Coverage for pygeodesy/geodesicx/gxbases.py: 98%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Private L{geodesicx} base class, functions and constants. 

5 

6Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2024) 

7and licensed under the MIT/X11 License. For more information, see the 

8U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation. 

9''' 

10 

11from pygeodesy.basics import isodd, _MODS 

12from pygeodesy.constants import _EPSmin as _TINY, _0_0 

13from pygeodesy.errors import _or, _xkwds_item2 

14from pygeodesy.fmath import hypot as _hypot 

15# from pygeodesy.interns import _numpy_ # _MODS 

16from pygeodesy.karney import _CapsBase, GeodesicError, _2cos2x, \ 

17 _norm2, _sincos2d, _sum3 

18# from pygeodesy.lazily import _ALL_MODS as _MODS # from .basics 

19 

20from math import fabs, ldexp as _ldexp 

21 

22__all__ = () 

23__version__ = '24.09.07' 

24 

25# valid C{nC4}s and C{C4order}s, see _xnC4 below 

26_nC4s = {24: 2900, 27: 4032, 30: 5425} 

27# assert (_TINY * EPS) > 0 and (_TINY + EPS) == EPS # underflow guard 

28 

29 

30class _GeodesicBase(_CapsBase): # in .geodsolve 

31 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}. 

32 ''' 

33# def toRepr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

34# '''Return this C{GeodesicExact*} items string. 

35# 

36# @kwarg prec: The C{float} precision, number of decimal digits (0..9). 

37# Trailing zero decimals are stripped for B{C{prec}} values 

38# of 1 and above, but kept for negative B{C{prec}} values. 

39# @kwarg sep: Separator to join (C{str}). 

40# 

41# @return: C{GeodesicExact*} (C{str}). 

42# ''' 

43# return Fmt.PAREN(self.named, self.toStr(prec=prec, sep=sep)) 

44 pass 

45 

46 

47class _Gfloats(dict): 

48 '''(INTERNAL) Numpy or "Unique" floats. 

49 ''' 

50 n = 0 # total number of floats 

51 nC4 = 0 

52 

53 def __init__(self, nC4): # PYCHOK signature 

54 self.nC4 = nC4 

55 

56 def __call__(self, fs): 

57 '''Return a C{numpy.array} or C{tuple} of C{float}s. 

58 ''' 

59 np = _MODS.imported(_MODS.interns._numpy_) 

60 if np: # use numpy, already imported 

61 cs = np.array(fs, dtype=float) 

62 else: 

63 _f = self.setdefault # avoid duplicates 

64 cs = tuple(_f(f, f) for f in map(float, fs)) # PYCHOK as attr 

65 self.n += len(fs) 

66 return cs 

67 

68 

69def _cosSeries(c4s, sx, cx): # PYCHOK shared .geodesicx.gx and -.gxline 

70 '''(INTERNAL) I{Karney}'s cosine series expansion using U{Clenshaw 

71 summation<https://WikiPedia.org/wiki/Clenshaw_algorithm>}. 

72 ''' 

73 ar = _2cos2x(cx, sx) 

74 y0 = t0 = y1 = t1 = _0_0 

75 c4 = list(c4s) 

76 _c4 = c4.pop 

77 if isodd(len(c4)): 

78 y0 = _c4() 

79 while c4: 

80 # y1 = ar * y0 - y1 + c4.pop() 

81 # y0 = ar * y1 - y0 + c4.pop() 

82 y1, t1, _ = _sum3(-y1, -t1, ar * y0, ar * t0, _c4()) 

83 y0, t0, _ = _sum3(-y0, -t0, ar * y1, ar * t1, _c4()) 

84 # s = (y0 - y1) * cx 

85 s, t, _ = _sum3(cx * y0, _0_0, cx * t0, -cx * y1, -cx * t1) 

86 return s + t 

87 

88# Y0, Y1 = Fsum(), Fsum() 

89# ar = _2cos2x(cx, sx) 

90# c4 = list(c4s) 

91# _c4 = c4.pop 

92# if isodd(len(c4)): 

93# Y0 += _c4() 

94# while c4: 

95# # y1 = ar * y0 - y1 + c4.pop() 

96# # y0 = ar * y1 - y0 + c4.pop() 

97# Y1 = Y0 * ar - Y1 + _c4() 

98# Y0 = Y1 * ar - Y0 + _c4() 

99# # s = (y0 - y1) * cx 

100# return float((Y0 - Y1) * cx) 

101 

102 

103_f = float # in _f2 and .geodesicx._C4_24, _27 and _30 

104 

105 

106def _f2(hi, lo): # in .geodesicx._C4_24, _27 and _30 

107 '''(INTERNAL) For C{_coeffs}. 

108 ''' 

109 return _ldexp(_f(hi), 52) + _f(lo) 

110 

111 

112def _sincos12(sin1, cos1, sin2, cos2, sineg0=False): 

113 '''(INTERNAL) Compute the sine and cosine of angle 

114 M{ang12 = atan2(sin2, cos2) - atan2(sin1, cos1)}. 

115 

116 Negate C{sin1} to get C{sin12} and C{cos12} of the sum 

117 M{ang12 = atan2(sin2, cos2) + atan2(sin1, cos1)}. 

118 

119 @kwarg sineg0: If C{True}, make negative C{sin12} zero (C{bool}). 

120 

121 @return: 2-Tuple C{(sin12, cos12)}. 

122 ''' 

123 s = sin2 * cos1 - sin1 * cos2 

124 c = cos2 * cos1 + sin1 * sin2 

125 if sineg0 and s < 0: 

126 s = _0_0 # max(s, _0_0) or NEG0? 

127 return s, c 

128 

129 

130def _sin1cos2(sin1, cos1, sin2, cos2): 

131 '''(INTERNAL) Compute the C{sin1 * cos2} sine and its cosine. 

132 

133 @return: 2-Tuple C{(sin1 * cos2, hypot(sin1 * sin2, cos1)}. 

134 ''' 

135 s = sin1 * cos2 

136 c = _hypot(sin1 * sin2, cos1) 

137 return s, c # _norm2(s, c) 

138 

139 

140def _sinf1cos2d(lat, f1): 

141 '''(INTERNAL) See C{GeodesicExact} and C{_GeodesicLineExact}. 

142 ''' 

143 sbet, cbet = _sincos2d(lat) 

144 # ensure cbet1 = +epsilon at poles; doing the fix on beta means 

145 # that sig12 will be <= 2*tiny for two points at the same pole 

146 sbet, cbet = _norm2(sbet * f1, cbet) 

147 return sbet, (cbet if fabs(cbet) > _TINY else _TINY) 

148 

149 

150def _xnC4(**name_nC4): 

151 '''(INTERNAL) Validate C{C4order}. 

152 ''' 

153 n, nC4 = _xkwds_item2(name_nC4) 

154 if nC4 not in _nC4s or not isinstance(nC4, int): 

155 raise GeodesicError(n, nC4, txt_not_=_or(*map(str, _nC4s))) 

156 return _nC4s[nC4] 

157 

158 

159# **) MIT License 

160# 

161# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

162# 

163# Permission is hereby granted, free of charge, to any person obtaining a 

164# copy of this software and associated documentation files (the "Software"), 

165# to deal in the Software without restriction, including without limitation 

166# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

167# and/or sell copies of the Software, and to permit persons to whom the 

168# Software is furnished to do so, subject to the following conditions: 

169# 

170# The above copyright notice and this permission notice shall be included 

171# in all copies or substantial portions of the Software. 

172# 

173# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

174# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

175# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

176# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

177# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

178# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

179# OTHER DEALINGS IN THE SOFTWARE.