legendre.cc File Reference

Contains the code to calculate Legendre polynomials. More...

#include <cmath>
#include <limits>
#include <numeric>
#include <sstream>
#include "arts_conversions.h"
#include "exceptions.h"
#include "legendre.h"
#include "math_funcs.h"

Go to the source code of this file.

Classes
struct	Legendre::ColatitudeConversion
	Converts latitude to co-latitude with a small distance from the poles and flags if this was activated. More...

Namespaces
namespace	Legendre

Functions
bool	gsl_integration_glfixed_table_alloc (Vector &x, Vector &w, Index n)
	gsl_integration_glfixed_table_alloc More...
constexpr Numeric	Legendre::longitude_clamp (const Numeric lon)
	Clamps the longitude in the range [-180, 180) More...
std::pair< Matrix, Matrix >	Legendre::schmidt (const Numeric theta, const Index nmax) ARTS_NOEXCEPT
	Returns the Schmidt normalized Lagrange polynominal and its derivative. More...
SphericalField	Legendre::schmidt_fieldcalc (const Matrix &g, const Matrix &h, const Numeric r0, const Numeric r, const Numeric lat, const Numeric lon) ARTS_NOEXCEPT
	Computes the spherical field. More...
MatrixOfSphericalField	Legendre::schmidt_fieldcalc (const Matrix &g, const Matrix &h, const Numeric r0, const Vector &r, const Numeric lat, const Vector &lon) ARTS_NOEXCEPT
	Computes the spherical field for many radius and longitudes. More...
std::array< Numeric, 3 >	Legendre::to_geodetic (const std::array< Numeric, 3 > xyz, const std::array< Numeric, 2 > ell) noexcept
	Computes the altitude, latitude and longitude in relation to the ellopsiod using non-iterative method. More...

Detailed Description

Contains the code to calculate Legendre polynomials.

Author

Oliver Lemke

Date

2003-08-14

Definition in file legendre.cc.

Function Documentation

gsl_integration_glfixed_table_alloc()

bool gsl_integration_glfixed_table_alloc	(	Vector &	x,
		Vector &	w,
		Index	n
	)

gsl_integration_glfixed_table_alloc

This function determines the Gauss-Legendre abscissae and weights necessary for an n-point fixed order integration scheme. If possible, high precision precomputed coefficients are used. If precomputed weights are not available, lower precision coefficients are computed on the fly.

Code is taken from the GNU Scientific Library under GPLv3 license. Adapted to return ARTS datatypes.

Parameters

[out]	x	Vector with Gauss-Legendre abscissae.
[out]	w	Vector with Gauss-Legendre weights.
[in]	n	Integration scheme order.

Returns

true if precomputed values have been used.

Author

Oliver Lemke

Date

2018-05-29

Definition at line 1940 of file legendre.cc.

References ConstVectorView::get_c_array(), Vector::resize(), and w.

Referenced by AngularGridsSetFluxCalc().