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
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 ()
Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType
using	ItemType

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,

\[ W(u) = \begin{cases}\;\dfrac{3}{4\pi} & \quad{\text{if }} 0 \leq u \leq 1 \\ \; 0 & \quad{\text{else}} \end{cases}. \]

This function satisfies the required normalization

\[ 4\pi \int_0^\infty W(u)\, u^2\, {\text{d}}u = 1. \]

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

\[\Sigma(q) = \begin{cases} \;\dfrac{3}{2\pi} \sqrt{1-q^2} & \quad\text{if } 0 \leq q \leq 1, \\ \; 0 & \quad{\text{else}}. \end{cases} \]

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 \({\cal{X}}\), and solving the equation

\[ {\cal{X}} = 4\pi\,W(u)\,u^2\, {\text{d}}u \]

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

Implements SmoothingKernel.

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

• UniformSmoothingKernel.hpp