UniformSmoothingKernel Class Reference

#include <UniformSmoothingKernel.hpp>

Inheritance diagram for UniformSmoothingKernel:

Public Member Functions
double	columnDensity (double q) const override
double	density (double u) const override
double	generateRadius () const override
virtual double	columnDensity (double q) const =0
virtual double	density (double u) const =0
virtual double	generateRadius () const =0
Public Member Functions inherited from SimulationItem
template<class T >
T *	find (bool setup=true) const
template<class T >
T *	interface (int levels=-999999, bool setup=true) const
virtual string	itemName () const
void	setup ()
string	typeAndName () const
Public Member Functions inherited from Item
	Item (const Item &)=delete
virtual	~Item ()
void	addChild (Item *child)
const vector< Item * > &	children () const
virtual void	clearItemListProperty (const PropertyDef *property)
void	destroyChild (Item *child)
virtual bool	getBoolProperty (const PropertyDef *property) const
virtual vector< double >	getDoubleListProperty (const PropertyDef *property) const
virtual double	getDoubleProperty (const PropertyDef *property) const
virtual string	getEnumProperty (const PropertyDef *property) const
virtual int	getIntProperty (const PropertyDef *property) const
virtual vector< Item * >	getItemListProperty (const PropertyDef *property) const
virtual Item *	getItemProperty (const PropertyDef *property) const
virtual string	getStringProperty (const PropertyDef *property) const
int	getUtilityProperty (string name) const
virtual void	insertIntoItemListProperty (const PropertyDef *property, int index, Item *item)
Item &	operator= (const Item &)=delete
Item *	parent () const
virtual void	removeFromItemListProperty (const PropertyDef *property, int index)
virtual void	setBoolProperty (const PropertyDef *property, bool value)
virtual void	setDoubleListProperty (const PropertyDef *property, vector< double > value)
virtual void	setDoubleProperty (const PropertyDef *property, double value)
virtual void	setEnumProperty (const PropertyDef *property, string value)
virtual void	setIntProperty (const PropertyDef *property, int value)
virtual void	setItemProperty (const PropertyDef *property, Item *item)
virtual void	setStringProperty (const PropertyDef *property, string value)
void	setUtilityProperty (string name, int value)
virtual string	type () const

Protected Member Functions
	UniformSmoothingKernel ()
Protected Member Functions inherited from SmoothingKernel
	SmoothingKernel ()
Random *	random () const
void	setupSelfBefore () override
Protected Member Functions inherited from SimulationItem
	SimulationItem ()
virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const
virtual void	setupSelfAfter ()
virtual void	setupSelfBefore ()
Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType = SmoothingKernel
using	ItemType = UniformSmoothingKernel

Friends
class	ItemRegistry

Detailed Description

The UniformSmoothingKernel class is a subclass of the abstract SmoothingKernel class, and describes a smoothing kernel with a uniform density and a compact support. It is completely described by the simple kernel density,

$$W(u)=\{\begin{array}{ll}{\displaystyle \frac{3}{4\pi }}& \text{if }0\le u\le 1\\ 0& \text{else}\end{array}.$$

This function satisfies the required normalization

$$4\pi {\int }_0^{\mathrm{\infty }}W(u)u^2\text{d}u=1.$$

Constructor & Destructor Documentation

UniformSmoothingKernel()

UniformSmoothingKernel::UniformSmoothingKernel ( )

inlineprotected

Default constructor for concrete Item subclass UniformSmoothingKernel : "a uniform smoothing kernel" .

Member Function Documentation

columnDensity()

double UniformSmoothingKernel::columnDensity ( double  q ) const

overridevirtual

This function returns the column density $\mathrm{\Sigma }(q)=2{\int }_q^1\frac{W(u)u\text{d}u}{\sqrt{u^2-q^2}}$ of the smoothing kernel as a function of the normalized impact radius $q=r_{\text{i}}/h$. For the uniform smoothing kernel, we obtain

$$\mathrm{\Sigma }(q)=\{\begin{array}{ll}{\displaystyle \frac{3}{2\pi }}\sqrt{1-q^2}& \text{if }0\le q\le 1,\\ 0& \text{else}.\end{array}$$

Implements SmoothingKernel.

density()

double UniformSmoothingKernel::density ( double  u ) const

overridevirtual

This function returns the density $W(u)$ of the smoothing kernel as a function of the normalized radius $u$. It just implements the analytical formula given in the class header.

Implements SmoothingKernel.

generateRadius()

double UniformSmoothingKernel::generateRadius ( ) const

overridevirtual

This function generates a random normalized radius $u$ from the smoothing kernel by drawing a number from the one-dimensional probability density $p(u)\text{d}u=4\pi W(u)u^2\text{d}u$. This is accomplished by generating a uniform deviate $\mathcal{X}$, and solving the equation

$$\mathcal{X}=4\pi W(u)u^2\text{d}u$$

for $u$. For the uniform smoothing kernel, we obtain the simple expression $u=\sqrt[3]{\mathcal{X}}$.

Implements SmoothingKernel.

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

• UniformSmoothingKernel.hpp