Coverage for pygeodesy/auxilats/auxDLat.py: 95%
150 statements
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« prev ^ index » next coverage.py v7.6.1, created at 2025-01-06 12:20 -0500
1# -*- coding: utf-8 -*-
3u'''Class L{AuxDLat} transcoded to Python from I{Karney}'s C++ class U{DAuxLatitude
4<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>}
5in I{GeographicLib version 2.2+}.
7Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2022-2024) and licensed
8under the MIT/X11 License. For more information, see the U{GeographicLib
9<https://GeographicLib.SourceForge.io>} documentation.
10'''
11# make sure int/int division yields float quotient, see .basics
12from __future__ import division as _; del _ # PYCHOK semicolon
14from pygeodesy.auxilats.auxily import Aux, _Datan, _Dasinh, _Dm, _sc, _sn, \
15 AuxError
16from pygeodesy.auxilats.auxLat import AuxLat, _ALL_DOCS
17from pygeodesy.basics import map1, _reverange
18from pygeodesy.constants import INF, NAN, isfinite, isinf, isnan, _0_0, _0_5, \
19 _1_0, _2_0, _N_2_0, _naninf, _over, _1_over
20from pygeodesy.elliptic import Elliptic as _Ef, Fsum
21# from pygeodesy.errors import AuxError # from .auxilats.auxily
22# from pygeodesy.fsums import Fsum # from .elliptic
23# from pygeodesy.lazily import _ALL_DOCS # from .auxilats.auxLat
24from pygeodesy.utily import atan1, atan2 # from .auxilats.auxily
26from math import cos, sin, sqrt
28__all__ = ()
29__version__ = '24.11.24'
32class AuxDLat(AuxLat):
33 '''Class to compute C{Divided Differences} of I{Auxiliary}
34 latitudes and other C{Divided Differences} needed for
35 L{RhumbAux} and L{RhumbLineAux} calculations.
36 '''
38 def CParametric(self, Zeta1, Zeta2):
39 '''Short for C{.Dconvert(Aux.BETA, B{Zeta1}, B{Zeta2})}.
40 '''
41 return self.Dconvert(Aux.BETA, Zeta1, Zeta2)
43 def CRectifying(self, Zeta1, Zeta2):
44 '''Short for C{.Dconvert(Aux.MU, B{Zeta1}, B{Zeta2})}.
45 '''
46 return self.Dconvert(Aux.MU, Zeta1, Zeta2)
48 def _Datanhee(self, x, y):
49 # atan(e*sn(tphi))/e:
50 # Datan(e*sn(x),e*sn(y))*Dsn(x,y)/Datan(x,y)
51 # asinh(e1*sn(fm1*tphi)):
52 # Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
53 # e1 * Dsn(fm1*x, fm1*y) *fm1 / (e * Datan(x,y))
54 # = Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
55 # Dsn(fm1*x, fm1*y) / Datan(x,y)
56 if self.f < 0:
57 e = self._e
58 r = _Datan(e * _sn(x), e * _sn(y))
59 else:
60 x *= self._fm1
61 y *= self._fm1
62 e1 = self._e1
63 r = _Dasinh(e1 * _sn(x), e1 * _sn(y))
64 return _Dsn(x, y) * r
66 def Dconvert(self, auxout, Zeta1, Zeta2):
67 '''I{Divided Difference} of one auxiliary latitude wrt another.
68 '''
69 auxin = Zeta1._AUX
70 # assert Zeta2._AUX == auxin
71 try:
72 if auxout != auxin:
73 cs = self._coeffs(auxout, auxin)
74 # assert len(cs) == self.ALorder
75 r = _DClenshaw(True, Zeta1, Zeta2, cs, self.ALorder)
76 else:
77 r = _1_0
78 except AuxError: # no _coeffs
79 r = NAN
80 return r
82 def DE(self, X, Y):
83 # We assume that X and Y are in [-90d, 90d] and
84 # have the same sign. If not we would include
85 # if (Xn.y() * Yn.y() < 0)
86 # return d != 0 ? (E(X) - E(Y)) / d : 1
87 # The general formula fails for x = y = 0d and
88 # x = y = 90d. Probably this is fixable (the
89 # formula works for other x = y. But let's
90 # also stipulate that x != y.
92 # Make both y positive, so we can do the swap a <-> b trick
93 sx, cx, x = X._yxr_normalized(True)
94 sy, cy, y = Y._yxr_normalized(True)
95 k2, d = -self._e12, (y - x)
96 # Switch prolate to oblate, then use formulas for k2 < 0
97 if self.f < 0: # XXX and False?
98 sx, cx = cx, sx
99 sy, cy = cy, sy
100 d, k2 = -d, self._e2
101 # See DLMF: Eqs (19.11.2) and (19.11.4) letting
102 Dt = _Dsin(x, y) * (sx + sy)
103 if Dt:
104 t = _sxk2y(sx, sy, k2) + _sxk2y(sy, sx, k2)
105 Dt = _over(Dt, t * (cx + cy))
106 t = d * Dt
107 t2 = _1_0 + t**2
108 Dt *= _2_0 / t2
109 sk2 = (d * Dt)**2 * k2
110 d2 = _1_0 - sk2
111 c2 = ((_1_0 - t) * (_1_0 + t) / t2)**2 if t else _1_0
112 # E(z)/sin(z)
113 Dt *= _Ef._RFRD(c2, d2, _1_0, sk2) - k2 * sx * sy
114 return Dt
116 def DIsometric(self, Phi1, Phi2):
117 '''I{Divided Difference} of the isometric wrt the geographic latitude.
118 '''
119 tx, ty = Phi1.tan, Phi2.tan
120 if isnan(ty) or isnan(tx): # PYCHOK no cover
121 r = NAN
122 elif isinf(ty) or isinf(tx): # PYCHOK no cover
123 r = INF
124 else: # psi = asinh(tan(Phi)) - e^2 * atanhee(tan(Phi))
125 r = self._Datanhee(tx, ty) * self._e2
126 r = _over(_Dasinh(tx, ty) - r, _Datan(tx, ty))
127 return r
129 def DParametric(self, Phi1, Phi2):
130 '''I{Divided Difference} of the parametric wrt the geographic latitude.
131 '''
132 fm1, e2m1 = self._fm1, self._e2m1
133 tx, ty = Phi1.tan, Phi2.tan
134 # DbetaDphi = Datan(fm1*tx, fm1*ty) * fm1 / Datan(tx, ty)
135 # Datan(x, y) = 1 / (1 + x^2) if x == y
136 # = (atan1(y) - atan1(x)) / (y-x) if x*y < 0
137 # = atan1(y-x, x*y + 1) / (y-x) if x*y > 0
138 txy = tx * ty
139 if txy < 0 or (isinf(ty) and not tx):
140 _a = atan1
141 r = _a(fm1 * ty) - _a(fm1 * tx)
142 r = _over(r, _a(ty) - _a(tx))
143 elif tx == ty: # includes tx = ty = inf
144 if txy > 1: # == tx**2
145 txy = _1_over(txy)
146 r = txy + e2m1
147 else:
148 r = txy * e2m1 + _1_0
149 r = _over((txy + _1_0) * fm1, r)
150 else:
151 if txy > 1:
152 tx = _1_over(tx)
153 ty = _1_over(ty)
154 txy = _1_over(txy)
155 t = txy + e2m1
156 else:
157 t = txy * e2m1 + _1_0
158 r = ty - tx
159 r = _over(atan2(r * fm1, t), atan2(r, txy + _1_0))
160 return r
162 def DRectifying(self, Phi1, Phi2):
163 '''I{Divided Difference} of the rectifying wrt the geographic latitude.
164 '''
165 # Stipulate that Phi1 and Phi2 are in [-90d, 90d]
166 x, y = Phi1.toRadians, Phi2.toRadians
167 if y == x: # isnear0
168 Mu1 = self.Rectifying(Phi1, diff=True)
169 tphi1, r = Phi1.tan, Mu1.diff
170 if isfinite(tphi1):
171 r *= _over(_sc(tphi1), _sc(Mu1.tan))**2
172 else: # PYCHOK no cover
173 r = _1_over(r)
174 elif (x * y) < 0:
175 r = _over(self.Rectifying(Phi2).toRadians -
176 self.Rectifying(Phi1).toRadians, y - x)
177 else:
178 r = _over(self.b, self.RectifyingRadius(True))
179 r *= self.DE(*map1(self.Parametric, Phi1, Phi2))
180 r *= self.DParametric(Phi1, Phi2)
181 return r # or INF or NAN
184def _DClenshaw(sinp, Zeta1, Zeta2, cs, K):
185 '''(INTERNAL) I{Divided Difference} of L{AuxLat._Clenshaw}.
187 @return: C{float} if B{C{sinp}} otherwise a C{Fsum}.
188 '''
189 s1, c1, r1 = Zeta1._yxr_normalized(False)
190 s2, c2, r2 = Zeta2._yxr_normalized(False)
191 Delta = r2 - r1
192 # Evaluate (Clenshaw(sinp, szeta2, czeta2, cs, K) -
193 # Clenshaw(sinp, szeta1, czeta1, cs, K)) / Delta
194 # or f = sin if sinp else cos
195 # sum(cs[k] * (f((2*k+2) * Zeta2) -
196 # f((2*k+2) * Zeta2))) / Delta
197 #
198 # Delta is EITHER 1, giving the plain difference OR (Zeta2 - Zeta1)
199 # in radians, giving the I{Divided Difference}. Other values will
200 # produce nonsense.
201 #
202 # Suffices a and b denote [1,1], [2,1] elements of matrix/vector
203 cp = cm = c2 * c1
204 t = s2 * s1
205 cp -= t # not +
206 cm += t # not -
208 sp = s2 * c1
209 t = c2 * s1
210 smd = ((sin(Delta) / Delta) if Delta != _1_0 else
211 (sp - t)) if Delta else _1_0
212 sp += t
214 xa = cp * cm * _2_0
215 xb = sp * smd * _N_2_0
216 xD = xb * Delta**2
218 if isfinite(xD) and isfinite(xb) and isfinite(xa):
219 U0a, U1a = Fsum(), Fsum()
220 U0b, U1b = Fsum(), Fsum()
221 for k in _reverange(K): # assert len(cs) == K
222 # t = x . U0 - U1 + cs[k] * I
223 U1a -= U0a * xa + U0b * xD + cs[k]
224 U1b -= U0a * xb + U0b * xa
225 U1a, U0a = U0a, -U1a
226 U1b, U0b = U0b, -U1b
227 # F0a = (sp if sinp else cp) * cm
228 # F0b = (cp if sinp else -sp) * smd
229 # Fm1a = 0 if sinp else 1 # Fm1b = 0
230 # return (U0b * F0a + U0a * F0b - U1b * Fm1a) * 2
231 if sinp:
232 U1b = _0_0
233 else:
234 sp, cp = cp, -sp
235 U0b *= sp * cm
236 U0a *= cp * smd
237 U0a += U0b
238 U0a = _Dm(U0a, U1b, _2_0)
239 r = float(U0a) if sinp else U0a # Fsum
240 else:
241 r = _naninf(xD, xb, xa)
242 return r
245def _Dsin(x, y): # see also .rhumb.ekx._Dsin
246 r = cos((x + y) * _0_5)
247 d = (x - y) * _0_5
248 if d:
249 r *= sin(d) / d
250 return r
253def _Dsn(x, y):
254 # (sn(y) - sn(x)) / (y - x)
255 if x != y:
256 snx, sny = _sn(x), _sn(y)
257 if (x * y) > 0:
258 scx, scy = _sc(x), _sc(y)
259 r = _over((snx / scy) + (sny / scx),
260 (snx + sny) * scy * scx)
261 else:
262 r = (sny - snx) / (y - x)
263 elif x:
264 r = _1_over(_sc(x) * (x**2 + _1_0)) # == 1 / sqrt3(x**2 + 1)
265 else:
266 r = _1_0
267 return r
270def _sxk2y(sx, sy, k2):
271 # .DE helper
272 sy *= sy * k2
273 if sy:
274 try:
275 sx *= sqrt(_1_0 - sy)
276 except ValueError: # domain error
277 sx = NAN
278 return sx
281__all__ += _ALL_DOCS(AuxDLat)
283# **) MIT License
284#
285# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved.
286#
287# Permission is hereby granted, free of charge, to any person obtaining a
288# copy of this software and associated documentation files (the "Software"),
289# to deal in the Software without restriction, including without limitation
290# the rights to use, copy, modify, merge, publish, distribute, sublicense,
291# and/or sell copies of the Software, and to permit persons to whom the
292# Software is furnished to do so, subject to the following conditions:
293#
294# The above copyright notice and this permission notice shall be included
295# in all copies or substantial portions of the Software.
296#
297# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
298# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
299# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
300# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
301# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
302# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
303# OTHER DEALINGS IN THE SOFTWARE.