EllipticFunction.hpp
Go to the documentation of this file.
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 
584  Math::real Delta(real sn, real cn) const {
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
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:91
Scalar * y
Key F(std::uint64_t j)
void Reset(real k2=0, real alpha2=0)
JacobiRotation< float > G
Elliptic integrals and functions.
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 y set format x g set format y g set format x2 g set format y2 g set format z g set angles radians set nogrid set key title set key left top Right noreverse box linetype linewidth samplen spacing width set nolabel set noarrow set nologscale set logscale x set set pointsize set encoding default set nopolar set noparametric set set set set surface set nocontour set clabel set mapping cartesian set nohidden3d set cntrparam order set cntrparam linear set cntrparam levels auto set cntrparam points set size set set xzeroaxis lt lw set x2zeroaxis lt lw set yzeroaxis lt lw set y2zeroaxis lt lw set tics in set ticslevel set tics set mxtics default set mytics default set mx2tics default set my2tics default set xtics border mirror norotate autofreq set ytics border mirror norotate autofreq set ztics border nomirror norotate autofreq set nox2tics set noy2tics set timestamp bottom norotate set rrange [*:*] noreverse nowriteback set trange [*:*] noreverse nowriteback set urange [*:*] noreverse nowriteback set vrange [*:*] noreverse nowriteback set xlabel matrix size set x2label set timefmt d m y n H
Namespace for GeographicLib.
EllipticFunction(real k2, real alpha2, real kp2, real alphap2)
DiscreteKey E(5, 2)
Math::real Delta(real sn, real cn) const
Header for GeographicLib::Constants class.
float * p
Jet< T, N > sqrt(const Jet< T, N > &f)
Definition: jet.h:418
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
EllipticFunction(real k2=0, real alpha2=0)


gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:34:12