LogarithmicCoordinates1D< NT > Class Template Reference

Points on [start, stop], including both ends, with spacing growing exponentially in the index. More...

#include <coordinates.hh>

Public Types
using	ctype = NT
	Scalar type.

Public Member Functions
	LogarithmicCoordinates1D (size_t grid_extent, double start, double stop, double bias)
template<typename NT2 >
	LogarithmicCoordinates1D (const LogarithmicCoordinates1D< NT2 > &other)
	Convert from another precision.
LogarithmicCoordinates1D	prefix (size_t n) const
	The first n points of this grid, as a grid of the same type.
size_t KOKKOS_FORCEINLINE_FUNCTION	parent_size () const
	Number of points of the grid this one is a prefix() of; size() unless it is a prefix.
device::array< size_t, 1 > KOKKOS_FORCEINLINE_FUNCTION	from_linear_index (size_t i) const
	The multi-index {i} of point i.
template<typename IT >
NT KOKKOS_FORCEINLINE_FUNCTION	forward (const IT &x) const
	The coordinate \(x(i)\) at grid index x (real values allowed).
template<typename IT >
device::array< NT, 1 > KOKKOS_FORCEINLINE_FUNCTION	forward (const device::array< IT, 1 > &x) const
	As forward(x[0]).
NT KOKKOS_FORCEINLINE_FUNCTION	backward (const NT &y) const
	The inverse map: the (fractional) grid index of the coordinate y.
NT KOKKOS_FORCEINLINE_FUNCTION	backward_derivative (const NT &y) const
	\(di/dx\) at the coordinate y.
size_t KOKKOS_FORCEINLINE_FUNCTION	size () const
	Number of points N.
device::array< size_t, 1 > KOKKOS_FORCEINLINE_FUNCTION	sizes () const
	{N}.
std::string	to_string () const
	"LogarithmicCoordinates1D(start, stop, bias, N)"; identifies the grid.

Public Attributes
const NT	start
	The parameters.
const NT	stop
const NT	bias

Static Public Attributes
static constexpr size_t	dim = 1
	One axis.

Friends
template<typename NT2 >
bool	operator== (const LogarithmicCoordinates1D< NT > &lhs, const LogarithmicCoordinates1D< NT2 > &rhs)
	Same precision, parameters and number of points (and the same parent, for a prefix).

Detailed Description

template<typename NT = double>
requires std::is_floating_point_v<NT>
class DiFfRG::LogarithmicCoordinates1D< NT >

Points on [start, stop], including both ends, with spacing growing exponentially in the index.

With N = grid_extent ≥ 2, bias b ≠ 0 and grid index i (real values allowed):

\[ x(i) = \mathrm{start} + (\mathrm{stop} - \mathrm{start})\,\frac{e^{b\,i/(N-1)} - 1}{e^{b} - 1}\,. \]

For b > 0 the points cluster near start (consecutive spacings grow by the factor \(e^{b/(N-1)}\)), for b < 0 near stop; b → 0 approaches LinearCoordinates1D.

Template Parameters

NT	Scalar type of the coordinates.

Member Typedef Documentation

ctype

template<typename NT = double>

using ctype = NT

Scalar type.

Constructor & Destructor Documentation

LogarithmicCoordinates1D() [1/2]

template<typename NT = double>

LogarithmicCoordinates1D ( size_t grid_extent, double start, double stop, double bias )

inline

grid_extent points (≥ 2) from start to stop with bias (≠ 0); throws otherwise. Constants are computed in double.

LogarithmicCoordinates1D() [2/2]

template<typename NT = double>

template<typename NT2 >

LogarithmicCoordinates1D ( const LogarithmicCoordinates1D< NT2 > & other )

inline

Convert from another precision.

Member Function Documentation

backward()

template<typename NT = double>

NT KOKKOS_FORCEINLINE_FUNCTION backward ( const NT & y ) const

inline

The inverse map: the (fractional) grid index of the coordinate y.

backward_derivative()

template<typename NT = double>

NT KOKKOS_FORCEINLINE_FUNCTION backward_derivative ( const NT & y ) const

inline

\(di/dx\) at the coordinate y.

forward() [1/2]

template<typename NT = double>

template<typename IT >

device::array< NT, 1 > KOKKOS_FORCEINLINE_FUNCTION forward ( const device::array< IT, 1 > & x ) const

inline

As forward(x[0]).

forward() [2/2]

template<typename NT = double>

template<typename IT >

NT KOKKOS_FORCEINLINE_FUNCTION forward ( const IT & x ) const

inline

The coordinate \(x(i)\) at grid index x (real values allowed).

from_linear_index()

template<typename NT = double>

device::array< size_t, 1 > KOKKOS_FORCEINLINE_FUNCTION from_linear_index ( size_t i ) const

inline

The multi-index {i} of point i.

parent_size()

template<typename NT = double>

size_t KOKKOS_FORCEINLINE_FUNCTION parent_size ( ) const

inline

Number of points of the grid this one is a prefix() of; size() unless it is a prefix.

prefix()

template<typename NT = double>

LogarithmicCoordinates1D prefix ( size_t n ) const

inline

The first n points of this grid, as a grid of the same type.

forward(i) is bit-identical to that of the full grid for i < n, and backward() is unchanged; use it to skip the upper end of a grid without changing the coordinate type. The prefix keeps the parameters and point count of the full grid (parent_size()); to_string() appends ".prefix(n)".

Parameters

n	Number of points kept, 1 ≤ n ≤ size().

size()

template<typename NT = double>

size_t KOKKOS_FORCEINLINE_FUNCTION size ( ) const

inline

Number of points N.

sizes()

template<typename NT = double>

device::array< size_t, 1 > KOKKOS_FORCEINLINE_FUNCTION sizes ( ) const

inline

{N}.

to_string()

template<typename NT = double>

std::string to_string ( ) const

inline

"LogarithmicCoordinates1D(start, stop, bias, N)"; identifies the grid.

Friends And Related Symbol Documentation

operator==

template<typename NT = double>

template<typename NT2 >

bool operator== ( const LogarithmicCoordinates1D< NT > & lhs, const LogarithmicCoordinates1D< NT2 > & rhs )

friend

Same precision, parameters and number of points (and the same parent, for a prefix).

Member Data Documentation

bias

template<typename NT = double>

const NT bias

dim

template<typename NT = double>

size_t dim = 1

staticconstexpr

One axis.

start

template<typename NT = double>

const NT start

The parameters.

stop

template<typename NT = double>

const NT stop

---

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

• /home/runner/work/DiFfRG/DiFfRG/DiFfRG/include/DiFfRG/discretization/coordinates/coordinates.hh