Coverage for pygeodesy/geodesicx/gxbases.py: 98%
40 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-04-11 14:35 -0400
2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private L{geodesicx} base class, functions and constants.
6Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2022)
7and licensed under the MIT/X11 License. For more information, see the
8U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.
9'''
11# from pygeodesy.basics import isodd # from .karney
12from pygeodesy.constants import _0_0, _2_0
13from pygeodesy.errors import _not_, _or
14# from pygeodesy.interns import _not_ # from .errors
15from pygeodesy.karney import _CapsBase, GeodesicError, isodd, _hypot, _sum2_
17from math import ldexp as _ldexp
19__all__ = ()
20__version__ = '23.03.25'
22# valid C{nC4}s and C{C4order}s, see _xnC4 below
23_nC4s = {24: 2900, 27: 4032, 30: 5425}
26class _GeodesicBase(_CapsBase): # in .geodsolve
27 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
28 '''
29# def toRepr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
30# '''Return this C{GeodesicExact*} items string.
31#
32# @kwarg prec: The C{float} precision, number of decimal digits (0..9).
33# Trailing zero decimals are stripped for B{C{prec}} values
34# of 1 and above, but kept for negative B{C{prec}} values.
35# @kwarg sep: Separator to join (C{str}).
36#
37# @return: C{GeodesicExact*} (C{str}).
38# '''
39# return Fmt.PAREN(self.named, self.toStr(prec=prec, sep=sep))
40 pass
43def _cosSeries(c4s, sx, cx): # PYCHOK shared .geodesicx.gx and -.gxline
44 '''(INTERNAL) I{Karney}'s cosine series expansion using U{Clenshaw
45 summation<https://WikiPedia.org/wiki/Clenshaw_algorithm>}.
46 '''
47 ar = _2_0 * (cx - sx) * (cx + sx) # 2 * cos(2 * x)
48 y0 = t0 = y1 = t1 = _0_0
49 n = len(c4s) # c4s = list(c4s)
50 if isodd(n):
51 n -= 1
52 y0 = c4s[n] # c4s.pop()
53 _s2_ = _sum2_
54 for n in range(n - 1, 0, -2): # reversed
55 # y1 = ar * y0 - y1 + c4s.pop()
56 # y0 = ar * y1 - y0 + c4s.pop()
57 y1, t1 = _s2_(ar * y0, ar * t0, -y1, -t1, c4s[n])
58 y0, t0 = _s2_(ar * y1, ar * t1, -y0, -t0, c4s[n - 1])
59 s, _ = _s2_(cx * y0, cx * t0, -cx * y1, -cx * t1)
60 return s # cx * (y0 - y1)
63_f = float # in _f2 and .geodesicx._C4_24, _27 and _30
66def _f2(hi, lo): # in .geodesicx._C4_24, _27 and _30
67 '''(INTERNAL) For C{_coeffs}.
68 '''
69 return _ldexp(_f(hi), 52) + _f(lo)
72def _sincos12(sin1, cos1, sin2, cos2, sineg0=False): # PYCHOK shared
73 '''(INTERNAL) Compute the sine and cosine of angle
74 M{ang12 = atan2(sin2, cos2) - atan2(sin1, cos1)}.
76 Use C{-sin1} to get C{sin12} and C{cos12} of the sum
77 M{ang12 = atan2(sin2, cos2) + atan2(sin1, cos1)}.
79 @kwarg sineg0: If C{True}, make negative C{sin12} zero (C{bool}).
81 @return: 2-Tuple C{(sin12, cos12)}.
82 '''
83 s = sin2 * cos1 - sin1 * cos2
84 c = cos2 * cos1 + sin1 * sin2
85 if sineg0 and s < 0:
86 s = _0_0 # max(s, _0_0) or NEG0?
87 return s, c
90def _sin1cos2(sin1, cos1, sin2, cos2): # PYCHOK shared
91 '''(INTERNAL) Compute the C{sin1 * cos2} sine and its cosine.
93 @return: 2-Tuple C{(sin1 * cos2, hypot(sin1 * sin2, cos1)}.
94 '''
95 s = sin1 * cos2
96 c = _hypot(sin1 * sin2, cos1)
97 return s, c # _norm2(s, c)
100def _xnC4(**name_nC4):
101 '''(INTERNAL) Validate C{C4order}.
102 '''
103 n, nC4 = name_nC4.popitem()
104 if nC4 not in _nC4s or not isinstance(nC4, int):
105 raise GeodesicError(n, nC4, txt=_not_(_or(*map(str, _nC4s))))
106 return _nC4s[nC4]
109# **) MIT License
110#
111# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
112#
113# Permission is hereby granted, free of charge, to any person obtaining a
114# copy of this software and associated documentation files (the "Software"),
115# to deal in the Software without restriction, including without limitation
116# the rights to use, copy, modify, merge, publish, distribute, sublicense,
117# and/or sell copies of the Software, and to permit persons to whom the
118# Software is furnished to do so, subject to the following conditions:
119#
120# The above copyright notice and this permission notice shall be included
121# in all copies or substantial portions of the Software.
122#
123# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
124# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
125# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
126# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
127# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
128# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
129# OTHER DEALINGS IN THE SOFTWARE.