Coverage for pygeodesy/auxilats/_CX_6.py: 100%

6 statements  

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Coefficients for C{_AUXLATITUDE_ORDER} 6 from I{Karney}'s C++ class U{AuxLatitude 

5<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} 

6transcoded to a Python C{_Rdict[auxout][auxin]} of C{_Rtuple}s. 

7 

8Copyright (C) Charles Karney (2022-2024) Karney@Alum.MIT.edu> and licensed under the 

9MIT/X11 License. For more information, see <https://GeographicLib.SourceForge.io>. 

10''' 

11from pygeodesy.auxilats.auxily import Aux 

12from pygeodesy.auxilats._CX_Rs import _Rcoeffs, _Rdict, _Rtuple 

13 

14__all__ = () 

15__version__ = '25.04.09' 

16 

17_coeffs_6 = _Rcoeffs(6, { # GEOGRAPHICLIB_AUXLATITUDE_ORDER == 6 

18 Aux.PHI: _Rdict(78, 

19 # C[phi,phi] skipped 

20 _Rtuple(Aux.BETA, 12, # C[phi,beta]; even coeffs only 

21 '0, 0, 1, 0, 0, 1/2, 0, 1/3, 0, 1/4, 1/5, 1/6'), 

22 _Rtuple(Aux.THETA, 12, # C[phi,theta]; even coeffs only 

23 '2, -2, 2, 6, -4, 2, -8, 8/3, -16, 4, 32/5, 32/3'), 

24 _Rtuple(Aux.MU, 12, # C[phi,mu]; even coeffs only 

25 '269/512, -27/32, 3/2, 6759/4096, -55/32, 21/16, -417/128', 

26 '151/96, -15543/2560, 1097/512, 8011/2560, 293393/61440'), 

27 _Rtuple(Aux.CHI, 21, # C[phi,chi] 

28 '-2854/675, 26/45, 116/45, -2, -2/3, 2, 2323/945, 2704/315, -227/45', 

29 '-8/5, 7/3, 73814/2835, -1262/105, -136/35, 56/15, -399572/14175', 

30 '-332/35, 4279/630, -144838/6237, 4174/315, 601676/22275'), 

31 _Rtuple(Aux.XI, 21, # C[phi,xi] 

32 '28112932/212837625, 60136/467775, -2582/14175, -16/35, 4/45', 

33 '4/3, 251310128/638512875, -21016/51975, -11966/14175, 152/945', 

34 '46/45, -8797648/10945935, -94388/66825, 3802/14175, 3044/2835', 

35 '-1472637812/638512875, 41072/93555, 6059/4725, 455935736/638512875', 

36 '768272/467775, 4210684958/1915538625') 

37 ), 

38 Aux.BETA: _Rdict(78, 

39 _Rtuple(Aux.PHI, 12, # C[beta,phi]; even coeffs only 

40 '0, 0, -1, 0, 0, 1/2, 0, -1/3, 0, 1/4, -1/5, 1/6'), 

41 # C[beta,beta] skipped 

42 _Rtuple(Aux.THETA, 12, # C[beta,theta]; even coeffs only 

43 '0, 0, 1, 0, 0, 1/2, 0, 1/3, 0, 1/4, 1/5, 1/6'), 

44 _Rtuple(Aux.MU, 12, # C[beta,mu]; even coeffs only 

45 '205/1536, -9/32, 1/2, 1335/4096, -37/96, 5/16, -75/128', 

46 '29/96, -2391/2560, 539/1536, 3467/7680, 38081/61440'), 

47 _Rtuple(Aux.CHI, 21, # C[beta,chi] 

48 '-3118/4725, -1/3, 38/45, -1/3, -2/3, 1, -247/270, 50/21, -7/9', 

49 '-14/15, 5/6, 17564/2835, -5/3, -34/21, 16/15, -49877/14175', 

50 '-28/9, 2069/1260, -28244/4455, 883/315, 797222/155925'), 

51 _Rtuple(Aux.XI, 21, # C[beta,xi] 

52 '7947332/212837625, 11824/467775, -1082/14175, -46/315, 4/45', 

53 '1/3, 39946703/638512875, -16672/155925, -338/2025, 68/945', 

54 '17/90, -255454/1563705, -101069/467775, 1102/14175, 461/2835', 

55 '-189032762/638512875, 1786/18711, 3161/18900', 

56 '80274086/638512875, 88868/467775, 880980241/3831077250') 

57 ), 

58 Aux.THETA: _Rdict(78, 

59 _Rtuple(Aux.PHI, 12, # C[theta,phi]; even coeffs only 

60 '-2, 2, -2, 6, -4, 2, 8, -8/3, -16, 4, -32/5, 32/3'), 

61 _Rtuple(Aux.BETA, 12, # C[theta,beta]; even coeffs only 

62 '0, 0, -1, 0, 0, 1/2, 0, -1/3, 0, 1/4, -1/5, 1/6'), 

63 # C[theta,theta] skipped 

64 _Rtuple(Aux.MU, 12, # C[theta,mu]; even coeffs only 

65 '499/1536, -23/32, -1/2, 6565/12288, -5/96, 5/16, -77/128', 

66 '1/32, -4037/7680, 283/1536, 1301/7680, 17089/61440'), 

67 _Rtuple(Aux.CHI, 21, # C[theta,chi] 

68 '-3658/4725, 2/9, 4/9, -2/3, -2/3, 0, 61/135, 68/45, -23/45', 

69 '-4/15, 1/3, 9446/2835, -46/35, -24/35, 2/5, -34712/14175', 

70 '-80/63, 83/126, -2362/891, 52/45, 335882/155925'), 

71 _Rtuple(Aux.XI, 21, # C[theta,xi] 

72 '216932/2627625, 109042/467775, -2102/14175, -158/315, 4/45', 

73 '-2/3, 117952358/638512875, -7256/155925, 934/14175, -16/945', 

74 '16/45, -7391576/54729675, -25286/66825, 922/14175, -232/2835', 

75 '-67048172/638512875, 268/18711, 719/4725', 

76 '46774256/638512875, 14354/467775, 253129538/1915538625') 

77 ), 

78 Aux.MU: _Rdict(78, 

79 _Rtuple(Aux.PHI, 12, # C[mu,phi]; even coeffs only 

80 '-3/32, 9/16, -3/2, 135/2048, -15/32, 15/16, 105/256, -35/48', 

81 '-189/512, 315/512, -693/1280, 1001/2048'), 

82 _Rtuple(Aux.BETA, 12, # C[mu,beta]; even coeffs only 

83 '-1/32, 3/16, -1/2, -9/2048, 1/32, -1/16, 3/256, -1/48', 

84 '3/512, -5/512, -7/1280, -7/2048'), 

85 _Rtuple(Aux.THETA, 12, # C[mu,theta]; even coeffs only 

86 '-15/32, 13/16, 1/2, -1673/2048, 33/32, -1/16, 349/256, -5/16', 

87 '963/512, -261/512, -921/1280, -6037/6144'), 

88 # C[mu,mu] skipped 

89 _Rtuple(Aux.CHI, 21, # C[mu,chi] 

90 '7891/37800, -127/288, 41/180, 5/16, -2/3, 1/2', 

91 '-1983433/1935360, 281/630, 557/1440, -3/5, 13/48', 

92 '167603/181440, 15061/26880, -103/140, 61/240', 

93 '6601661/7257600, -179/168, 49561/161280', 

94 '-3418889/1995840, 34729/80640, 212378941/319334400'), 

95 _Rtuple(Aux.XI, 21, # C[mu,xi] 

96 '12674323/851350500, -384229/14968800, -1609/28350, 121/1680', 

97 '4/45, -1/6, -31621753811/1307674368000, -431/17325, 16463/453600', 

98 '26/945, -29/720, -32844781/1751349600, 3746047/119750400, 449/28350', 

99 '-1003/45360, 10650637121/326918592000, 629/53460, -40457/2419200', 

100 '205072597/20432412000, -1800439/119750400, -59109051671/3923023104000') 

101 ), 

102 Aux.CHI: _Rdict(105, 

103 _Rtuple(Aux.PHI, 21, # C[chi,phi] 

104 '4642/4725, 32/45, -82/45, 4/3, 2/3, -2, -1522/945, 904/315', 

105 '-13/9, -16/15, 5/3, -12686/2835, 8/5, 34/21, -26/15, -24832/14175', 

106 '-12/5, 1237/630, 109598/31185, -734/315, 444337/155925'), 

107 _Rtuple(Aux.BETA, 21, # C[chi,beta] 

108 '-998/4725, 2/5, -16/45, 0, 2/3, -1, -2/27, -22/105, 19/45', 

109 '-2/5, 1/6, 116/567, -22/105, 16/105, -1/15, 2123/14175, -8/105', 

110 '17/1260, 128/4455, -1/105, 149/311850'), 

111 _Rtuple(Aux.THETA, 21, # C[chi,theta] 

112 '1042/4725, -14/45, -2/9, 2/3, 2/3, 0, -712/945, -4/45, 43/45', 

113 '4/15, -1/3, 274/2835, 124/105, 2/105, -2/5, 21068/14175, -16/105', 

114 '-55/126, -9202/31185, -22/45, -90263/155925'), 

115 _Rtuple(Aux.MU, 21, # C[chi,mu] 

116 '-96199/604800, 81/512, 1/360, -37/96, 2/3, -1/2', 

117 '1118711/3870720, -46/105, 437/1440, -1/15, -1/48', 

118 '-5569/90720, 209/4480, 37/840, -17/480', 

119 '830251/7257600, 11/504, -4397/161280', 

120 '108847/3991680, -4583/161280, -20648693/638668800'), 

121 # C[chi,chi] skipped 

122 _Rtuple(Aux.XI, 21, # C[chi,xi] 

123 '-55271278/212837625, 27128/93555, -2312/14175, -88/315, 34/45', 

124 '-2/3, 106691108/638512875, -65864/155925, 6079/14175, -184/945', 

125 '1/45, 5921152/54729675, -14246/467775, 772/14175, -106/2835', 

126 '75594328/638512875, -5312/467775, -167/9450', 

127 '2837636/638512875, -248/13365, -34761247/1915538625') 

128 ), 

129 Aux.XI: _Rdict(105, 

130 _Rtuple(Aux.PHI, 21, # C[xi,phi] 

131 '-44732/2837835, 20824/467775, 538/4725, 88/315, -4/45, -4/3', 

132 '-12467764/212837625, -37192/467775, -2482/14175, 8/105, 34/45', 

133 '100320856/1915538625, 54968/467775, -898/14175, -1532/2835', 

134 '-5884124/70945875, 24496/467775, 6007/14175', 

135 '-839792/19348875, -23356/66825, 570284222/1915538625'), 

136 _Rtuple(Aux.BETA, 21, # C[xi,beta] 

137 '-70496/8513505, 2476/467775, 34/675, 32/315, -4/45, -1/3', 

138 '53836/212837625, 3992/467775, 74/2025, -4/315, -7/90', 

139 '-661844/1915538625, 7052/467775, 2/14175, -83/2835', 

140 '1425778/212837625, 934/467775, -797/56700', 

141 '390088/212837625, -3673/467775, -18623681/3831077250'), 

142 _Rtuple(Aux.THETA, 21, # C[xi,theta] 

143 '-4286228/42567525, -193082/467775, 778/4725, 62/105, -4/45, 2/3', 

144 '-61623938/70945875, 92696/467775, 12338/14175, -32/315, 4/45', 

145 '427003576/1915538625, 612536/467775, -1618/14175, -524/2835', 

146 '427770788/212837625, -8324/66825, -5933/14175', 

147 '-9153184/70945875, -320044/467775, -1978771378/1915538625'), 

148 _Rtuple(Aux.MU, 21, # C[xi,mu] 

149 '-9292991/302702400, 7764059/239500800, 1297/18900, -817/10080, -4/45, 1/6', 

150 '36019108271/871782912000, 35474/467775, -29609/453600, -2/35, 49/720', 

151 '3026004511/30648618000, -4306823/59875200, -2917/56700, 4463/90720', 

152 '-368661577/4036032000, -102293/1871100, 331799/7257600', 

153 '-875457073/13621608000, 11744233/239500800, 453002260127/7846046208000'), 

154 _Rtuple(Aux.CHI, 21, # C[xi,chi] 

155 '2706758/42567525, -55222/93555, 2458/4725, 46/315, -34/45, 2/3', 

156 '-340492279/212837625, 516944/467775, 3413/14175, -256/315, 19/45', 

157 '4430783356/1915538625, 206834/467775, -15958/14175, 248/567', 

158 '62016436/70945875, -832976/467775, 16049/28350', 

159 '-651151712/212837625, 15602/18711, 2561772812/1915538625') # PYCHOK exported 

160 # C[xi,xi] skipped 

161 ) 

162}) 

163# _ptrs_6 = (0, 0, 12, 24, 36, 57, 78, 90, 90, 102, 114, 135, 

164# 156, 168, 180, 180, 192, 213, 234, 246, 258, 270, 270, 291, 

165# 312, 333, 354, 375, 396, 396, 417, 438, 459, 480, 501, 522, 

166# 522) # PYCHOK exported 

167del _Rcoeffs, _Rdict, _Rtuple 

168 

169# **) MIT License 

170# 

171# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

172# 

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

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

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

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

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

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

179# 

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

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

182# 

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

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

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

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

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

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

189# OTHER DEALINGS IN THE SOFTWARE.