GeographicLib
1.21
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Spherical Harmonic series with a correction to the coefficients. More...
#include <GeographicLib/SphericalHarmonic1.hpp>
Public Types | |
enum | normalization { FULL, SCHMIDT } |
Public Member Functions | |
SphericalHarmonic1 (const std::vector< real > &C, const std::vector< real > &S, int N, const std::vector< real > &C1, const std::vector< real > &S1, int N1, real a, unsigned norm=FULL) | |
SphericalHarmonic1 (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, real a, unsigned norm=FULL) | |
SphericalHarmonic1 () | |
Math::real | operator() (real tau, real x, real y, real z) const throw () |
Math::real | operator() (real tau, real x, real y, real z, real &gradx, real &grady, real &gradz) const throw () |
CircularEngine | Circle (real tau, real p, real z, bool gradp) const |
const SphericalEngine::coeff & | Coefficients () const throw () |
const SphericalEngine::coeff & | Coefficients1 () const throw () |
Spherical Harmonic series with a correction to the coefficients.
This classes is similar to SphericalHarmonic, except that the coefficients Cnm are replaced by Cnm + tau C'nm (and similarly for Snm).
Example of use:
// Example of using the GeographicLib::SphericalHarmonic1 class // $Id: 9d964d2e64c201179a88e51697b508414ff8c800 $ #include <iostream> #include <exception> #include <vector> #include <GeographicLib/SphericalHarmonic1.hpp> using namespace std; using namespace GeographicLib; int main() { try { int N = 3, N1 = 2; // The maxium degrees double ca[] = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; // cosine coefficients vector<double> C(ca, ca + (N + 1) * (N + 2) / 2); double sa[] = {6, 5, 4, 3, 2, 1}; // sine coefficients vector<double> S(sa, sa + N * (N + 1) / 2); double cb[] = {1, 2, 3, 4, 5, 6}; vector<double> C1(cb, cb + (N1 + 1) * (N1 + 2) / 2); double sb[] = {3, 2, 1}; vector<double> S1(sb, sb + N1 * (N1 + 1) / 2); double a = 1; SphericalHarmonic1 h(C, S, N, C1, S1, N1, a); double tau = 0.1, x = 2, y = 3, z = 1; double v, vx, vy, vz; v = h(tau, x, y, z, vx, vy, vz); cout << v << " " << vx << " " << vy << " " << vz << "\n"; } catch (const exception& e) { cerr << "Caught exception: " << e.what() << "\n"; return 1; } return 0; }
Supported normalizations for associate Legendre polynomials.
FULL |
Fully normalized associated Legendre polynomials. See SphericalHarmonic::FULL for documentation. |
SCHMIDT |
Schmidt semi-normalized associated Legendre polynomials. See SphericalHarmonic::SCHMIDT for documentation. |
Definition at line 37 of file SphericalHarmonic1.hpp.
GeographicLib::SphericalHarmonic1::SphericalHarmonic1 | ( | const std::vector< real > & | C, |
const std::vector< real > & | S, | ||
int | N, | ||
const std::vector< real > & | C1, | ||
const std::vector< real > & | S1, | ||
int | N1, | ||
real | a, | ||
unsigned | norm = FULL |
||
) | [inline] |
Constructor with a full set of coefficients specified.
[in] | C | the coefficients Cnm. |
[in] | S | the coefficients Snm. |
[in] | N | the maximum degree and order of the sum |
[in] | C1 | the coefficients C'nm. |
[in] | S1 | the coefficients S'nm. |
[in] | N1 | the maximum degree and order of the correction coefficients C'nm and S'nm. |
[in] | a | the reference radius appearing in the definition of the sum. |
[in] | norm | the normalization for the associated Legendre polynomials, either SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT. |
See SphericalHarmonic for the way the coefficients should be stored. N1 should satisfy N1 <= N.
The class stores pointers to the first elements of C, S, C', and S'. These arrays should not be altered or destroyed during the lifetime of a SphericalHarmonic object.
Definition at line 89 of file SphericalHarmonic1.hpp.
GeographicLib::SphericalHarmonic1::SphericalHarmonic1 | ( | 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, | ||
real | a, | ||
unsigned | norm = FULL |
||
) | [inline] |
Constructor with a subset of coefficients specified.
[in] | C | the coefficients Cnm. |
[in] | S | the coefficients Snm. |
[in] | N | the degree used to determine the layout of C and S. |
[in] | nmx | the maximum degree used in the sum. The sum over n is from 0 thru nmx. |
[in] | mmx | the maximum order used in the sum. The sum over m is from 0 thru min(n, mmx). |
[in] | C1 | the coefficients C'nm. |
[in] | S1 | the coefficients S'nm. |
[in] | N1 | the degree used to determine the layout of C' and S'. |
[in] | nmx1 | the maximum degree used for C' and S'. |
[in] | mmx1 | the maximum order used for C' and S'. |
[in] | a | the reference radius appearing in the definition of the sum. |
[in] | norm | the normalization for the associated Legendre polynomials, either SphericalHarmonic1::FULL (the default) or SphericalHarmonic1::SCHMIDT. |
The class stores pointers to the first elements of C, S, C', and S'. These arrays should not be altered or destroyed during the lifetime of a SphericalHarmonic object.
Definition at line 130 of file SphericalHarmonic1.hpp.
GeographicLib::SphericalHarmonic1::SphericalHarmonic1 | ( | ) | [inline] |
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.
Definition at line 152 of file SphericalHarmonic1.hpp.
Math::real GeographicLib::SphericalHarmonic1::operator() | ( | real | tau, |
real | x, | ||
real | y, | ||
real | z | ||
) | const throw () [inline] |
Compute a spherical harmonic sum with a correction term.
[in] | tau | multiplier for correction coefficients C' and S'. |
[in] | x | cartesian coordinate. |
[in] | y | cartesian coordinate. |
[in] | z | cartesian coordinate. |
This routine requires constant memory and thus never throws an exception.
Definition at line 166 of file SphericalHarmonic1.hpp.
Math::real GeographicLib::SphericalHarmonic1::operator() | ( | real | tau, |
real | x, | ||
real | y, | ||
real | z, | ||
real & | gradx, | ||
real & | grady, | ||
real & | gradz | ||
) | const throw () [inline] |
Compute a spherical harmonic sum with a correction term and its gradient.
[in] | tau | multiplier for correction coefficients C' and S'. |
[in] | x | cartesian coordinate. |
[in] | y | cartesian coordinate. |
[in] | z | cartesian coordinate. |
[out] | gradx | x component of the gradient |
[out] | grady | y component of the gradient |
[out] | gradz | z component of the gradient |
This is the same as the previous function, except that the components of the gradients of the sum in the x, y, and z directions are computed. This routine requires constant memory and thus never throws an exception.
Definition at line 201 of file SphericalHarmonic1.hpp.
CircularEngine GeographicLib::SphericalHarmonic1::Circle | ( | real | tau, |
real | p, | ||
real | z, | ||
bool | gradp | ||
) | const [inline] |
Create a CircularEngine to allow the efficient evaluation of several points on a circle of latitude at a fixed value of tau.
[in] | tau | the multiplier for the correction coefficients. |
[in] | p | the radius of the circle. |
[in] | z | the height of the circle above the equatorial plane. |
[in] | gradp | if true the returned object will be able to compute the gradient of the sum. |
SphericalHarmonic1::operator()() exchanges the order of the sums in the definition, i.e., sum(n = 0..N)[sum(m = 0..n)[...]] becomes sum(m = 0..N)[sum(n = m..N)[...]]. SphericalHarmonic1::Circle performs the inner sum over degree n (which entails about N2 operations). Calling CircularEngine::operator()() on the returned object performs the outer sum over the order m (about N operations). This routine may throw a bad_alloc exception in the CircularEngine constructor.
See SphericalHarmonic::Circle for an example of its use.
Definition at line 240 of file SphericalHarmonic1.hpp.
Referenced by GeographicLib::GravityModel::Circle().
const SphericalEngine::coeff& GeographicLib::SphericalHarmonic1::Coefficients | ( | ) | const throw () [inline] |
Definition at line 264 of file SphericalHarmonic1.hpp.
const SphericalEngine::coeff& GeographicLib::SphericalHarmonic1::Coefficients1 | ( | ) | const throw () [inline] |
Definition at line 269 of file SphericalHarmonic1.hpp.