Grid

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Non-uniform radial grid with Jacobian, suitable for atomic structure calculations.

Defines a mapping from a uniform grid u = {0, du, 2du, ...} to a non-uniform grid r(u), along with the Jacobian dr/du and the convenience quantity (1/r)(dr/du).

Three grid types are supported (see GridType):

• loglinear (default): logarithmic at small r, linear at large r; controlled by the turning point b.
• logarithmic: r = r0 * exp(u); good for tightly bound states.
• linear: uniform spacing in r.

Grid points and Jacobians are stored as std::vector<double> and can be iterated over directly (const iterators only).

#include <Grid.hpp>

Public Member Functions
	Grid (double in_r0, double in_rmax, std::size_t in_num_points, GridType in_gridtype, double in_b=0)
	Construct grid directly from parameters.
	Grid (const GridParameters &in)
	Construct grid from a GridParameters struct.
auto	r0 () const
	Minimum (first) grid point r[0].
auto	front () const
	Minimum (first) grid point r[0]; alias for r0()
auto	rmax () const
	Maximum (last) grid point r[N-1].
auto	back () const
	Maximum (last) grid point r[N-1]; alias for rmax()
auto	num_points () const
	Number of grid points.
auto	size () const
	Number of grid points; alias for num_points()
auto	du () const
	Uniform step size du.
auto	type () const
	Grid type (loglinear, logarithmic, or linear)
auto	loglin_b () const
	Log-linear turning point b: roughly logarithmic for r<b, linear for r>b.
const std::vector< double > &	r () const
	Full grid vector r.
auto	r (std::size_t i) const
	Grid point r[i], with range checking.
auto	at (std::size_t i) const
	Grid point r[i], with range checking; alias for r(i)
auto	operator() (std::size_t i) const
	Grid point r[i], with range checking; alias for r(i)
const std::vector< double > &	drdu () const
	Full Jacobian vector dr/du.
auto	drdu (std::size_t i) const
	Jacobian (dr/du)[i], with range checking.
const std::vector< double > &	drduor () const
	Full vector of (1/r)(dr/du)
auto	drduor (std::size_t i) const
	(1/r)(dr/du)[i], with range checking
std::size_t	getIndex (double x, bool require_nearest=false) const
	Returns the grid index closest to x. If require_nearest is false, returns the index of the largest grid point x.
std::string	gridParameters () const
	Returns a human-readable string of grid parameters.
std::vector< double >	rpow (double k) const
	Returns a vector of r^k for each grid point.
auto	begin () const
	Const iterator to first grid point.
auto	end () const
	Const iterator past last grid point.
auto	cbegin () const
	Const iterator to first grid point.
auto	cend () const
	Const iterator past last grid point.
auto	rbegin () const
	Const reverse iterator to last grid point.
auto	rend () const
	Const reverse iterator before first grid point.
auto	crbegin () const
	Const reverse iterator to last grid point.
auto	crend () const
	Const reverse iterator before first grid point.
void	extend_to (double new_rmax)
	Extends the grid to at least new_rmax.
GridParameters	params () const
	Returns a GridParameters struct that can be used to reconstruct this grid.

Static Public Member Functions
static double	calc_du_from_num_points (double in_r0, double in_rmax, std::size_t in_num_points, GridType in_gridtype, double in_b=0)
	Given r0, rmax, and num_points, calculates the uniform step size du.
static std::size_t	calc_num_points_from_du (double in_r0, double in_rmax, double in_du, GridType in_gridtype, double in_b=0)
	Given r0, rmax, and du, calculates the number of grid points.

Constructor & Destructor Documentation

Grid() [1/2]

Grid::Grid	(	double	in_r0,
		double	in_rmax,
		std::size_t	in_num_points,
		GridType	in_gridtype,
		double	in_b = 0
	)

Construct grid directly from parameters.

Grid() [2/2]

Grid::Grid

(

const GridParameters &

in

)

Construct grid from a GridParameters struct.

Member Function Documentation

r0()

auto Grid::r0 ( ) const

inline

Minimum (first) grid point r[0].

front()

auto Grid::front ( ) const

inline

Minimum (first) grid point r[0]; alias for r0()

rmax()

auto Grid::rmax ( ) const

inline

Maximum (last) grid point r[N-1].

back()

auto Grid::back ( ) const

inline

Maximum (last) grid point r[N-1]; alias for rmax()

num_points()

auto Grid::num_points ( ) const

inline

Number of grid points.

size()

auto Grid::size ( ) const

inline

Number of grid points; alias for num_points()

du()

auto Grid::du ( ) const

inline

Uniform step size du.

type()

auto Grid::type ( ) const

inline

Grid type (loglinear, logarithmic, or linear)

loglin_b()

auto Grid::loglin_b ( ) const

inline

Log-linear turning point b: roughly logarithmic for r<b, linear for r>b.

r() [1/2]

const std::vector< double > & Grid::r ( ) const

inline

Full grid vector r.

r() [2/2]

auto Grid::r ( std::size_t  i ) const

inline

Grid point r[i], with range checking.

at()

auto Grid::at ( std::size_t  i ) const

inline

Grid point r[i], with range checking; alias for r(i)

operator()()

auto Grid::operator() ( std::size_t  i ) const

inline

Grid point r[i], with range checking; alias for r(i)

drdu() [1/2]

const std::vector< double > & Grid::drdu ( ) const

inline

Full Jacobian vector dr/du.

drdu() [2/2]

auto Grid::drdu ( std::size_t  i ) const

inline

Jacobian (dr/du)[i], with range checking.

drduor() [1/2]

const std::vector< double > & Grid::drduor ( ) const

inline

Full vector of (1/r)(dr/du)

drduor() [2/2]

auto Grid::drduor ( std::size_t  i ) const

inline

(1/r)(dr/du)[i], with range checking

getIndex()

std::size_t Grid::getIndex	(	double	x,
		bool	require_nearest = false
	)		const

Returns the grid index closest to x. If require_nearest is false, returns the index of the largest grid point x.

gridParameters()

std::string Grid::gridParameters

(

)

const

Returns a human-readable string of grid parameters.

rpow()

std::vector< double > Grid::rpow

(

double

k

)

const

Returns a vector of r^k for each grid point.

begin()

auto Grid::begin ( ) const

inline

Const iterator to first grid point.

end()

auto Grid::end ( ) const

inline

Const iterator past last grid point.

cbegin()

auto Grid::cbegin ( ) const

inline

Const iterator to first grid point.

cend()

auto Grid::cend ( ) const

inline

Const iterator past last grid point.

rbegin()

auto Grid::rbegin ( ) const

inline

Const reverse iterator to last grid point.

rend()

auto Grid::rend ( ) const

inline

Const reverse iterator before first grid point.

crbegin()

auto Grid::crbegin ( ) const

inline

Const reverse iterator to last grid point.

crend()

auto Grid::crend ( ) const

inline

Const reverse iterator before first grid point.

extend_to()

void Grid::extend_to

(

double

new_rmax

)

Extends the grid to at least new_rmax.

This is the only mutating function; use with caution. The extended grid is not guaranteed to end exactly at new_rmax it will typically extend slightly beyond, as new points must land on the existing uniform u grid.

params()

GridParameters Grid::params ( ) const

inline

Returns a GridParameters struct that can be used to reconstruct this grid.

calc_du_from_num_points()

double Grid::calc_du_from_num_points ( double  in_r0, double  in_rmax, std::size_t  in_num_points, GridType  in_gridtype, double  in_b = 0  )

static

Given r0, rmax, and num_points, calculates the uniform step size du.

calc_num_points_from_du()

std::size_t Grid::calc_num_points_from_du ( double  in_r0, double  in_rmax, double  in_du, GridType  in_gridtype, double  in_b = 0  )

static

Given r0, rmax, and du, calculates the number of grid points.

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

• Maths/Grid.hpp
• Maths/Grid.cpp