Coverage for pygeodesy/auxilats/auxily.py: 94%
105 statements
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« prev ^ index » next coverage.py v7.6.1, created at 2025-01-06 12:20 -0500
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 _ # PYCHOK semicolon
17# from pygeodesy import auxilats # _MODS
18from pygeodesy.constants import INF, NAN, isinf, isnan, _0_0, _0_5, _1_0, \
19 _copysign_1_0, _over, _1_over
20from pygeodesy.errors import AuxError
21from pygeodesy.fmath import hypot1 as _sc, hypot2_
22from pygeodesy.interns import NN, _DOT_, _UNDER_ # PYCHOK used!
23from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS # PYCHOK used!
24from pygeodesy.utily import atan1
26from math import asinh, copysign
28__all__ = ()
29__version__ = '24.09.03'
32class Aux(object):
33 '''Enum-style Aux names.
34 '''
35 _coeffs = {}
36 GEOGRAPHIC = PHI = GEODETIC = 0
37 PARAMETRIC = BETA = REDUCED = 1
38 GEOCENTRIC = THETA = 2 # all ...
39 RECTIFYING = MU = 3 # use n^2
40 CONFORMAL = CHI = 4 # use n
41 AUTHALIC = XI = 5 # use n
42 N = 6
43 N2 = 36
45 def __index__(self, aux):
46 # throws KeyError, not IndexError
47 return _Aux2Greek[aux]
49 def __len__(self):
50 return Aux.N
52 def _CXcoeffs(self, aL): # in .auxLat.AuxLat._CXcoeffs
53 '''(INTERNAL) Get the C{_CX_4._coeffs_4}, C{_CX_6._coeffs_6}
54 or C{_CS_8._coeffs_8} coefficients, once.
55 '''
56 try:
57 _coeffs = Aux._coeffs[aL]
58 except KeyError:
59 try: # from pygeodesy.auxilats._CX_x import _coeffs_x as _coeffs
60 _CX_x = _DOT_(_MODS.auxilats.__name__, _UNDER_('_CX', aL))
61 _coeffs = _MODS.getattr(_CX_x, _UNDER_('_coeffs', aL))
62 except (AttributeError, ImportError, KeyError, TypeError) as x:
63 raise AuxError(ALorder=aL, cause=x)
64 Aux._coeffs[aL] = _coeffs._validate(aL, Aux.len(aL))
65 return _coeffs
67 def _1d(self, auxout, auxin):
68 '''Get the 1-d index into N^2 coeffs.
69 '''
70 N = Aux.N
71 if 0 <= auxout < N and 0 <= auxin < N:
72 return N * auxout + auxin
73 raise AuxError(auxout=auxout, auxin=auxin, N=N)
75 def Greek(self, aux):
76 '''Get an angle's name (C{str}).
77 '''
78 return _Aux2Greek.get(aux, NN)
80 def len(self, ALorder): # PYCHOK no cover
81 aL = ALorder # aka Lmax
82 mu = Aux.MU * (Aux.MU + 1)
83 nu = Aux.N2 - Aux.N - mu
84 return (mu * (aL * (aL + 3) - (aL // 2) * 2) // 4 +
85 nu * (aL * (aL + 1)) // 2)
87 def power(self, auxout, auxin):
88 '''Get the C{convert} exponent (C{int} or C{None}).
89 '''
90 self._1d(auxout, auxin) # validate
91 return (auxout - auxin) if max(auxin, auxout) < Aux.MU else None
93 def use_n2(self, aux):
94 return aux not in (Aux.CHI, Aux.XI)
96Aux = Aux() # PYCHOK singleton
98_Aux2Greek = {Aux.AUTHALIC: 'Xi',
99 Aux.CONFORMAL: 'Chi',
100 Aux.GEOCENTRIC: 'Theta',
101 Aux.GEODETIC: 'Phi', # == .GEOGRAPHIC
102 Aux.PARAMETRIC: 'Beta', # == .REDUCED
103 Aux.RECTIFYING: 'Mu'}
104_Greek2Aux = dict(map(reversed, _Aux2Greek.items())) # PYCHOK exported
105# _Greek2Aux.update((_g.upper(), _x) for _g, _x in _Greek2Aux.items())
108def _Dasinh(x, y):
109 d = y - x
110 if isinf(d): # PYCHOK no cover
111 r = _0_0
112 elif isnan(d): # PYCHOK no cover
113 r = NAN
114 elif d:
115 xy = x * y
116 if xy > 0:
117 hx, hy = _sc(x), _sc(y)
118 if xy < 1:
119 hx, hy = hy, hx
120 else:
121 x = _1_0 / x
122 y = _1_0 / y
123 r = _over(x + y, hx * x + hy * y)
124 r = asinh(r * d) / d
125 else:
126 r = (asinh(y) - asinh(x)) / d
127 else:
128 r = _1_over(_sc(x))
129 return r
132def _Datan(x, y):
133 xy = x * y
134 r = xy + _1_0
135 if isnan(r): # PYCHOK no cover
136 pass
137 elif x == y:
138 r = _1_over(r)
139 elif x > 0 and isinf(xy): # PYCHOK no cover
140 r = _0_0
141 else:
142 d = y - x
143 if (r + xy) > 0:
144 r = atan1(d, r) / d # atan(d / r) / d
145 else:
146 r = (atan1(y) - atan1(x)) / d
147 return r
150def _Dh(x, y):
151 r = x + y
152 if isnan(r):
153 pass # N.B. NAN for inf-inf
154 elif isinf(x): # PYCHOK no cover
155 r = copysign(_0_5, x)
156 elif isinf(y): # PYCHOK no cover
157 r = copysign(_0_5, y)
158 else:
159 snx, sny = _sn(x), _sn(y)
160 dy = sny * y
161 dx = snx * x
162 d = dy + dx
163 if (d * _0_5):
164 if (x * y) > 0:
165 r *= hypot2_(snx / _sc(y), snx * sny,
166 sny / _sc(x)) / (d + d)
167 else:
168 r = _over((dy - dx) * _0_5, y - x)
169 else: # underflow and x == y == d == 0
170 r *= _0_5 # PYCHOK no cover
171 return r
174def _Dlam(x, y): # Chi1.tan, Chi2.tan
175 # I{Divided difference} of the isometric latitude
176 # with respect to the conformal latitude
177 if isnan(x) or isnan(y): # PYCHOK no cover
178 r = NAN
179 elif isinf(x) or isinf(y): # PYCHOK no cover
180 r = INF
181 elif x == y:
182 r = _sc(x)
183 else:
184 r = _over(_Dasinh(x, y), _Datan(x, y))
185 return r
188def _Dm(X, Y, s): # in .auxDLat, .auxDST
189 # Return M{(X - Y) * s}, inplace X
190 X -= Y
191 X *= s
192 return X # Fsum
195def _Dp0Dpsi(x, y): # Chi1.tan, Chi2.tan
196 # I{Divided difference} of the spherical rhumb area
197 # term with respect to the isometric latitude
198 r = x + y
199 if isnan(r): # PYCHOK no cover
200 pass # NAN for inf-inf
201 elif isinf(x): # PYCHOK no cover
202 r = _copysign_1_0(x)
203 elif isinf(y): # PYCHOK no cover
204 r = _copysign_1_0(y)
205 elif x == y:
206 r = _sn(x)
207 else:
208 r = _Dasinh(_h(x), _h(y))
209 r = _over(_Dh(x, y) * r, _Dasinh(x, y))
210 return r
213def _h(tx):
214 '''(INTERNAL) M{h(tan(x)) = tan(x) * sin(x) / 2}
215 '''
216 if tx:
217 tx *= _sn(tx) * _0_5
218 return tx # preserve signed-0
221def _sn(tx):
222 '''(INTERNAL) M{sin(x) = tan(x) / sqrt(tan(x)**2 + 1)}.
223 '''
224 if tx:
225 tx = _copysign_1_0(tx) if isinf(tx) else (
226 NAN if isnan(tx) else (tx / _sc(tx)))
227 return tx # preserve signed-0
230__all__ += _ALL_DOCS(Aux.__class__)
232# **) MIT License
233#
234# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved.
235#
236# Permission is hereby granted, free of charge, to any person obtaining a
237# copy of this software and associated documentation files (the "Software"),
238# to deal in the Software without restriction, including without limitation
239# the rights to use, copy, modify, merge, publish, distribute, sublicense,
240# and/or sell copies of the Software, and to permit persons to whom the
241# Software is furnished to do so, subject to the following conditions:
242#
243# The above copyright notice and this permission notice shall be included
244# in all copies or substantial portions of the Software.
245#
246# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
247# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
248# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
249# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
250# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
251# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
252# OTHER DEALINGS IN THE SOFTWARE.