Coverage for pygeodesy/auxilats/auxDLat.py: 91%
149 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-09-15 09:43 -0400
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>} (2022-2023) 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
25from math import atan, atan2, cos, sin, sqrt
27__all__ = ()
28__version__ = '23.09.14'
31class AuxDLat(AuxLat):
32 '''Class to compute C{Divided Differences} of I{Auxiliary}
33 latitudes and other C{Divided Differences} needed for
34 L{RhumbAux} and L{RhumbLineAux} calculations.
35 '''
37 def CParametric(self, Zeta1, Zeta2):
38 '''Short for C{.Dconvert(Aux.BETA, B{Zeta1}, B{Zeta2})}.
39 '''
40 return self.Dconvert(Aux.BETA, Zeta1, Zeta2)
42 def CRectifying(self, Zeta1, Zeta2):
43 '''Short for C{.Dconvert(Aux.MU, B{Zeta1}, B{Zeta2})}.
44 '''
45 return self.Dconvert(Aux.MU, Zeta1, Zeta2)
47 def _Datanhee(self, x, y):
48 # atan(e*sn(tphi))/e:
49 # Datan(e*sn(x),e*sn(y))*Dsn(x,y)/Datan(x,y)
50 # asinh(e1*sn(fm1*tphi)):
51 # Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
52 # e1 * Dsn(fm1*x, fm1*y) *fm1 / (e * Datan(x,y))
53 # = Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
54 # Dsn(fm1*x, fm1*y) / Datan(x,y)
55 if self.f < 0:
56 e = self._e
57 r = _Datan(e * _sn(x), e * _sn(y))
58 else:
59 x *= self._fm1
60 y *= self._fm1
61 e1 = self._e1
62 r = _Dasinh(e1 * _sn(x), e1 * _sn(y))
63 return _Dsn(x, y) * r
65 def Dconvert(self, auxout, Zeta1, Zeta2):
66 '''I{Divided Difference} of one auxiliary latitude wrt another.
67 '''
68 auxin = Zeta1._AUX
69 # assert Zeta2._AUX == auxin
70 try:
71 if auxout != auxin:
72 cs = self._coeffs(auxout, auxin)
73 # assert len(cs) == self.ALorder
74 r = _DClenshaw(True, Zeta1, Zeta2, cs, self.ALorder)
75 else:
76 r = _1_0
77 except AuxError: # no _coeffs
78 r = NAN
79 return r
81 def DE(self, X, Y):
82 # We assume that X and Y are in [-90d, 90d] and
83 # have the same sign. If not we would include
84 # if (Xn.y() * Yn.y() < 0)
85 # return d != 0 ? (E(X) - E(Y)) / d : 1
86 # The general formula fails for x = y = 0d and
87 # x = y = 90d. Probably this is fixable (the
88 # formula works for other x = y. But let's
89 # also stipulate that x != y.
91 # Make both y positive, so we can do the swap a <-> b trick
92 sx, cx, x = X._yxr_normalized(True)
93 sy, cy, y = Y._yxr_normalized(True)
94 k2, d = -self._e12, (y - x)
95 # Switch prolate to oblate, then use formulas for k2 < 0
96 if self.f < 0: # XXX and False?
97 sx, cx = cx, sx
98 sy, cy = cy, sy
99 d, k2 = -d, self._e2
100 # See DLMF: Eqs (19.11.2) and (19.11.4) letting
101 Dt = _Dsin(x, y) * (sx + sy)
102 if Dt:
103 t = _sxk2y(sx, sy, k2) + _sxk2y(sy, sx, k2)
104 Dt = _over(Dt, t * (cx + cy))
105 t = d * Dt
106 t2 = _1_0 + t**2
107 Dt *= _2_0 / t2
108 sk2 = (d * Dt)**2 * k2
109 d2 = _1_0 - sk2
110 c2 = ((_1_0 - t) * (_1_0 + t) / t2)**2 if t else _1_0
111 # E(z)/sin(z)
112 Dt *= _Ef._RFRD(c2, d2, _1_0, sk2) - k2 * sx * sy
113 return Dt
115 def DIsometric(self, Phi1, Phi2):
116 '''I{Divided Difference} of the isometric wrt the geographic latitude.
117 '''
118 tx, ty = Phi1.tan, Phi2.tan
119 if isnan(ty) or isnan(tx): # PYCHOK no cover
120 r = NAN
121 elif isinf(ty) or isinf(tx): # PYCHOK no cover
122 r = INF
123 else: # psi = asinh(tan(Phi)) - e^2 * atanhee(tan(Phi))
124 r = self._Datanhee(tx, ty) * self._e2
125 r = _over(_Dasinh(tx, ty) - r, _Datan(tx, ty))
126 return r
128 def DParametric(self, Phi1, Phi2):
129 '''I{Divided Difference} of the parametric wrt the geographic latitude.
130 '''
131 fm1, e2m1 = self._fm1, self._e2m1
132 tx, ty = Phi1.tan, Phi2.tan
133 # DbetaDphi = Datan(fm1*tx, fm1*ty) * fm1 / Datan(tx, ty)
134 # Datan(x, y) = 1 / (1 + x^2), if x == y
135 # = (atan(y) - atan(x)) / (y-x), if x*y < 0
136 # = atan((y-x) / (1 + x*y)) / (y-x), if x*y > 0
137 txy = tx * ty
138 if txy < 0 or (isinf(ty) and not tx):
139 _a = atan
140 r = _over(_a(fm1 * ty) - _a(fm1 * tx), _a(ty) - _a(tx))
141 elif tx == ty: # includes tx = ty = inf
142 if txy > 1: # == tx**2
143 txy = _1_over(txy)
144 r = txy + e2m1
145 else:
146 r = txy * e2m1 + _1_0
147 r = _over(fm1 * (txy + _1_0), r)
148 else:
149 if txy > 1:
150 tx = _1_over(tx)
151 ty = _1_over(ty)
152 txy = tx * ty
153 t = txy + e2m1
154 else:
155 t = txy * e2m1 + _1_0
156 r = ty - tx
157 r = _over(atan2(r * fm1, t), atan2(r, _1_0 + txy))
158 return r
160 def DRectifying(self, Phi1, Phi2):
161 '''I{Divided Difference} of the rectifying wrt the geographic latitude.
162 '''
163 # Stipulate that Phi1 and Phi2 are in [-90d, 90d]
164 x, y = Phi1.toRadians, Phi2.toRadians
165 if y == x: # isnear0
166 Mu1 = self.Rectifying(Phi1, diff=True)
167 tphi1, r = Phi1.tan, Mu1.diff
168 if isfinite(tphi1):
169 r *= _over(_sc(tphi1), _sc(Mu1.tan))**2
170 else: # PYCHOK no cover
171 r = _1_over(r)
172 elif (x * y) < 0:
173 r = _over(self.Rectifying(Phi2).toRadians -
174 self.Rectifying(Phi1).toRadians, y - x)
175 else:
176 r = _over(self.b, self.RectifyingRadius(True))
177 r *= self.DE(*map1(self.Parametric, Phi1, Phi2))
178 r *= self.DParametric(Phi1, Phi2)
179 return r # or INF or NAN
182def _DClenshaw(sinp, Zeta1, Zeta2, cs, K):
183 '''(INTERNAL) I{Divided Difference} of L{AuxLat._Clenshaw}.
185 @return: C{Fsum} if B{C{sinp}} otherwise a C{float}.
186 '''
187 s1, c1, r1 = Zeta1._yxr_normalized(False)
188 s2, c2, r2 = Zeta2._yxr_normalized(False)
189 Delta = r2 - r1
190 # Evaluate (Clenshaw(sinp, szeta2, czeta2, cs, K) -
191 # Clenshaw(sinp, szeta1, czeta1, cs, K)) / Delta
192 # or f = sin if sinp else cos
193 # sum(cs[k] * (f((2*k+2) * Zeta2) -
194 # f((2*k+2) * Zeta2))) / Delta
195 #
196 # Delta is EITHER 1, giving the plain difference OR (Zeta2 - Zeta1)
197 # in radians, giving the I{Divided Difference}. Other values will
198 # produce nonsense.
199 #
200 # Suffices a and b denote [1,1], [2,1] elements of matrix/vector
201 cp = cm = c2 * c1
202 t = s2 * s1
203 cp -= t # not +
204 cm += t # not -
206 sp = s2 * c1
207 t = c2 * s1
208 smd = ((sin(Delta) / Delta) if Delta != _1_0 else
209 (sp - t)) if Delta else _1_0
210 sp += t
212 xa = cp * cm * _2_0
213 xb = sp * smd * _N_2_0
214 xD = xb * Delta**2
216 if isfinite(xD) and isfinite(xb) and isfinite(xa):
217 U0a, U1a = Fsum(), Fsum()
218 U0b, U1b = Fsum(), Fsum()
219 for k in _reverange(K): # assert len(cs) == K
220 # t = x . U0 - U1 + cs[k] * I
221 U1a -= U0a * xa + U0b * xD + cs[k]
222 U1b -= U0a * xb + U0b * xa
223 U1a, U0a = U0a, -U1a
224 U1b, U0b = U0b, -U1b
225 # F0a = (sp if sinp else cp) * cm
226 # F0b = (cp if sinp else -sp) * smd
227 # Fm1a = 0 if sinp else 1 # Fm1b = 0
228 # return (U0b * F0a + U0a * F0b - U1b * Fm1a) * 2
229 if sinp:
230 U1b = _0_0
231 else:
232 sp, cp = cp, -sp
233 U0b *= sp * cm
234 U0a *= cp * smd
235 U0a += U0b
236 U0a = _Dm(U0a, U1b, _2_0)
237 r = float(U0a) if sinp else U0a # Fsum
238 else:
239 r = _naninf(xD, xb, xa)
240 return r
243def _Dsin(x, y): # see also .rhumbx._Dsin
244 r = cos((x + y) * _0_5)
245 d = (x - y) * _0_5
246 if d:
247 r *= sin(d) / d
248 return r
251def _Dsn(x, y):
252 # (sn(y) - sn(x)) / (y - x)
253 if x != y:
254 snx, sny = _sn(x), _sn(y)
255 if (x * y) > 0:
256 scx, scy = _sc(x), _sc(y)
257 r = _over((snx / scy) + (sny / scx),
258 (snx + sny) * scy * scx)
259 else:
260 r = (sny - snx) / (y - x)
261 elif x:
262 r = _1_over(_sc(x) * (x**2 + _1_0)) # == 1 / sqrt3(x**2 + 1)
263 else:
264 r = _1_0
265 return r
268def _sxk2y(sx, sy, k2):
269 # .DE helper
270 sy *= sy * k2
271 if sy:
272 try:
273 sx *= sqrt(_1_0 - sy)
274 except ValueError: # domain error
275 sx = NAN
276 return sx
279__all__ += _ALL_DOCS(AuxDLat)
281# **) MIT License
282#
283# Copyright (C) 2023-2023 -- mrJean1 at Gmail -- All Rights Reserved.
284#
285# Permission is hereby granted, free of charge, to any person obtaining a
286# copy of this software and associated documentation files (the "Software"),
287# to deal in the Software without restriction, including without limitation
288# the rights to use, copy, modify, merge, publish, distribute, sublicense,
289# and/or sell copies of the Software, and to permit persons to whom the
290# Software is furnished to do so, subject to the following conditions:
291#
292# The above copyright notice and this permission notice shall be included
293# in all copies or substantial portions of the Software.
294#
295# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
296# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
297# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
298# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
299# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
300# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
301# OTHER DEALINGS IN THE SOFTWARE.