuple(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
1695# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1696# 72 ITRF2008@2000xITRF90 xform=TRFXform7Tuple(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
1697# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1698# 73 ITRF2008@2000xITRF91 xform=TRFXform7Tuple(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
1699# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1700# 74 ITRF2008@2000xITRF92 xform=TRFXform7Tuple(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
1701# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1702# 75 ITRF2008@2000xITRF93 xform=TRFXform7Tuple(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
1703# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
1704# 76 ITRF2008@2000xITRF94 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1705# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1706# 77 ITRF2008@2000xITRF96 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1707# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1708# 78 ITRF2008@2000xITRF97 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1709# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1710# 79 ITRF2008@2005xITRF2005 xform=TRFXform7Tuple(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
1711# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1712# 80 ITRF2014@2015xETRF2000 xform=TRFXform7Tuple(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
1713# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1714# 81 ITRF2014@2015xETRF2014 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
1715# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1716# 82 ITRF2014@2015xETRF2020 xform=TRFXform7Tuple(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
1717# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1718# 83 ITRF2014@2020xGDA2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1719# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
1720# 84 ITRF2014@2010xITRF2000 xform=TRFXform7Tuple(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
1721# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1722# 85 ITRF2014@2010xITRF2005 xform=TRFXform7Tuple(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
1723# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1724# 86 ITRF2014@2010xITRF2008 xform=TRFXform7Tuple(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
1725# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1726# 87 ITRF2014@2010xITRF88 xform=TRFXform7Tuple(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
1727# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1728# 88 ITRF2014@2010xITRF89 xform=TRFXform7Tuple(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
1729# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1730# 89 ITRF2014@2010xITRF90 xform=TRFXform7Tuple(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
1731# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1732# 90 ITRF2014@2010xITRF91 xform=TRFXform7Tuple(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
1733# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1734# 91 ITRF2014@2010xITRF92 xform=TRFXform7Tuple(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
1735# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1736# 92 ITRF2014@2010xITRF93 xform=TRFXform7Tuple(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
1737# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1738# 93 ITRF2014@2010xITRF94 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1739# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1740# 94 ITRF2014@2010xITRF96 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1741# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1742# 95 ITRF2014@2010xITRF97 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1743# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1744# 96 ITRF2020@2015xETRF2000 xform=TRFXform7Tuple(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
1745# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1746# 97 ITRF2020@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
1747# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1748# 98 ITRF2020@2015xETRF2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
1749# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1750# 99 ITRF2020@2015xITRF2000 xform=TRFXform7Tuple(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
1751# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1752# 100 ITRF2020@2015xITRF2005 xform=TRFXform7Tuple(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
1753# rates=TRFXform7Tuple(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1754# 101 ITRF2020@2015xITRF2008 xform=TRFXform7Tuple(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
1755# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1756# 102 ITRF2020@2015xITRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
1757# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1758# 103 ITRF2020@2015xITRF88 xform=TRFXform7Tuple(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
1759# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1760# 104 ITRF2020@2015xITRF89 xform=TRFXform7Tuple(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
1761# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1762# 105 ITRF2020@2015xITRF90 xform=TRFXform7Tuple(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
1763# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1764# 106 ITRF2020@2015xITRF91 xform=TRFXform7Tuple(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
1765# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1766# 107 ITRF2020@2015xITRF92 xform=TRFXform7Tuple(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
1767# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1768# 108 ITRF2020@2015xITRF93 xform=TRFXform7Tuple(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
1769# rates=TRFXform7Tuple(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1770# 109 ITRF2020@2015xITRF94 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1771# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1772# 110 ITRF2020@2015xITRF96 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1773# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1774# 111 ITRF2020@2015xITRF97 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1775# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)