Public Types
enum	KernelFunction { KernelFunction::gaussian, KernelFunction::triangular, KernelFunction::uniform, KernelFunction::cutoff_function_w1_dealii, KernelFunction::cutoff_function_c1_dealii }

Public Member Functions
	ParticlePDF (const unsigned int granularity, const double bandwidth, const KernelFunction kernel_function)

	ParticlePDF (const double bandwidth, const KernelFunction kernel_function)

void	fill_from_particle_range (const typename Particles::ParticleHandler< dim >::particle_iterator_range &particle_range, const std::vector< typename Particles::ParticleHandler< dim >::particle_iterator_range > &particle_ranges_to_sum_over, const unsigned int n_particles_in_cell, const typename ::Mapping< dim > &mapping)

void	insert_kernel_sum_from_particle_range (const Point< dim > &reference_point, const std::array< unsigned int, dim > &table_index, const typename Triangulation< dim >::cell_iterator &cell, const std::vector< typename Particles::ParticleHandler< dim >::particle_iterator_range > &particle_ranges_to_sum_over, const typename ::Mapping< dim > &mapping)

void	add_value_to_function_table (const unsigned int x_index, const unsigned int y_index, const unsigned int z_index, const double input_value)

void	add_value_to_function_table (const std::array< unsigned int, dim > &index_point, const double input_value)

void	add_value_to_function_table (const double input_value, const types::particle_index reference_particle_id)

double	evaluate_function_at_index (const unsigned int x_index, const unsigned int y_index, const unsigned int z_index) const

void	compute_statistical_values ()

double	get_max () const

double	get_min () const

Point< dim >	get_max_position () const

std::vector< Point< dim > >	get_min_positions () const

double	get_standard_deviation () const

types::particle_index	get_max_particle () const

types::particle_index	get_min_particle () const

Private Member Functions
double	apply_selected_kernel_function (const double distance) const

double	kernelfunction_uniform (const double distance) const

double	kernelfunction_triangular (const double distance) const

double	kernelfunction_gaussian (const double distance) const

Private Attributes
Table< dim, double >	function_output_table

double	bandwidth

KernelFunction	kernel_function

unsigned int	granularity

double	max

double	min

Point< dim >	max_position

std::vector< Point< dim > >	min_positions

double	standard_deviation

double	mean

small_vector< double >	function_output_vector

bool	is_defined_per_particle

types::particle_index	max_particle_index

types::particle_index	min_particle_index

Detailed Description

template<int dim>
class aspect::Particle::ParticlePDF< dim >

This class computes the point-density function that describes the clustering of particles. ParticlePDF holds the values of the point-density function at every point at which the function is defined. The function is defined either at granularity^dim regular intervals throughout each cell, or at the position of each particle in the cell. ParticlePDF computes statistical values from the point-density function including the mean and standard deviation.

Definition at line 48 of file distribution.h.

Member Enumeration Documentation

§ KernelFunction

template<int dim>

enum aspect::Particle::ParticlePDF::KernelFunction

strong

The KernelFunctions enum class is a data structure which contains the kernel functions available for use in the Kernel Density Estimator.

Enumerator
gaussian
triangular
uniform
cutoff_function_w1_dealii
cutoff_function_c1_dealii

Definition at line 57 of file distribution.h.

Constructor & Destructor Documentation

§ ParticlePDF() [1/2]

template<int dim>

aspect::Particle::ParticlePDF< dim >::ParticlePDF	(	const unsigned int	granularity,
		const double	bandwidth,
		const KernelFunction	kernel_function
	)

This is the constructor for ParticlePDF. This constructor is called when creating a point-density function which is defined at regular intervals throughout a cell.

Parameters

granularity	determines the number of reference points at which the point density function is computed. The point density function is only defined at these reference points.
bandwidth	determines the bandwidth to be used in the kernel function.
kernel_function	determines which kernel function to use when generating the point-density function.

§ ParticlePDF() [2/2]

template<int dim>

aspect::Particle::ParticlePDF< dim >::ParticlePDF	(	const double	bandwidth,
		const KernelFunction	kernel_function
	)

This is the constructor for ParticlePDF. This constructor is called when creating a point-density function which is defined at the positions of the particles within the cell, as opposed to at regular intervals based on a granularity value.

Parameters

bandwidth	determines the bandwidth to be used in the kernel function.
kernel_function	determines which kernel function to use when generating the point-density function.

Member Function Documentation

§ fill_from_particle_range()

template<int dim>

void aspect::Particle::ParticlePDF< dim >::fill_from_particle_range	(	const typename Particles::ParticleHandler< dim >::particle_iterator_range &	particle_range,
		const std::vector< typename Particles::ParticleHandler< dim >::particle_iterator_range > &	particle_ranges_to_sum_over,
		const unsigned int	n_particles_in_cell,
		const typename ::Mapping< dim > &	mapping
	)

Fills the point-density function with values from the particles in the given cell.

Parameters

particle_range	The particle_iterator_range to operate on.
particle_ranges_to_sum_over	The particle_iterator_range of the current and neighboring cells. The KDE uses both the particles in the given cell and those in neighboring cells when constructing the point density function.
n_particles_in_cell	The number of particles belonging to the particle manager in question within the cell.
mapping	A reference to a mapping object to use to translate cell coordinates into real coordinates. `fill_from_particle_range` does not use this parameter directly but passes it to `insert_kernel_sum_from_particle_range.`

§ insert_kernel_sum_from_particle_range()

template<int dim>

void aspect::Particle::ParticlePDF< dim >::insert_kernel_sum_from_particle_range	(	const Point< dim > &	reference_point,
		const std::array< unsigned int, dim > &	table_index,
		const typename Triangulation< dim >::cell_iterator &	cell,
		const std::vector< typename Particles::ParticleHandler< dim >::particle_iterator_range > &	particle_ranges_to_sum_over,
		const typename ::Mapping< dim > &	mapping
	)

This function is only called from fill_from_particle_range. It iterates through every particle in the cell and sums the value of the kernel function between the reference point and the position of the cell.

Parameters

reference_point	The point from which to get the value of the kernel function.
table_index	The index in the PDF to insert the data into.
n_particles_in_cell	The number of particles in the cell.
cell	The cell in which to apply the kernel function
particle_ranges_to_sum_over	The particle_iterator_range to sum particles from.
mapping	A reference to a mapping object to use to translate cell coordinates into real coordinates

§ add_value_to_function_table() [1/3]

template<int dim>

void aspect::Particle::ParticlePDF< dim >::add_value_to_function_table	(	const unsigned int	x_index,
		const unsigned int	y_index,
		const unsigned int	z_index,
		const double	input_value
	)

Inserts a value into the point-density function.

Parameters

x_index	The x index in the point-density function to insert at.
y_index	The y index in the point-density function to insert at.
z_index	The z index in the point-density function to insert at.
input_value	The value to insert into the point-density function.

§ add_value_to_function_table() [2/3]

template<int dim>

void aspect::Particle::ParticlePDF< dim >::add_value_to_function_table	(	const std::array< unsigned int, dim > &	index_point,
		const double	input_value
	)

Inserts a value into the point-density function.

Parameters

index_point	The index in the point-density function to insert at.
input_value	The value to insert into the point-density function.

§ add_value_to_function_table() [3/3]

template<int dim>

void aspect::Particle::ParticlePDF< dim >::add_value_to_function_table	(	const double	input_value,
		const types::particle_index	reference_particle_id
	)

Inserts a value into the point-density function. This version of the function is intended to be used when is_defined_per_particle is true.

Parameters

input_value	The value to insert into the point-density function.
reference_particle_id	the id of the particle from which the input value is taken in reference to.

§ evaluate_function_at_index()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::evaluate_function_at_index	(	const unsigned int	x_index,
		const unsigned int	y_index,
		const unsigned int	z_index
	)		const

Returns the value of the function at the given index.

Parameters

x_index	The x index in the point-density function to evaluate at.
y_index	The y index in the point-density function to evaluate at.
z_index	The z index in the point-density function to evaluate at.

§ compute_statistical_values()

template<int dim>

void aspect::Particle::ParticlePDF< dim >::compute_statistical_values ( )

Calculates the relevant statistics from the contents of the PDF.

§ get_max()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::get_max ( ) const

Returns the maximum of the point-density function.

§ get_min()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::get_min ( ) const

Returns the minimum of the point-density function.

§ get_max_position()

template<int dim>

Point<dim> aspect::Particle::ParticlePDF< dim >::get_max_position ( ) const

Returns the location of the maximum of the point-density function.

§ get_min_positions()

template<int dim>

std::vector<Point<dim> > aspect::Particle::ParticlePDF< dim >::get_min_positions ( ) const

Returns the location of the minimum of the point-density function.

§ get_standard_deviation()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::get_standard_deviation ( ) const

Returns the standard deviation of the point-density function.

§ get_max_particle()

template<int dim>

types::particle_index aspect::Particle::ParticlePDF< dim >::get_max_particle ( ) const

Returns the index of the particle whose position has the highest point-density value. This function only works if the particle density function is defined per particle, instead of being defined on a grid.

§ get_min_particle()

template<int dim>

types::particle_index aspect::Particle::ParticlePDF< dim >::get_min_particle ( ) const

Returns the index of the particle whose position has the lowest point-density value. This function only works if the particle density function is defined per particle, instead of being defined on a grid.

§ apply_selected_kernel_function()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::apply_selected_kernel_function ( const double distance ) const

private

Returns the value of the selected kernel function.

Parameters

distance the distance to pass to the selected kernel function.

§ kernelfunction_uniform()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::kernelfunction_uniform ( const double distance ) const

private

The Uniform kernel function returns a value of 1.0 as long as the distance is less than the KDE's bandwidth.

Parameters

distance the output of the kernel function depends on the distance between the reference point and the center of the kernel function.

§ kernelfunction_triangular()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::kernelfunction_triangular ( const double distance ) const

private

The Triangular kernel function returns a value of 1.0 minus the distance variable.

Parameters

distance the output of the kernel function depends on the distance between the reference point and the center of the kernel function.

§ kernelfunction_gaussian()

template<int dim>

double aspect::Particle::ParticlePDF< dim >::kernelfunction_gaussian ( const double distance ) const

private

The gaussian function returns the value of a gaussian distribution at the specified distance.

Parameters

distance the output of the kernel function depends on the distance between the reference point and the center of the kernel function.

Member Data Documentation

§ function_output_table

template<int dim>

Table<dim,double> aspect::Particle::ParticlePDF< dim >::function_output_table

private

function_output_table holds the output of the point-density function at every point where the function is defined, as long as the function has been generated at regular intervals throughout the cell (as opposed to being defined at the position of each particle.

Definition at line 234 of file distribution.h.

§ bandwidth

template<int dim>

double aspect::Particle::ParticlePDF< dim >::bandwidth

private

The bandwidth variable scales the point-density function. Choosing an appropriate bandwidth is important because a bandwidth value which is too low or too high can result in oversmoothing or undersmoothing of the point-density function. Oversmoothing or undersmoothing results in a function which represents the underlying data less accurately.

Definition at line 244 of file distribution.h.

§ kernel_function

template<int dim>

KernelFunction aspect::Particle::ParticlePDF< dim >::kernel_function

private

kernel_function is an internal variable to keep track of which kernel function is being used by the ParticlePDF.

Definition at line 250 of file distribution.h.

§ granularity

template<int dim>

unsigned int aspect::Particle::ParticlePDF< dim >::granularity

private

granularity determines the number of inputs at which the point-density function is defined. The function is defined for granularity^dim inputs.

Definition at line 257 of file distribution.h.

§ max

template<int dim>

double aspect::Particle::ParticlePDF< dim >::max

private

max holds the maximum value of the point-density function after it has been computed.

Definition at line 262 of file distribution.h.

§ min

template<int dim>

double aspect::Particle::ParticlePDF< dim >::min

private

min holds the minimum value of the point-density function after it has been computed.

Definition at line 267 of file distribution.h.

§ max_position

template<int dim>

Point<dim> aspect::Particle::ParticlePDF< dim >::max_position

private

max_position holds position within the cell where the maximum point density was measured.

Definition at line 272 of file distribution.h.

§ min_positions

template<int dim>

std::vector<Point<dim> > aspect::Particle::ParticlePDF< dim >::min_positions

private

min_positions holds positions within the cell where the minimum point density was measured. This is a std::vector because there is a chance that there will be multiple minimum positions with the same value, especially when particles are already arranged in a regular pattern.

Definition at line 279 of file distribution.h.

§ standard_deviation

template<int dim>

double aspect::Particle::ParticlePDF< dim >::standard_deviation

private

standard_deviation holds the standard_deviation of the point-density function after it has been computed.

Definition at line 284 of file distribution.h.

§ mean

template<int dim>

double aspect::Particle::ParticlePDF< dim >::mean

private

mean holds the mean value of the point-density function after it has been computed.

Definition at line 289 of file distribution.h.

§ function_output_vector

template<int dim>

small_vector<double> aspect::Particle::ParticlePDF< dim >::function_output_vector

private

function_output_vector holds the output generated by summing the kernel functions from the positions of each particle in the cell, as opposed to summing the function at regular intervals throughout the cell.

Definition at line 296 of file distribution.h.

§ is_defined_per_particle

template<int dim>

bool aspect::Particle::ParticlePDF< dim >::is_defined_per_particle

private

is_defined_per_particle keeps track of whether or not this point-density function is defined at regular intervals throughout the cell or if the function is defined at the position of each particle in the cell.

Definition at line 303 of file distribution.h.

§ max_particle_index

template<int dim>

types::particle_index aspect::Particle::ParticlePDF< dim >::max_particle_index

private

The index of the particle in the cell with the maximum point-density function value.

Definition at line 309 of file distribution.h.

§ min_particle_index

template<int dim>

types::particle_index aspect::Particle::ParticlePDF< dim >::min_particle_index

private

The index of the particle in the cell with the minimum point-density function value.

Definition at line 315 of file distribution.h.

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

/home/bob/source/include/aspect/particle/distribution.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<int dim> class aspect::Particle::ParticlePDF< dim >

Member Enumeration Documentation

§ KernelFunction

Constructor & Destructor Documentation

§ ParticlePDF() [1/2]

§ ParticlePDF() [2/2]

Member Function Documentation

§ fill_from_particle_range()

§ insert_kernel_sum_from_particle_range()

§ add_value_to_function_table() [1/3]

§ add_value_to_function_table() [2/3]

§ add_value_to_function_table() [3/3]

§ evaluate_function_at_index()

§ compute_statistical_values()

§ get_max()

§ get_min()

§ get_max_position()

§ get_min_positions()

§ get_standard_deviation()

§ get_max_particle()

§ get_min_particle()

§ apply_selected_kernel_function()

§ kernelfunction_uniform()

§ kernelfunction_triangular()

§ kernelfunction_gaussian()

Member Data Documentation

§ function_output_table

§ bandwidth

§ kernel_function

§ granularity

§ max

§ min

§ max_position

§ min_positions

§ standard_deviation

§ mean

§ function_output_vector

§ is_defined_per_particle

§ max_particle_index

§ min_particle_index

template<int dim>
class aspect::Particle::ParticlePDF< dim >