1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) I{Auxiliary} latitudes' classes, constants and functions.

5

6 Class L{AuxAngle} transcoded to Python from I{Karney}'s C++ class U{AuxAngle

7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}

8 in I{GeographicLib version 2.2+}.

9

10 Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2022-2023) and licensed

11 under 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

15 from __future__ import division as _; del _ # PYCHOK semicolon

16

17# from pygeodesy import auxilats # _MODS

18 from pygeodesy.constants import INF, NAN, isinf, isnan, _0_0, _0_5, _1_0, \

19 _copysign_1_0, _over, _1_over

20 from pygeodesy.errors import AuxError

21 from pygeodesy.fmath import hypot1 as _sc, hypot2_

22 from pygeodesy.interns import NN, _DOT_, _UNDER_ # PYCHOK used!

23 from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS # PYCHOK used!

24 from pygeodesy.utily import atan1

25

26 from math import asinh, copysign

27

28__all__ = ()

29__version__ = '24.09.03'

30

31

32 class 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

44

45 def __index__(self, aux):

46 # throws KeyError, not IndexError

47 return _Aux2Greek[aux]

48

49 def __len__(self):

50 return Aux.N

51

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

66

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)

74

75 def Greek(self, aux):

76 '''Get an angle's name (C{str}).

77 '''

78 return _Aux2Greek.get(aux, NN)

79

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)

86

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

92

93 def use_n2(self, aux):

94 return aux not in (Aux.CHI, Aux.XI)

95

96 Aux = Aux() # PYCHOK singleton

97

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())

106

107

108 def _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

130

131

132 def _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

148

149

150 def _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

172

173

174 def _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

186

187

188 def _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

193

194

195 def _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

211

212

213 def _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

219

220

221 def _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

228

229

230__all__ += _ALL_DOCS(Aux.__class__)

231

232# **) MIT License

233#

234# Copyright (C) 2023-2024 -- 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.