EllipticFunction.hpp
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1 
10 #if !defined(GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP)
11 #define GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP 1
12 
14 
15 namespace GeographicLib {
16 
63  private:
64  typedef Math::real real;
65 
66  enum { num_ = 13 }; // Max depth required for sncndn; probably 5 is enough.
67  real _k2, _kp2, _alpha2, _alphap2, _eps;
68  real _Kc, _Ec, _Dc, _Pic, _Gc, _Hc;
69  public:
72 
89  EllipticFunction(real k2 = 0, real alpha2 = 0)
90  { Reset(k2, alpha2); }
91 
111  EllipticFunction(real k2, real alpha2, real kp2, real alphap2)
112  { Reset(k2, alpha2, kp2, alphap2); }
113 
125  void Reset(real k2 = 0, real alpha2 = 0)
126  { Reset(k2, alpha2, 1 - k2, 1 - alpha2); }
127 
147  void Reset(real k2, real alpha2, real kp2, real alphap2);
148 
150 
153 
157  Math::real k2() const { return _k2; }
158 
163  Math::real kp2() const { return _kp2; }
164 
168  Math::real alpha2() const { return _alpha2; }
169 
174  Math::real alphap2() const { return _alphap2; }
176 
179 
190  Math::real K() const { return _Kc; }
191 
202  Math::real E() const { return _Ec; }
203 
215  Math::real D() const { return _Dc; }
216 
223  Math::real KE() const { return _k2 * _Dc; }
224 
237  Math::real Pi() const { return _Pic; }
238 
250  Math::real G() const { return _Gc; }
251 
264  Math::real H() const { return _Hc; }
266 
269 
281  Math::real F(real phi) const;
282 
294  Math::real E(real phi) const;
295 
303  Math::real Ed(real ang) const;
304 
312  Math::real Einv(real x) const;
313 
327  Math::real Pi(real phi) const;
328 
341  Math::real D(real phi) const;
342 
368  Math::real G(real phi) const;
369 
396  Math::real H(real phi) const;
398 
411  Math::real F(real sn, real cn, real dn) const;
412 
423  Math::real E(real sn, real cn, real dn) const;
424 
436  Math::real Pi(real sn, real cn, real dn) const;
437 
448  Math::real D(real sn, real cn, real dn) const;
449 
461  Math::real G(real sn, real cn, real dn) const;
462 
474  Math::real H(real sn, real cn, real dn) const;
476 
479 
490  Math::real deltaF(real sn, real cn, real dn) const;
491 
502  Math::real deltaE(real sn, real cn, real dn) const;
503 
512  Math::real deltaEinv(real stau, real ctau) const;
513 
524  Math::real deltaPi(real sn, real cn, real dn) const;
525 
536  Math::real deltaD(real sn, real cn, real dn) const;
537 
548  Math::real deltaG(real sn, real cn, real dn) const;
549 
560  Math::real deltaH(real sn, real cn, real dn) const;
562 
565 
574  void sncndn(real x, real& sn, real& cn, real& dn) const;
575 
585  using std::sqrt;
586  return sqrt(_k2 < 0 ? 1 - _k2 * sn*sn : _kp2 + _k2 * cn*cn);
587  }
589 
592 
607  static real RF(real x, real y, real z);
608 
617  static real RF(real x, real y);
618 
632  static real RC(real x, real y);
633 
652  static real RG(real x, real y, real z);
653 
662  static real RG(real x, real y);
663 
678  static real RJ(real x, real y, real z, real p);
679 
694  static real RD(real x, real y, real z);
696 
697  };
698 
699 } // namespace GeographicLib
700 
701 #endif // GEOGRAPHICLIB_ELLIPTICFUNCTION_HPP
H
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Definition: gnuplot_common_settings.hh:74
GeographicLib::EllipticFunction::Delta
Math::real Delta(real sn, real cn) const
Definition: EllipticFunction.hpp:584
GeographicLib::EllipticFunction::EllipticFunction
EllipticFunction(real k2=0, real alpha2=0)
Definition: EllipticFunction.hpp:89
GeographicLib::EllipticFunction::D
Math::real D() const
Definition: EllipticFunction.hpp:215
D
MatrixXcd D
Definition: EigenSolver_EigenSolver_MatrixType.cpp:14
GeographicLib
Namespace for GeographicLib.
Definition: JacobiConformal.hpp:15
GeographicLib::EllipticFunction::alpha2
Math::real alpha2() const
Definition: EllipticFunction.hpp:168
GeographicLib::EllipticFunction::k2
Math::real k2() const
Definition: EllipticFunction.hpp:157
GeographicLib::EllipticFunction::kp2
Math::real kp2() const
Definition: EllipticFunction.hpp:163
x
set noclip points set clip one set noclip two set bar set border lt lw set xdata set ydata set zdata set x2data set y2data set boxwidth set dummy x
Definition: gnuplot_common_settings.hh:12
GeographicLib::EllipticFunction::Reset
void Reset(real k2=0, real alpha2=0)
Definition: EllipticFunction.hpp:125
GeographicLib::EllipticFunction::real
Math::real real
Definition: EllipticFunction.hpp:64
GeographicLib::EllipticFunction
Elliptic integrals and functions.
Definition: EllipticFunction.hpp:62
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:91
GeographicLib::Math::real
double real
Definition: Math.hpp:129
GeographicLib::EllipticFunction::G
Math::real G() const
Definition: EllipticFunction.hpp:250
GeographicLib::EllipticFunction::alphap2
Math::real alphap2() const
Definition: EllipticFunction.hpp:174
GeographicLib::EllipticFunction::K
Math::real K() const
Definition: EllipticFunction.hpp:190
GeographicLib::EllipticFunction::EllipticFunction
EllipticFunction(real k2, real alpha2, real kp2, real alphap2)
Definition: EllipticFunction.hpp:111
cn
static double cn[6]
Definition: fresnl.c:83
GeographicLib::EllipticFunction::H
Math::real H() const
Definition: EllipticFunction.hpp:264
pybind_wrapper_test_script.z
z
Definition: pybind_wrapper_test_script.py:61
Constants.hpp
Header for GeographicLib::Constants class.
gtsam::symbol_shorthand::F
Key F(std::uint64_t j)
Definition: inference/Symbol.h:153
GeographicLib::EllipticFunction::_kp2
real _kp2
Definition: EllipticFunction.hpp:67
y
Scalar * y
Definition: level1_cplx_impl.h:124
E
DiscreteKey E(5, 2)
GeographicLib::EllipticFunction::_Pic
real _Pic
Definition: EllipticFunction.hpp:68
sn
static double sn[6]
Definition: fresnl.c:63
p
float * p
Definition: Tutorial_Map_using.cpp:9
G
JacobiRotation< float > G
Definition: Jacobi_makeGivens.cpp:2
GeographicLib::EllipticFunction::Pi
Math::real Pi() const
Definition: EllipticFunction.hpp:237
GeographicLib::EllipticFunction::KE
Math::real KE() const
Definition: EllipticFunction.hpp:223
GeographicLib::EllipticFunction::E
Math::real E() const
Definition: EllipticFunction.hpp:202
real
Definition: main.h:100
ceres::sqrt
Jet< T, N > sqrt(const Jet< T, N > &f)
Definition: jet.h:418


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autogenerated on Fri Nov 1 2024 03:32:29