mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio > Class Template Reference

The N x M trapezoidal rule on the torus with minor radius 1 and major radius AspectRatio. More...

#include <TrapezoidalTorus.hpp>

Public Types
using	value_type = Scalar

Static Public Member Functions
static constexpr Kokkos::Array< Scalar, 3 *num_points >	points ()
	The points as (x, y, z) triples, ring by ring in theta from the outer equator, by increasing phi in a ring.
static constexpr Kokkos::Array< Scalar, num_points >	weights ()
	The num_points weights, in the order of points().
template<class Function>
static constexpr auto	integrate (const Function &f)
	sum_i w_i f(x_i, y_i, z_i), approximating the integral of f over the torus.

Static Public Attributes
static constexpr unsigned	num_poloidal = N
static constexpr unsigned	num_toroidal = M
static constexpr unsigned	num_points = N * M
static constexpr double	aspect_ratio = AspectRatio

Detailed Description

template<class Scalar, unsigned N, unsigned M, double AspectRatio>
class mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >

The points and weights are correctly rounded to Scalar and computed by the compiler, so every member is a constant expression. Like GaussLegendreSphere's rule, it integrates over a unit-scale surface; scale for other minor radii.

Member Typedef Documentation

value_type

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

using mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::value_type = Scalar

Member Function Documentation

points()

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

constexpr Kokkos::Array< Scalar, 3 *num_points > mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::points ( )

inlinestaticconstexpr

weights()

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

constexpr Kokkos::Array< Scalar, num_points > mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::weights ( )

inlinestaticconstexpr

integrate()

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

template<class Function>

constexpr auto mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::integrate ( const Function & f )

inlinestaticconstexpr

Member Data Documentation

num_poloidal

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

unsigned mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::num_poloidal = N

staticconstexpr

num_toroidal

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

unsigned mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::num_toroidal = M

staticconstexpr

num_points

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

unsigned mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::num_points = N * M

staticconstexpr

aspect_ratio

template<class Scalar, unsigned N, unsigned M, double AspectRatio>

double mundy::TrapezoidalTorus< Scalar, N, M, AspectRatio >::aspect_ratio = AspectRatio

staticconstexpr