Coverage for pygeodesy/auxilats/auxily.py: 94%
108 statements
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« prev ^ index » next coverage.py v7.6.1, created at 2025-05-29 12:40 -0400
2# -*- coding: utf-8 -*-
4u'''(INTERNAL) I{Auxiliary} latitudes' 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 _ # noqa: E702 ;
17# from pygeodesy import auxilats # _MODS
18from pygeodesy.auxilats._CX_Rs import _Rkey
19from pygeodesy.basics import _isin, typename
20from pygeodesy.constants import INF, NAN, isinf, isnan, _0_0, _0_5, _1_0, \
21 _copysign_1_0, _over, _1_over
22from pygeodesy.errors import AuxError
23from pygeodesy.fmath import hypot1 as _sc, hypot2_
24# from pygeodesy.internals import typename # from .basics
25from pygeodesy.interns import NN, _DOT_, _UNDER_ # PYCHOK used!
26from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS # PYCHOK used!
27from pygeodesy.utily import atan1
29from math import asinh, copysign
31__all__ = ()
32__version__ = '25.05.12'
35class Aux(object):
36 '''Enum-style Aux names.
37 '''
38 _coeffs = {}
39 GEOGRAPHIC = PHI = GEODETIC = _Rkey(0)
40 PARAMETRIC = BETA = REDUCED = _Rkey(1)
41 GEOCENTRIC = THETA = _Rkey(2) # all ...
42 RECTIFYING = MU = _Rkey(3) # use n^2
43 CONFORMAL = CHI = _Rkey(4) # use n
44 AUTHALIC = XI = _Rkey(5) # use n
45 N = 6
46 N2 = 36
48 def __index__(self, aux):
49 # throws KeyError, not IndexError
50 return _Aux2Greek[aux]
52 def __len__(self):
53 return Aux.N
55 def _CXcoeffs(self, aL): # in .auxLat.AuxLat._CXcoeffs
56 '''(INTERNAL) Get the C{_CX_4._coeffs_4}, C{_CX_6._coeffs_6}
57 or C{_CS_8._coeffs_8} coefficients, once.
58 '''
59 try:
60 _coeffs = Aux._coeffs[aL]
61 except KeyError:
62 try: # from pygeodesy.auxilats._CX_x import _coeffs_x as _coeffs
63 _CX_x = _DOT_(typename(_MODS.auxilats), _UNDER_('_CX', aL))
64 _coeffs = _MODS.getattr(_CX_x, _UNDER_('_coeffs', aL))
65 except (AttributeError, ImportError, KeyError, TypeError) as x:
66 raise AuxError(ALorder=aL, cause=x)
67 Aux._coeffs[aL] = _coeffs._validate(aL, Aux.len(aL))
68 return _coeffs
70 def _1d(self, auxout, auxin):
71 '''Get the 1-d index into N^2 coeffs.
72 '''
73 N = Aux.N
74 if 0 <= auxout < N and 0 <= auxin < N:
75 return N * auxout + auxin
76 raise AuxError(auxout=auxout, auxin=auxin, N=N)
78 def Greek(self, aux):
79 '''Get an angle's name (C{str}).
80 '''
81 return _Aux2Greek.get(aux, NN)
83 def len(self, ALorder): # PYCHOK no cover
84 aL = ALorder # aka Lmax
85 mu = Aux.MU * (Aux.MU + 1)
86 nu = Aux.N2 - Aux.N - mu
87 return (mu * (aL * (aL + 3) - (aL // 2) * 2) // 4 +
88 nu * (aL * (aL + 1)) // 2)
90 def power(self, auxout, auxin):
91 '''Get the C{convert} exponent (C{int} or C{None}).
92 '''
93 self._1d(auxout, auxin) # validate
94 return (auxout - auxin) if max(auxin, auxout) < Aux.MU else None
96 def use_n2(self, aux):
97 return not _isin(aux, Aux.CHI, Aux.XI)
99Aux = Aux() # PYCHOK singleton
101_Aux2Greek = {Aux.AUTHALIC: 'Xi',
102 Aux.CONFORMAL: 'Chi',
103 Aux.GEOCENTRIC: 'Theta',
104 Aux.GEODETIC: 'Phi', # == .GEOGRAPHIC
105 Aux.PARAMETRIC: 'Beta', # == .REDUCED
106 Aux.RECTIFYING: 'Mu'}
107_Greek2Aux = dict(map(reversed, _Aux2Greek.items())) # PYCHOK exported
108# _Greek2Aux.update((_g.upper(), _x) for _g, _x in _Greek2Aux.items())
111def _Dasinh(x, y):
112 d = y - x
113 if isinf(d): # PYCHOK no cover
114 r = _0_0
115 elif isnan(d): # PYCHOK no cover
116 r = NAN
117 elif d:
118 xy = x * y
119 if xy > 0:
120 hx, hy = _sc(x), _sc(y)
121 if xy < 1:
122 hx, hy = hy, hx
123 else:
124 x = _1_0 / x
125 y = _1_0 / y
126 r = _over(x + y, hx * x + hy * y)
127 r = asinh(r * d) / d
128 else:
129 r = (asinh(y) - asinh(x)) / d
130 else:
131 r = _1_over(_sc(x))
132 return r
135def _Datan(x, y):
136 xy = x * y
137 r = xy + _1_0
138 if isnan(r): # PYCHOK no cover
139 pass
140 elif x == y:
141 r = _1_over(r)
142 elif x > 0 and isinf(xy): # PYCHOK no cover
143 r = _0_0
144 else:
145 d = y - x
146 if (r + xy) > 0:
147 r = atan1(d, r) / d # atan(d / r) / d
148 else:
149 r = (atan1(y) - atan1(x)) / d
150 return r
153def _Dh(x, y):
154 r = x + y
155 if isnan(r):
156 pass # N.B. NAN for inf-inf
157 elif isinf(x): # PYCHOK no cover
158 r = copysign(_0_5, x)
159 elif isinf(y): # PYCHOK no cover
160 r = copysign(_0_5, y)
161 else:
162 snx, sny = _sn(x), _sn(y)
163 dy = sny * y
164 dx = snx * x
165 d = dy + dx
166 if (d * _0_5):
167 if (x * y) > 0:
168 r *= hypot2_(snx / _sc(y), snx * sny,
169 sny / _sc(x)) / (d + d)
170 else:
171 r = _over((dy - dx) * _0_5, y - x)
172 else: # underflow and x == y == d == 0
173 r *= _0_5 # PYCHOK no cover
174 return r
177def _Dlam(x, y): # Chi1.tan, Chi2.tan
178 # I{Divided difference} of the isometric latitude
179 # with respect to the conformal latitude
180 if isnan(x) or isnan(y): # PYCHOK no cover
181 r = NAN
182 elif isinf(x) or isinf(y): # PYCHOK no cover
183 r = INF
184 elif x == y:
185 r = _sc(x)
186 else:
187 r = _over(_Dasinh(x, y), _Datan(x, y))
188 return r
191def _Dm(X, Y, s): # in .auxDLat, .auxDST
192 # Return M{(X - Y) * s}, inplace X
193 X -= Y
194 X *= s
195 return X # Fsum
198def _Dp0Dpsi(x, y): # Chi1.tan, Chi2.tan
199 # I{Divided difference} of the spherical rhumb area
200 # term with respect to the isometric latitude
201 r = x + y
202 if isnan(r): # PYCHOK no cover
203 pass # NAN for inf-inf
204 elif isinf(x): # PYCHOK no cover
205 r = _copysign_1_0(x)
206 elif isinf(y): # PYCHOK no cover
207 r = _copysign_1_0(y)
208 elif x == y:
209 r = _sn(x)
210 else:
211 r = _Dasinh(_h(x), _h(y))
212 r = _over(_Dh(x, y) * r, _Dasinh(x, y))
213 return r
216def _h(tx):
217 '''(INTERNAL) M{h(tan(x)) = tan(x) * sin(x) / 2}
218 '''
219 if tx:
220 tx *= _sn(tx) * _0_5
221 return tx # preserve signed-0
224def _sn(tx):
225 '''(INTERNAL) M{sin(x) = tan(x) / sqrt(tan(x)**2 + 1)}.
226 '''
227 if tx:
228 tx = _copysign_1_0(tx) if isinf(tx) else (
229 NAN if isnan(tx) else (tx / _sc(tx)))
230 return tx # preserve signed-0
233__all__ += _ALL_DOCS(Aux.__class__)
234del _Rkey
236# **) MIT License
237#
238# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved.
239#
240# Permission is hereby granted, free of charge, to any person obtaining a
241# copy of this software and associated documentation files (the "Software"),
242# to deal in the Software without restriction, including without limitation
243# the rights to use, copy, modify, merge, publish, distribute, sublicense,
244# and/or sell copies of the Software, and to permit persons to whom the
245# Software is furnished to do so, subject to the following conditions:
246#
247# The above copyright notice and this permission notice shall be included
248# in all copies or substantial portions of the Software.
249#
250# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
251# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
252# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
253# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
254# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
255# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
256# OTHER DEALINGS IN THE SOFTWARE.