Coverage for pygeodesy/auxilats/auxAngle.py: 96%
225 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) I{Auxiliary} latitudes' base classes, constants and functions.
6Class L{AuxAngle} transcoded to Python from I{Karney}'s C++ class U{AuxAngle
7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}
8in I{GeographicLib version 2.2+}.
10Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2022-2024) and licensed
11under the MIT/X11 License. For more information, see the U{GeographicLib
12<https://GeographicLib.SourceForge.io>} documentation.
13'''
14# make sure int/int division yields float quotient, see .basics
15from __future__ import division as _; del _ # PYCHOK semicolon
17from pygeodesy.auxilats.auxily import Aux, _Aux2Greek, AuxError
18from pygeodesy.basics import map1, map2, _xinstanceof
19from pygeodesy.constants import EPS, _INF_NAN_NINF, MAX, NAN, _0_0, _0_5, _1_0, \
20 _copysign_1_0, _over, _pos_self, isfinite, isnan
21# from pygeodesy.errors import AuxError # from .auxilats.auxily
22from pygeodesy.fmath import hypot, unstr
23from pygeodesy.fsums import _add_op_, _iadd_op_, _isub_op_, _sub_op_
24from pygeodesy.named import _Named, _ALL_DOCS, _MODS
25# from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS # from .named
26from pygeodesy.props import Property, Property_RO, property_RO, property_ROver, \
27 _update_all
28# from pygeodesy.streprs import unstr # from .fmath
29from pygeodesy.units import Degrees, Radians
30from pygeodesy.utily import atan2, atan2d, sincos2, sincos2d
32from math import asinh, copysign, degrees, fabs, radians, sinh
34__all__ = ()
35__version__ = '24.11.24'
37_0_INF_NAN_NINF = (0, _0_0) + _INF_NAN_NINF
38_MAX_2 = MAX * _0_5 # PYCHOK used!
39# del _INF_NAN_NINF, MAX
42class AuxAngle(_Named):
43 '''U{An accurate representation of angles
44 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}
45 '''
46 _AUX = None # overloaded/-ridden
47 _diff = NAN # default
48 _iter = None # like ._NamedBase
49 _y = _0_0
50 _x = _1_0
52 def __init__(self, y_angle=_0_0, x=_1_0, aux=None, **name):
53 '''New L{AuxAngle}.
55 @kwarg y_angle: The Y component (C{scalar}, including C{INF}, C{NAN}
56 and C{NINF}) or a previous L{AuxAngle} instance.
57 @kwarg x: The X component, required if C{B{y_angle}} is C{scalar},
58 ignored otherwise.
59 @kwarg aux: I{Auxiliary} kind (C{Aux.KIND}), like B{C{x}}.
60 @kwarg name: Optional C{B{name}=NN} see (C{str}).
62 @raise AuxError: Invalid B{C{y_angle}}, B{C{x}} or B{C{aux}}.
63 '''
64 try:
65 try:
66 yx = y_angle._yx
67 aux = y_angle._AUX
68 if self._diff != y_angle._diff:
69 self._diff = y_angle._diff
70 except AttributeError:
71 yx = y_angle, x
72 if aux in _AUXClass:
73 if self._AUX != aux:
74 self._AUX = aux
75 elif aux is not None:
76 raise ValueError() # _invalid_
77 except Exception as X:
78 raise AuxError(y=y_angle, x=x, aux=aux, cause=X)
79 self._y, self._x = _yx2(yx)
80 if name:
81 self.name = name
83 def __abs__(self):
84 '''Return this angle's absolute value (L{AuxAngle}).
85 '''
86 a = self._copy_2(self.__abs__)
87 a._yx = map2(fabs, self._yx)
88 return a
90 def __add__(self, other):
91 '''Return C{B{self} + B{other}} as an L{AuxAngle}.
93 @arg other: An L{AuxAngle}.
95 @return: The sum (L{AuxAngle}).
97 @raise TypeError: Invalid B{C{other}}.
98 '''
99 a = self._copy_2(self.__add__)
100 return a._iadd(other, _add_op_)
102 def __bool__(self): # PYCHOK not special in Python 2-
103 '''Return C{True} if this angle is non-zero.
104 '''
105 return bool(self.tan)
107 def __eq__(self, other):
108 '''Return C{B{self} == B{other}} as C{bool}.
109 '''
110 return not self.__ne__(other)
112 def __float__(self):
113 '''Return this angle's C{tan} (C{float}).
114 '''
115 return self.tan
117 def __iadd__(self, other):
118 '''Apply C{B{self} += B{other}} to this angle.
120 @arg other: An L{AuxAngle}.
122 @return: This angle, updated (L{AuxAngle}).
124 @raise TypeError: Invalid B{C{other}}.
125 '''
126 return self._iadd(other, _iadd_op_)
128 def __isub__(self, other):
129 '''Apply C{B{self} -= B{other}} to this angle.
131 @arg other: An L{AuxAngle}.
133 @return: This instance, updated (L{AuxAngle}).
135 @raise TypeError: Invalid B{C{other}} type.
136 '''
137 return self._iadd(-other, _isub_op_)
139 def __ne__(self, other):
140 '''Return C{B{self} != B{other}} as C{bool}.
141 '''
142 _xinstanceof(AuxAngle, other=other)
143 y, x, r = self._yxr_normalized()
144 s, c, t = other._yxr_normalized()
145 return fabs(y - s) > EPS or fabs(x - c) > EPS \
146 or fabs(r - t) > EPS
148 def __neg__(self):
149 '''Return I{a copy of} this angle, negated.
150 '''
151 a = self._copy_2(self.__neg__)
152 if a.y or not a.x:
153 a.y = -a.y
154 else:
155 a.x = -a.x
156 return a
158 def __pos__(self):
159 '''Return this angle I{as-is}, like C{float.__pos__()}.
160 '''
161 return self if _pos_self else self._copy_2(self.__pos__)
163 def __radd__(self, other):
164 '''Return C{B{other} + B{self}} as an L{AuxAngle}.
166 @see: Method L{AuxAngle.__add__}.
167 '''
168 a = self._copy_r2(other, self.__radd__)
169 return a._iadd(self, _add_op_)
171 def __rsub__(self, other):
172 '''Return C{B{other} - B{self}} as an L{AuxAngle}.
174 @see: Method L{AuxAngle.__sub__}.
175 '''
176 a = self._copy_r2(other, self.__rsub__)
177 return a._iadd(-self, _sub_op_)
179 def __str__(self):
180 n = _Aux2Greek.get(self._AUX, self.classname)
181 return unstr(n, y=self.y, x=self.x, tan=self.tan)
183 def __sub__(self, other):
184 '''Return C{B{self} - B{other}} as an L{AuxAngle}.
186 @arg other: An L{AuxAngle}.
188 @return: The difference (L{AuxAngle}).
190 @raise TypeError: Invalid B{C{other}} type.
191 '''
192 a = self._copy_2(self.__sub__)
193 return a._iadd(-other, _sub_op_)
195 def _iadd(self, other, *unused): # op
196 '''(INTERNAL) Apply C{B{self} += B{other}}.
197 '''
198 _xinstanceof(AuxAngle, other=other)
199 # ignore zero other to preserve signs of _y and _x
200 if other.tan:
201 s, c = other._yx
202 y, x = self._yx
203 self._yx = (y * c + x * s), \
204 (x * c - y * s)
205 return self
207 def _copy_2(self, which):
208 '''(INTERNAL) Copy for I{dyadic} operators.
209 '''
210 return _Named.copy(self, deep=False, name=which.__name__)
212 def _copy_r2(self, other, which):
213 '''(INTERNAL) Copy for I{reverse-dyadic} operators.
214 '''
215 _xinstanceof(AuxAngle, other=other)
216 return other._copy_2(which)
218 def copyquadrant(self, other):
219 '''Copy an B{C{other}} angle's quadrant into this angle (L{auxAngle}).
220 '''
221 _xinstanceof(AuxAngle, other=other)
222 self._yx = copysign(self.y, other.y), \
223 copysign(self.x, other.x)
224 return self
226 @Property_RO
227 def diff(self):
228 '''Get derivative C{dtan(Eta) / dtan(Phi)} (C{float} or C{NAN}).
229 '''
230 return self._diff
232 @staticmethod
233 def fromDegrees(deg, **aux_name):
234 '''Get an L{AuxAngle} from degrees.
235 '''
236 return _AuxClass(**aux_name)(*sincos2d(deg), **aux_name)
238 @staticmethod
239 def fromLambertianDegrees(psi, **aux_name):
240 '''Get an L{AuxAngle} from I{Lambertian} degrees.
241 '''
242 return _AuxClass(**aux_name)(sinh(radians(psi)), **aux_name)
244 @staticmethod
245 def fromLambertianRadians(psi, **aux_name):
246 '''Get an L{AuxAngle} from I{Lambertian} radians.
247 '''
248 return _AuxClass(**aux_name)(sinh(psi), **aux_name)
250 @staticmethod
251 def fromRadians(rad, **aux_name):
252 '''Get an L{AuxAngle} from radians.
253 '''
254 return _AuxClass(**aux_name)(*sincos2(rad), **aux_name)
256 @Property_RO
257 def iteration(self):
258 '''Get the iteration (C{int} or C{None}).
259 '''
260 return self._iter
262 def normal(self):
263 '''Normalize this angle I{in-place}.
265 @return: This angle, normalized (L{AuxAngle}).
266 '''
267 self._yx = self._yx_normalized
268 return self
270 @Property_RO
271 def normalized(self):
272 '''Get a normalized copy of this angle (L{AuxAngle}).
273 '''
274 y, x = self._yx_normalized
275 return self.classof(y, x, name=self.name, aux=self._AUX)
277 @property_ROver
278 def _RhumbAux(self):
279 '''(INTERNAL) Import the L{RhumbAux} class, I{once}.
280 '''
281 return _MODS.rhumb.aux_.RhumbAux # overwrite property_ROver
283 @Property_RO
284 def tan(self):
285 '''Get this angle's C{tan} (C{float}).
286 '''
287 y, x = self._yx
288 return _over(y, x) if isfinite(y) and y else y
290 def toBeta(self, rhumb):
291 '''Short for C{rhumb.auxDLat.convert(Aux.BETA, self, exact=rhumb.exact)}
292 '''
293 return self._toRhumbAux(rhumb, Aux.BETA)
295 def toChi(self, rhumb):
296 '''Short for C{rhumb.auxDLat.convert(Aux.CHI, self, exact=rhumb.exact)}
297 '''
298 return self._toRhumbAux(rhumb, Aux.CHI)
300 @Property_RO
301 def toDegrees(self):
302 '''Get this angle as L{Degrees}.
303 '''
304 return Degrees(atan2d(*self._yx), name=self.name)
306 @Property_RO
307 def toLambertianDegrees(self): # PYCHOK no cover
308 '''Get this angle's I{Lambertian} in L{Degrees}.
309 '''
310 r = self.toLambertianRadians
311 return Degrees(degrees(r), name=r.name)
313 @Property_RO
314 def toLambertianRadians(self):
315 '''Get this angle's I{Lambertian} in L{Radians}.
316 '''
317 return Radians(asinh(self.tan), name=self.name)
319 def toMu(self, rhumb):
320 '''Short for C{rhumb.auxDLat.convert(Aux.MU, self, exact=rhumb.exact)}
321 '''
322 return self._toRhumbAux(rhumb, Aux.MU)
324 def toPhi(self, rhumb):
325 '''Short for C{rhumb.auxDLat.convert(Aux.PHI, self, exact=rhumb.exact)}
326 '''
327 return self._toRhumbAux(rhumb, Aux.PHI)
329 @Property_RO
330 def toRadians(self):
331 '''Get this angle as L{Radians}.
332 '''
333 return Radians(atan2(*self._yx), name=self.name)
335 def _toRhumbAux(self, rhumb, aux):
336 '''(INTERNAL) Create an C{aux}-KIND angle from this angle.
337 '''
338 _xinstanceof(self._RhumbAux, rhumb=rhumb)
339 return rhumb._auxD.convert(aux, self, exact=rhumb.exact)
341 @Property
342 def x(self):
343 '''Get this angle's C{x} (C{float}).
344 '''
345 return self._x
347 @x.setter # PYCHOK setter!
348 def x(self, x): # PYCHOK no cover
349 '''Set this angle's C{x} (C{float}).
350 '''
351 x = float(x)
352 if self._x != x:
353 _update_all(self)
354 self._x = x
356 @property_RO
357 def _x_normalized(self):
358 '''(INTERNAL) Get the I{normalized} C{x}.
359 '''
360 _, x = self._yx_normalized
361 return x
363 @Property
364 def y(self):
365 '''Get this angle's C{y} (C{float}).
366 '''
367 return self._y
369 @y.setter # PYCHOK setter!
370 def y(self, y): # PYCHOK no cover
371 '''Set this angle's C{y} (C{float}).
372 '''
373 y = float(y)
374 if self.y != y:
375 _update_all(self)
376 self._y = y
378 @Property
379 def _yx(self):
380 '''(INTERNAL) Get this angle as 2-tuple C{(y, x)}.
381 '''
382 return self._y, self._x
384 @_yx.setter # PYCHOK setter!
385 def _yx(self, yx):
386 '''(INTERNAL) Set this angle's C{y} and C{x}.
387 '''
388 yx = _yx2(yx)
389 if self._yx != yx:
390 _update_all(self)
391 self._y, self._x = yx
393 @Property_RO
394 def _yx_normalized(self):
395 '''(INTERNAL) Get this angle as 2-tuple C{(y, x)}, I{normalized}.
396 '''
397 y, x = self._yx
398 if isfinite(y) and fabs(y) < _MAX_2 \
399 and fabs(x) < _MAX_2 \
400 and isfinite(self.tan):
401 h = hypot(y, x)
402 if h > 0 and y:
403 y = y / h # /= chokes PyChecker
404 x = x / h
405 if isnan(y): # PYCHOK no cover
406 y = _copysign_1_0(self.y)
407 if isnan(x): # PYCHOK no cover
408 x = _copysign_1_0(self.x)
409 else: # scalar 0
410 y, x = _0_0, _copysign_1_0(y * x)
411 else: # scalar NAN
412 y, x = NAN, _copysign_1_0(y * x)
413 return y, x
415 def _yxr_normalized(self, abs_y=False):
416 '''(INTERNAL) Get 3-tuple C{(y, x, r)}, I{normalized}
417 with C{y} or C{abs(y)} and C{r} as C{.toRadians}.
418 '''
419 y, x = self._yx_normalized
420 if abs_y:
421 y = fabs(y) # only y, not x
422 return y, x, atan2(y, x) # .toRadians
425class AuxBeta(AuxAngle):
426 '''A I{Parametric, Auxiliary} latitude.
427 '''
428 _AUX = Aux.BETA
430 @staticmethod
431 def fromDegrees(deg, **name):
432 '''Get an L{AuxBeta} from degrees.
433 '''
434 return AuxBeta(*sincos2d(deg), **name)
436 @staticmethod
437 def fromRadians(rad, **name):
438 '''Get an L{AuxBeta} from radians.
439 '''
440 return AuxBeta(*sincos2(rad), **name)
443class AuxChi(AuxAngle):
444 '''A I{Conformal, Auxiliary} latitude.
445 '''
446 _AUX = Aux.CHI
448 @staticmethod
449 def fromDegrees(deg, **name):
450 '''Get an L{AuxChi} from degrees.
451 '''
452 return AuxChi(*sincos2d(deg), **name)
455class AuxMu(AuxAngle):
456 '''A I{Rectifying, Auxiliary} latitude.
457 '''
458 _AUX = Aux.MU
460 @staticmethod
461 def fromDegrees(deg, **name):
462 '''Get an L{AuxMu} from degrees.
463 '''
464 return AuxMu(*sincos2d(deg), **name)
467class AuxPhi(AuxAngle):
468 '''A I{Geodetic or Geographic, Auxiliary} latitude.
469 '''
470 _AUX = Aux.PHI
471 _diff = _1_0 # see .auxLat._Newton
473 @staticmethod
474 def fromDegrees(deg, **name):
475 '''Get an L{AuxPhi} from degrees.
476 '''
477 return AuxPhi(*sincos2d(deg), **name)
480class AuxTheta(AuxAngle):
481 '''A I{Geocentric, Auxiliary} latitude.
482 '''
483 _AUX = Aux.THETA
485 @staticmethod
486 def fromDegrees(deg, **name):
487 '''Get an L{AuxTheta} from degrees.
488 '''
489 return AuxTheta(*sincos2d(deg), **name)
492class AuxXi(AuxAngle):
493 '''An I{Authalic, Auxiliary} latitude.
494 '''
495 _AUX = Aux.XI
497 @staticmethod
498 def fromDegrees(deg, **name):
499 '''Get an L{AuxXi} from degrees.
500 '''
501 return AuxXi(*sincos2d(deg), **name)
504_AUXClass = {Aux.BETA: AuxBeta,
505 Aux.CHI: AuxChi,
506 Aux.MU: AuxMu,
507 Aux.PHI: AuxPhi,
508 Aux.THETA: AuxTheta,
509 Aux.XI: AuxXi}
511def _AuxClass(aux=None, **unused): # PYCHOK C{classof(aux)}
512 return _AUXClass.get(aux, AuxAngle)
515def _yx2(yx):
516 '''(INTERNAL) Validate 2-tuple C{(y, x)}.
517 '''
518 try:
519 y, x = yx
520 y, x = map1(float, y, x)
521 if y in _0_INF_NAN_NINF:
522 x = _copysign_1_0(x)
523 except (TypeError, ValueError) as X:
524 raise AuxError(y=y, x=x, cause=X)
525 return y, x
528__all__ += _ALL_DOCS(AuxAngle, AuxBeta, AuxChi, AuxMu, AuxPhi, AuxTheta, AuxXi)
530# **) MIT License
531#
532# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved.
533#
534# Permission is hereby granted, free of charge, to any person obtaining a
535# copy of this software and associated documentation files (the "Software"),
536# to deal in the Software without restriction, including without limitation
537# the rights to use, copy, modify, merge, publish, distribute, sublicense,
538# and/or sell copies of the Software, and to permit persons to whom the
539# Software is furnished to do so, subject to the following conditions:
540#
541# The above copyright notice and this permission notice shall be included
542# in all copies or substantial portions of the Software.
543#
544# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
545# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
546# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
547# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
548# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
549# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
550# OTHER DEALINGS IN THE SOFTWARE.