Spherical harmonic sums for a circle. More...

#include <CircularEngine.hpp>

Public Member Functions
	CircularEngine ()

Math::real	operator() (real sinlon, real coslon) const

Math::real	operator() (real lon) const

Math::real	operator() (real sinlon, real coslon, real &gradx, real &grady, real &gradz) const

Math::real	operator() (real lon, real &gradx, real &grady, real &gradz) const

Private Types
enum	normalization { FULL = SphericalEngine::FULL, SCHMIDT = SphericalEngine::SCHMIDT }

typedef Math::real	real

Private Member Functions
	CircularEngine (int M, bool gradp, unsigned norm, real a, real r, real u, real t)

void	SetCoeff (int m, real wc, real ws)

void	SetCoeff (int m, real wc, real ws, real wrc, real wrs, real wtc, real wts)

Math::real	Value (bool gradp, real sl, real cl, real &gradx, real &grady, real &gradz) const

Private Attributes
real	_a

bool	_gradp

int	_M

unsigned	_norm

real	_q

real	_r

real	_t

real	_u

real	_uq

real	_uq2

std::vector< real >	_wc

std::vector< real >	_wrc

std::vector< real >	_wrs

std::vector< real >	_ws

std::vector< real >	_wtc

std::vector< real >	_wts

Friends
class	SphericalEngine

Detailed Description

Spherical harmonic sums for a circle.

The class is a companion to SphericalEngine. If the results of a spherical harmonic sum are needed for several points on a circle of constant latitude lat and height h, then SphericalEngine::Circle can compute the inner sum, which is independent of longitude lon, and produce a CircularEngine object. CircularEngine::operator()() can then be used to perform the outer sum for particular vales of lon. This can lead to substantial improvements in computational speed for high degree sum (approximately by a factor of N / 2 where N is the maximum degree).

CircularEngine is tightly linked to the internals of SphericalEngine. For that reason, the constructor for this class is private. Use SphericalHarmonic::Circle, SphericalHarmonic1::Circle, and SphericalHarmonic2::Circle to create instances of this class.

CircularEngine stores the coefficients needed to allow the summation over order to be performed in 2 or 6 vectors of length M + 1 (depending on whether gradients are to be calculated). For this reason the constructor may throw a std::bad_alloc exception.

Example of use:

// Example of using the GeographicLib::CircularEngine class
#include <iostream>
#include <exception>
#include <vector>
#include <GeographicLib/CircularEngine.hpp>
#include <GeographicLib/SphericalHarmonic.hpp>
using namespace std;
using namespace GeographicLib;
int main() {
  // This computes the same value as example-SphericalHarmonic.cpp using a
  // CircularEngine (which will be faster if many values on a circle of
  // latitude are to be found).
  try {
    int N = 3;                  // The maxium degree
    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 a = 1;
    SphericalHarmonic h(C, S, N, a);
    double x = 2, y = 3, z = 1, p = Math::hypot(x, y);
    CircularEngine circ = h.Circle(p, z, true);
    double v, vx, vy, vz;
    v = circ(x/p, y/p, vx, vy, vz);
    cout << v << " " << vx << " " << vy << " " << vz << "\n";
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

Definition at line 52 of file CircularEngine.hpp.

Member Typedef Documentation

typedef Math::real GeographicLib::CircularEngine::real

private

Definition at line 54 of file CircularEngine.hpp.

Member Enumeration Documentation

enum GeographicLib::CircularEngine::normalization

private

Enumerator
FULL
SCHMIDT

Definition at line 55 of file CircularEngine.hpp.

Constructor & Destructor Documentation

GeographicLib::CircularEngine::CircularEngine	(	int	M,
		bool	gradp,
		unsigned	norm,
		real	a,
		real	r,
		real	u,
		real	t
	)

inlineprivate

Definition at line 70 of file CircularEngine.hpp.

GeographicLib::CircularEngine::CircularEngine ( )

inline

A default constructor. CircularEngine::operator()() on the resulting object returns zero. The resulting object can be assigned to the result of SphericalHarmonic::Circle.

Definition at line 110 of file CircularEngine.hpp.

Member Function Documentation

Math::real GeographicLib::CircularEngine::operator()	(	real	sinlon,
		real	coslon
	)		const

inline

Evaluate the sum for a particular longitude given in terms of its sine and cosine.

Parameters

[in]	sinlon	the sine of the longitude.
[in]	coslon	the cosine of the longitude.

Returns: V the value of the sum.

The arguments must satisfy sinlon² + coslon² = 1.

Definition at line 128 of file CircularEngine.hpp.

Math::real GeographicLib::CircularEngine::operator() ( real lon ) const

inline

Evaluate the sum for a particular longitude.

Parameters

[in] lon the longitude (degrees).

Returns: V the value of the sum.

Definition at line 139 of file CircularEngine.hpp.

Math::real GeographicLib::CircularEngine::operator()	(	real	sinlon,
		real	coslon,
		real &	gradx,
		real &	grady,
		real &	gradz
	)		const

inline

Evaluate the sum and its gradient for a particular longitude given in terms of its sine and cosine.

Parameters

[in]	sinlon	the sine of the longitude.
[in]	coslon	the cosine of the longitude.
[out]	gradx	x component of the gradient.
[out]	grady	y component of the gradient.
[out]	gradz	z component of the gradient.

Returns: V the value of the sum.

The gradients will only be computed if the CircularEngine object was created with this capability (e.g., via gradp = true in SphericalHarmonic::Circle). If not, gradx, etc., will not be touched. The arguments must satisfy sinlon² + coslon² = 1.

Definition at line 162 of file CircularEngine.hpp.

Math::real GeographicLib::CircularEngine::operator()	(	real	lon,
		real &	gradx,
		real &	grady,
		real &	gradz
	)		const

inline

Evaluate the sum and its gradient for a particular longitude.

Parameters

[in]	lon	the longitude (degrees).
[out]	gradx	x component of the gradient.
[out]	grady	y component of the gradient.
[out]	gradz	z component of the gradient.

Returns: V the value of the sum.

The gradients will only be computed if the CircularEngine object was created with this capability (e.g., via gradp = true in SphericalHarmonic::Circle). If not, gradx, etc., will not be touched.

Definition at line 181 of file CircularEngine.hpp.

void GeographicLib::CircularEngine::SetCoeff	(	int	m,
		real	wc,
		real	ws
	)

inlineprivate

Definition at line 91 of file CircularEngine.hpp.

void GeographicLib::CircularEngine::SetCoeff	(	int	m,
		real	wc,
		real	ws,
		real	wrc,
		real	wrs,
		real	wtc,
		real	wts
	)

inlineprivate

Definition at line 94 of file CircularEngine.hpp.

Math::real GeographicLib::CircularEngine::Value	(	bool	gradp,
		real	sl,
		real	cl,
		real &	gradx,
		real &	grady,
		real &	gradz
	)		const

private

Definition at line 16 of file src/CircularEngine.cpp.

Friends And Related Function Documentation

friend class SphericalEngine

friend

Definition at line 69 of file CircularEngine.hpp.

Member Data Documentation

real GeographicLib::CircularEngine::_a

private

Definition at line 62 of file CircularEngine.hpp.

bool GeographicLib::CircularEngine::_gradp

private

Definition at line 60 of file CircularEngine.hpp.

int GeographicLib::CircularEngine::_M

private

Definition at line 59 of file CircularEngine.hpp.

unsigned GeographicLib::CircularEngine::_norm

private

Definition at line 61 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_q

private

Definition at line 64 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_r

private

Definition at line 62 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_t

private

Definition at line 62 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_u

private

Definition at line 62 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_uq

private

Definition at line 64 of file CircularEngine.hpp.

real GeographicLib::CircularEngine::_uq2

private

Definition at line 64 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_wc

private

Definition at line 63 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_wrc

private

Definition at line 63 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_wrs

private

Definition at line 63 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_ws

private

Definition at line 63 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_wtc

private

Definition at line 63 of file CircularEngine.hpp.

std::vector<real> GeographicLib::CircularEngine::_wts

private

Definition at line 63 of file CircularEngine.hpp.

The documentation for this class was generated from the following files:

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation