1

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

3

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

5

6 Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2023)

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

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

9'''

10

11# from pygeodesy.basics import isodd # from .karney

12 from pygeodesy.constants import _0_0, _2_0, _100_0

13 from pygeodesy.errors import _not_, _or

14# from pygeodesy.interns import _not_ # from .errors

15 from pygeodesy.karney import _CapsBase, GeodesicError, isodd, \

16 _hypot, _sum2_, _MODS

17

18 from math import ldexp as _ldexp

19

20__all__ = ()

21__version__ = '23.07.04'

22

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

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

25

26

27 class _GeodesicBase(_CapsBase): # in .geodsolve

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

29 '''

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

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

32#

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

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

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

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

37#

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

39# '''

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

41 pass

42

43

44 class _Gfloats(dict):

45 '''(INTERNAL) Uniquify floats.

46 '''

47 n = 0 # total number of floats

48 nC4 = 0

49

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

51 self.nC4 = nC4

52

53 def __call__(self, fs):

54 '''Return a tuple of "uniquified" floats.

55 '''

56 self.n += len(fs)

57 _f = self.setdefault

58 return tuple(_f(f, f) for f in map(float, fs)) # PYCHOK as attr

59

60 def prints(self):

61 n, u = self.n, len(self.keys())

62 d = (n - u) * _100_0 / n

63 _MODS.lazily.printf('_CX_%d: n=%d, u=%d, d=%.1f%%', self.nC4, n, u, d) # XXX

64

65

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

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

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

69 '''

70 ar = _2_0 * (cx - sx) * (cx + sx) # 2 * cos(2 * x)

71 y0 = t0 = y1 = t1 = _0_0

72 n = len(c4s) # c4s = list(c4s)

73 if isodd(n):

74 n -= 1

75 y0 = c4s[n] # c4s.pop()

76 _s2_ = _sum2_

77 for n in range(n - 1, 0, -2): # reversed

78 # y1 = ar * y0 - y1 + c4s.pop()

79 # y0 = ar * y1 - y0 + c4s.pop()

80 y1, t1 = _s2_(ar * y0, ar * t0, -y1, -t1, c4s[n])

81 y0, t0 = _s2_(ar * y1, ar * t1, -y0, -t0, c4s[n - 1])

82 s, _ = _s2_(cx * y0, cx * t0, -cx * y1, -cx * t1)

83 return s # cx * (y0 - y1)

84

85

86_f = float # in _f2 and .geodesicx._C4_24, _27 and _30

87

88

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

90 '''(INTERNAL) For C{_coeffs}.

91 '''

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

93

94

95 def _sincos12(sin1, cos1, sin2, cos2, sineg0=False): # PYCHOK shared

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

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

98

99 Use C{-sin1} to get C{sin12} and C{cos12} of the sum

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

101

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

103

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

105 '''

106 s = sin2 * cos1 - sin1 * cos2

107 c = cos2 * cos1 + sin1 * sin2

108 if sineg0 and s < 0:

109 s = _0_0 # max(s, _0_0) or NEG0?

110 return s, c

111

112

113 def _sin1cos2(sin1, cos1, sin2, cos2): # PYCHOK shared

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

115

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

117 '''

118 s = sin1 * cos2

119 c = _hypot(sin1 * sin2, cos1)

120 return s, c # _norm2(s, c)

121

122

123 def _xnC4(**name_nC4):

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

125 '''

126 n, nC4 = name_nC4.popitem()

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

128 raise GeodesicError(n, nC4, txt=_not_(_or(*map(str, _nC4s))))

129 return _nC4s[nC4]

130

131

132# **) MIT License

133#

134# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

135#

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

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

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

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

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

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

142#

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

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

145#

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

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

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

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

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

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

152# OTHER DEALINGS IN THE SOFTWARE.