MADNESS: madness::KernelRange Class Reference

MADNESS 0.10.1

#include <kernelrange.h>

Classes
struct	Data

struct	Restrictor
	restrictor function More...

Public Types
enum	Type { Hard , SoftErf }
	types of range restrictor functions More...

Public Member Functions
	KernelRange ()=default

	KernelRange (unsigned int N)

	KernelRange (unsigned int N, double sigma)

bool	finite () const

bool	finite_hard () const

bool	finite_soft () const

hashT	hash () const

int	iextent_x2 (double epsilon=extent_default_epsilon) const

bool	infinite () const

unsigned int	N () const

	operator bool () const

double	sigma () const

Type	type () const

double	value (double r) const

Static Public Attributes
static constexpr double	extent_default_epsilon = std::numeric_limits<double>::epsilon()

Private Member Functions
const Restrictor &	restrictor () const

Private Attributes
std::optional< Data >	data

Friends
bool	operator== (const KernelRange &r1, const KernelRange &r2)

Detailed Description

To limit the range of kernel K(x-y) it is multiplied (in user coordinates) by a restrictor function $ r(N/2 - |x-y|) $ , where $ r(x) $ is identity for unrestricted kernel or one of the choices encoded by KernelRange::Type

Member Enumeration Documentation

◆ Type

enum madness::KernelRange::Type

types of range restrictor functions

Enumerator
Hard	Heavyside (step) function: $r(x) \equiv \theta(x)$ .
SoftErf	erf approximation to Heavyside function: $r(x) \equiv \theta_\sigma(x) \equiv (1 + \erf(x/\sigma))/2$ ; in the limit $\sigma\to 0$ this becomes the Heaviside function.

Constructor & Destructor Documentation

◆ KernelRange() [1/3]

madness::KernelRange::KernelRange ( )

default

constructs a null (i.e., infinite) kernel range

Postcondition: this->infinite()==true

◆ KernelRange() [2/3]

madness::KernelRange::KernelRange	(	unsigned int	N,
		double	sigma
	)

inline

constructs a finite soft (sigma > 0) or hard (sigma==0) kernel range

Parameters

sigma regularization parameter (lengthscale in simulation [0,1] coordinate units) controls the softness of the range restrictor

Precondition: sigma>=0

Postcondition: this->soft()==true

References Hard, MADNESS_ASSERT, N(), sigma(), and SoftErf.

◆ KernelRange() [3/3]

madness::KernelRange::KernelRange ( unsigned int N )

inline

constructs a finite (hard) kernel range

Postcondition: this->hard()==true

References N().

Member Function Documentation

◆ finite()

bool madness::KernelRange::finite ( ) const

inline

Returns: true if range is limited

Referenced by finite_hard(), finite_soft(), infinite(), operator bool(), madness::Convolution1D< Q >::range_restricted(), and madness::GaussianConvolution1D< Q >::rnlp().

◆ finite_hard()

bool madness::KernelRange::finite_hard ( ) const

inline

Returns: true if range is limited using a hard window function (Heaviside)

References finite(), Hard, and type().

Referenced by madness::GaussianConvolution1D< Q >::rnlp().

◆ finite_soft()

bool madness::KernelRange::finite_soft ( ) const

inline

Returns: true if range is limited using a soft window function (sigmoid)

References finite(), Hard, and type().

Referenced by madness::GaussianConvolution1D< Q >::rnlp().

◆ hash()

hashT madness::KernelRange::hash ( ) const

inline

References madness::hash_combine(), madness::hash_value(), infinite(), N(), and restrictor().

◆ iextent_x2()

int madness::KernelRange::iextent_x2 ( double epsilon = extent_default_epsilon ) const

inline

Returns: max value of |x-y| (rounded up, in units of 1/2) for which r(N/2 - |x-y|) is greater than epsilon

References epsilon, infinite(), and MADNESS_ASSERT.

Referenced by madness::GaussianConvolution1D< Q >::rnlp(), and madness::Convolution1D< Q >::rnlp_is_zero().

◆ infinite()

bool madness::KernelRange::infinite ( ) const

inline

Returns: true if range is unlimited

References finite().

Referenced by hash(), iextent_x2(), and value().

◆ N()

unsigned int madness::KernelRange::N ( ) const

inline

Referenced by KernelRange(), KernelRange(), hash(), madness::GaussianConvolution1D< Q >::rnlp(), and value().

◆ operator bool()

madness::KernelRange::operator bool ( ) const

inlineexplicit

Returns: true if range is limited

References finite().

◆ restrictor()

const Restrictor & madness::KernelRange::restrictor ( ) const

inlineprivate

Referenced by hash(), sigma(), type(), and value().

◆ sigma()

double madness::KernelRange::sigma ( ) const

inline

References restrictor(), and madness::KernelRange::Restrictor::sigma().

Referenced by KernelRange(), and madness::GaussianConvolution1D< Q >::rnlp().

◆ type()

Type madness::KernelRange::type ( ) const

inline

References restrictor(), and madness::KernelRange::Restrictor::type().

Referenced by finite_hard(), and finite_soft().

◆ value()

double madness::KernelRange::value ( double r ) const

inline

Returns: value of restrictor function at N/2 - abs(r)

References std::abs(), infinite(), N(), restrictor(), and madness::KernelRange::Restrictor::value().

Referenced by madness::KernelRange::Data::compute_iextent_x2(), and madness::GaussianConvolution1D< Q >::rnlp().

Friends And Related Symbol Documentation

◆ operator==

bool operator==	(	const KernelRange &	r1,
		const KernelRange &	r2
	)

friend

Returns: true if r1 and r2 are equal

Member Data Documentation

◆ data

std::optional<Data> madness::KernelRange::data

private

◆ extent_default_epsilon

constexpr double madness::KernelRange::extent_default_epsilon = std::numeric_limits<double>::epsilon()

staticconstexpr

Referenced by madness::KernelRange::Data::iextent_x2().

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

kernelrange.h