/usr/include/GeographicLib/SphericalHarmonic2.hpp is in libgeographic-dev 1.49-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 | /**
* \file SphericalHarmonic2.hpp
* \brief Header for GeographicLib::SphericalHarmonic2 class
*
* Copyright (c) Charles Karney (2011-2012) <charles@karney.com> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP)
#define GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP 1
#include <vector>
#include <GeographicLib/Constants.hpp>
#include <GeographicLib/SphericalEngine.hpp>
#include <GeographicLib/CircularEngine.hpp>
namespace GeographicLib {
/**
* \brief Spherical harmonic series with two corrections to the coefficients
*
* This classes is similar to SphericalHarmonic, except that the coefficients
* <i>C</i><sub><i>nm</i></sub> are replaced by
* <i>C</i><sub><i>nm</i></sub> + \e tau' <i>C'</i><sub><i>nm</i></sub> + \e
* tau'' <i>C''</i><sub><i>nm</i></sub> (and similarly for
* <i>S</i><sub><i>nm</i></sub>).
*
* Example of use:
* \include example-SphericalHarmonic2.cpp
**********************************************************************/
// Don't include the GEOGRPAHIC_EXPORT because this header-only class isn't
// used by any other classes in the library.
class /*GEOGRAPHICLIB_EXPORT*/ SphericalHarmonic2 {
public:
/**
* Supported normalizations for associate Legendre polynomials.
**********************************************************************/
enum normalization {
/**
* Fully normalized associated Legendre polynomials. See
* SphericalHarmonic::FULL for documentation.
*
* @hideinitializer
**********************************************************************/
FULL = SphericalEngine::FULL,
/**
* Schmidt semi-normalized associated Legendre polynomials. See
* SphericalHarmonic::SCHMIDT for documentation.
*
* @hideinitializer
**********************************************************************/
SCHMIDT = SphericalEngine::SCHMIDT,
};
private:
typedef Math::real real;
SphericalEngine::coeff _c[3];
real _a;
unsigned _norm;
public:
/**
* Constructor with a full set of coefficients specified.
*
* @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
* @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
* @param[in] N the maximum degree and order of the sum
* @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
* @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
* @param[in] N1 the maximum degree and order of the first correction
* coefficients <i>C'</i><sub><i>nm</i></sub> and
* <i>S'</i><sub><i>nm</i></sub>.
* @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
* @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
* @param[in] N2 the maximum degree and order of the second correction
* coefficients <i>C'</i><sub><i>nm</i></sub> and
* <i>S'</i><sub><i>nm</i></sub>.
* @param[in] a the reference radius appearing in the definition of the
* sum.
* @param[in] norm the normalization for the associated Legendre
* polynomials, either SphericalHarmonic2::FULL (the default) or
* SphericalHarmonic2::SCHMIDT.
* @exception GeographicErr if \e N and \e N1 do not satisfy \e N ≥
* \e N1 ≥ −1, and similarly for \e N2.
* @exception GeographicErr if any of the vectors of coefficients is not
* large enough.
*
* See SphericalHarmonic for the way the coefficients should be stored. \e
* N1 and \e N2 should satisfy \e N1 ≤ \e N and \e N2 ≤ \e N.
*
* The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
* C', \e S', \e C'', and \e S''. These arrays should not be altered or
* destroyed during the lifetime of a SphericalHarmonic object.
**********************************************************************/
SphericalHarmonic2(const std::vector<real>& C,
const std::vector<real>& S,
int N,
const std::vector<real>& C1,
const std::vector<real>& S1,
int N1,
const std::vector<real>& C2,
const std::vector<real>& S2,
int N2,
real a, unsigned norm = FULL)
: _a(a)
, _norm(norm) {
if (!(N1 <= N && N2 <= N))
throw GeographicErr("N1 and N2 cannot be larger that N");
_c[0] = SphericalEngine::coeff(C, S, N);
_c[1] = SphericalEngine::coeff(C1, S1, N1);
_c[2] = SphericalEngine::coeff(C2, S2, N2);
}
/**
* Constructor with a subset of coefficients specified.
*
* @param[in] C the coefficients <i>C</i><sub><i>nm</i></sub>.
* @param[in] S the coefficients <i>S</i><sub><i>nm</i></sub>.
* @param[in] N the degree used to determine the layout of \e C and \e S.
* @param[in] nmx the maximum degree used in the sum. The sum over \e n is
* from 0 thru \e nmx.
* @param[in] mmx the maximum order used in the sum. The sum over \e m is
* from 0 thru min(\e n, \e mmx).
* @param[in] C1 the coefficients <i>C'</i><sub><i>nm</i></sub>.
* @param[in] S1 the coefficients <i>S'</i><sub><i>nm</i></sub>.
* @param[in] N1 the degree used to determine the layout of \e C' and \e
* S'.
* @param[in] nmx1 the maximum degree used for \e C' and \e S'.
* @param[in] mmx1 the maximum order used for \e C' and \e S'.
* @param[in] C2 the coefficients <i>C''</i><sub><i>nm</i></sub>.
* @param[in] S2 the coefficients <i>S''</i><sub><i>nm</i></sub>.
* @param[in] N2 the degree used to determine the layout of \e C'' and \e
* S''.
* @param[in] nmx2 the maximum degree used for \e C'' and \e S''.
* @param[in] mmx2 the maximum order used for \e C'' and \e S''.
* @param[in] a the reference radius appearing in the definition of the
* sum.
* @param[in] norm the normalization for the associated Legendre
* polynomials, either SphericalHarmonic2::FULL (the default) or
* SphericalHarmonic2::SCHMIDT.
* @exception GeographicErr if the parameters do not satisfy \e N ≥ \e
* nmx ≥ \e mmx ≥ −1; \e N1 ≥ \e nmx1 ≥ \e mmx1 ≥
* −1; \e N ≥ \e N1; \e nmx ≥ \e nmx1; \e mmx ≥ \e mmx1;
* and similarly for \e N2, \e nmx2, and \e mmx2.
* @exception GeographicErr if any of the vectors of coefficients is not
* large enough.
*
* The class stores <i>pointers</i> to the first elements of \e C, \e S, \e
* C', \e S', \e C'', and \e S''. These arrays should not be altered or
* destroyed during the lifetime of a SphericalHarmonic object.
**********************************************************************/
SphericalHarmonic2(const std::vector<real>& C,
const std::vector<real>& S,
int N, int nmx, int mmx,
const std::vector<real>& C1,
const std::vector<real>& S1,
int N1, int nmx1, int mmx1,
const std::vector<real>& C2,
const std::vector<real>& S2,
int N2, int nmx2, int mmx2,
real a, unsigned norm = FULL)
: _a(a)
, _norm(norm) {
if (!(nmx1 <= nmx && nmx2 <= nmx))
throw GeographicErr("nmx1 and nmx2 cannot be larger that nmx");
if (!(mmx1 <= mmx && mmx2 <= mmx))
throw GeographicErr("mmx1 and mmx2 cannot be larger that mmx");
_c[0] = SphericalEngine::coeff(C, S, N, nmx, mmx);
_c[1] = SphericalEngine::coeff(C1, S1, N1, nmx1, mmx1);
_c[2] = SphericalEngine::coeff(C2, S2, N2, nmx2, mmx2);
}
/**
* A default constructor so that the object can be created when the
* constructor for another object is initialized. This default object can
* then be reset with the default copy assignment operator.
**********************************************************************/
SphericalHarmonic2() {}
/**
* Compute a spherical harmonic sum with two correction terms.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] x cartesian coordinate.
* @param[in] y cartesian coordinate.
* @param[in] z cartesian coordinate.
* @return \e V the spherical harmonic sum.
*
* This routine requires constant memory and thus never throws an
* exception.
**********************************************************************/
Math::real operator()(real tau1, real tau2, real x, real y, real z)
const {
real f[] = {1, tau1, tau2};
real v = 0;
real dummy;
switch (_norm) {
case FULL:
v = SphericalEngine::Value<false, SphericalEngine::FULL, 3>
(_c, f, x, y, z, _a, dummy, dummy, dummy);
break;
case SCHMIDT:
v = SphericalEngine::Value<false, SphericalEngine::SCHMIDT, 3>
(_c, f, x, y, z, _a, dummy, dummy, dummy);
break;
}
return v;
}
/**
* Compute a spherical harmonic sum with two correction terms and its
* gradient.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] x cartesian coordinate.
* @param[in] y cartesian coordinate.
* @param[in] z cartesian coordinate.
* @param[out] gradx \e x component of the gradient
* @param[out] grady \e y component of the gradient
* @param[out] gradz \e z component of the gradient
* @return \e V the spherical harmonic sum.
*
* This is the same as the previous function, except that the components of
* the gradients of the sum in the \e x, \e y, and \e z directions are
* computed. This routine requires constant memory and thus never throws
* an exception.
**********************************************************************/
Math::real operator()(real tau1, real tau2, real x, real y, real z,
real& gradx, real& grady, real& gradz) const {
real f[] = {1, tau1, tau2};
real v = 0;
switch (_norm) {
case FULL:
v = SphericalEngine::Value<true, SphericalEngine::FULL, 3>
(_c, f, x, y, z, _a, gradx, grady, gradz);
break;
case SCHMIDT:
v = SphericalEngine::Value<true, SphericalEngine::SCHMIDT, 3>
(_c, f, x, y, z, _a, gradx, grady, gradz);
break;
}
return v;
}
/**
* Create a CircularEngine to allow the efficient evaluation of several
* points on a circle of latitude at fixed values of \e tau1 and \e tau2.
*
* @param[in] tau1 multiplier for correction coefficients \e C' and \e S'.
* @param[in] tau2 multiplier for correction coefficients \e C'' and \e
* S''.
* @param[in] p the radius of the circle.
* @param[in] z the height of the circle above the equatorial plane.
* @param[in] gradp if true the returned object will be able to compute the
* gradient of the sum.
* @exception std::bad_alloc if the memory for the CircularEngine can't be
* allocated.
* @return the CircularEngine object.
*
* SphericalHarmonic2::operator()() exchanges the order of the sums in the
* definition, i.e., ∑<sub><i>n</i> = 0..<i>N</i></sub>
* ∑<sub><i>m</i> = 0..<i>n</i></sub> becomes ∑<sub><i>m</i> =
* 0..<i>N</i></sub> ∑<sub><i>n</i> = <i>m</i>..<i>N</i></sub>..
* SphericalHarmonic2::Circle performs the inner sum over degree \e n
* (which entails about <i>N</i><sup>2</sup> operations). Calling
* CircularEngine::operator()() on the returned object performs the outer
* sum over the order \e m (about \e N operations).
*
* See SphericalHarmonic::Circle for an example of its use.
**********************************************************************/
CircularEngine Circle(real tau1, real tau2, real p, real z, bool gradp)
const {
real f[] = {1, tau1, tau2};
switch (_norm) {
case FULL:
return gradp ?
SphericalEngine::Circle<true, SphericalEngine::FULL, 3>
(_c, f, p, z, _a) :
SphericalEngine::Circle<false, SphericalEngine::FULL, 3>
(_c, f, p, z, _a);
break;
case SCHMIDT:
default: // To avoid compiler warnings
return gradp ?
SphericalEngine::Circle<true, SphericalEngine::SCHMIDT, 3>
(_c, f, p, z, _a) :
SphericalEngine::Circle<false, SphericalEngine::SCHMIDT, 3>
(_c, f, p, z, _a);
break;
}
}
/**
* @return the zeroth SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients() const
{ return _c[0]; }
/**
* @return the first SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients1() const
{ return _c[1]; }
/**
* @return the second SphericalEngine::coeff object.
**********************************************************************/
const SphericalEngine::coeff& Coefficients2() const
{ return _c[2]; }
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_SPHERICALHARMONIC2_HPP
|