Legendre Namespace Reference

Classes
struct	ColatitudeConversion
	Converts latitude to co-latitude with a small distance from the poles and flags if this was activated. More...
struct	SphericalField
	Stores the up (U), south (S), east (E) values of a field relative to the sphere. More...

Typedefs
using	MatrixOfSphericalField = Grid< SphericalField, 2 >
	Holds a SphericalField for multiple dimensions (radius times longitudes)

Functions
constexpr Numeric	longitude_clamp (const Numeric lon)
	Clamps the longitude in the range [-180, 180)
std::pair< Matrix, Matrix >	schmidt (const Numeric theta, const Index nmax) ARTS_NOEXCEPT
	Returns the Schmidt normalized Lagrange polynominal and its derivative.
SphericalField	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.
MatrixOfSphericalField	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.
std::array< Numeric, 3 >	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.

Typedef Documentation

MatrixOfSphericalField

using Legendre::MatrixOfSphericalField = typedef Grid<SphericalField, 2>

Holds a SphericalField for multiple dimensions (radius times longitudes)

Definition at line 25 of file legendre.h.

Function Documentation

longitude_clamp()

constexpr Numeric Legendre::longitude_clamp ( const Numeric  lon )

constexpr

Clamps the longitude in the range [-180, 180)

Definition at line 20 of file legendre.cc.

References longitude_clamp().

Referenced by longitude_clamp(), schmidt_fieldcalc(), and schmidt_fieldcalc().

schmidt()

std::pair< Matrix, Matrix > Legendre::schmidt	(	const Numeric	theta,
		const Index	nmax
	)

Returns the Schmidt normalized Lagrange polynominal and its derivative.

The derivative is undefined if theta is 0 or pi, so the function cannot be called with these values

This function is taken from the implementation by Isabela de Oliveira Martins at https://github.com/de-oliveira/IsabelaFunctions/blob/master/IsabelaFunctions/fieldmodel.py (2021-05-06). It implements the calculations step-by-step, updating both main and derivative based on previous values.

Parameters

[in]	theta	Colatitude in radians
[in]	nmax	Max number of n

Returns

The pair of (nmax+1) x (nmax+1) matrices, order: main and derivative

Definition at line 45 of file legendre.cc.

References ARTS_ASSERT, Constant::pi, and Math::pow2().

Referenced by schmidt_fieldcalc(), and schmidt_fieldcalc().

schmidt_fieldcalc() [1/2]

SphericalField Legendre::schmidt_fieldcalc	(	const Matrix &	g,
		const Matrix &	h,
		const Numeric	r0,
		const Numeric	r,
		const Numeric	lat,
		const Numeric	lon
	)

Computes the spherical field.

If latitude is beyond a limit, the longitude is set to zero and the latitude at the limit away from the pole is used. For these position, the absolute of the horizontal component is kept around in the south-facing component and the east-facing component is set to zero

The latitude limit is defined in the ColatitudeConversion struct.

The longitude is constrained to the range [-180, 180) to have consistent behavior at the daytime border.

This function is taken from the implementation by Isabela de Oliveira Martins at https://github.com/de-oliveira/IsabelaFunctions/blob/master/IsabelaFunctions/fieldmodel.py (2021-05-06).

Parameters

[in]	g	A N x N matrix of g-coefficients
[in]	h	A N x N matrix of h-coefficients
[in]	r0	The reference radius (spherical)
[in]	r	The actual radius (spherical)
[in]	lat	The latitude (spherical)
[in]	lon	The longitude (spherical)

Returns

A spherical field

Definition at line 104 of file legendre.cc.

References ARTS_ASSERT, Conversion::cosd(), Legendre::SphericalField::E, longitude_clamp(), Legendre::SphericalField::S, schmidt(), Conversion::sind(), Legendre::SphericalField::total_horizontal(), and Legendre::SphericalField::U.

Referenced by IGRF::compute_impl().

schmidt_fieldcalc() [2/2]

MatrixOfSphericalField Legendre::schmidt_fieldcalc	(	const Matrix &	g,
		const Matrix &	h,
		const Numeric	r0,
		const Vector &	r,
		const Numeric	lat,
		const Vector &	lon
	)

Computes the spherical field for many radius and longitudes.

See purely Numeric implementation for more information.

Parameters

[in]	g	A N x N matrix of g-coefficients
[in]	h	A N x N matrix of h-coefficients
[in]	r0	The reference radius (spherical)
[in]	r	The actual radius (spherical)
[in]	lat	The latitude (spherical)
[in]	lon	The longitude (spherical)

Returns

A spherical field

Definition at line 156 of file legendre.cc.

References ARTS_ASSERT, Conversion::cosd(), Legendre::SphericalField::E, longitude_clamp(), Legendre::SphericalField::S, schmidt(), Conversion::sind(), Legendre::SphericalField::total_horizontal(), and Legendre::SphericalField::U.

to_geodetic()

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.

Definition at line 231 of file legendre.cc.

References a, Conversion::atan2d(), b, c, Math::pow2(), Math::pow3(), and Math::pow4().