A class for refining the optimal transport potential using a softmax operation. More...

#include <SoftmaxRefinement.h>

Classes
struct	CopyData
	A struct to hold copy data for parallel assembly. More...

struct	ScratchData
	A struct to hold scratch data for parallel assembly. More...

Public Member Functions
void	set_distance_function (const std::function< double(const Point< spacedim > &, const Point< spacedim > &)> &dist)
	Sets the distance function to be used.

	SoftmaxRefinement (MPI_Comm mpi_comm, const DoFHandler< dim, spacedim > &dof_handler, const Mapping< dim, spacedim > &mapping, const FiniteElement< dim, spacedim > &fe, const LinearAlgebra::distributed::Vector< double > &source_density, unsigned int quadrature_order, double distance_threshold, bool use_log_sum_exp_trick=true)
	Constructor for the SoftmaxRefinement class.

Vector< double >	compute_refinement (const std::vector< Point< spacedim > > &target_points_fine, const Vector< double > &target_density_fine, const std::vector< Point< spacedim > > &target_points_coarse, const Vector< double > &target_density_coarse, const Vector< double > &potential_coarse, double regularization_param, int current_level, const std::vector< std::vector< std::vector< size_t > > > &child_indices)
	Computes the refined potential.

Private Types
using	IndexedPoint = std::pair< Point< spacedim >, std::size_t >

using	RTreeParams = boost::geometry::index::rstar< 8 >

using	RTree = boost::geometry::index::rtree< IndexedPoint, RTreeParams >

Private Member Functions
void	setup_rtree ()
	Sets up the R-tree.

std::vector< std::size_t >	find_nearest_target_points (const Point< spacedim > &query_point) const
	Finds the nearest target points to a query point.

void	local_assemble (const typename DoFHandler< dim, spacedim >::active_cell_iterator &cell, ScratchData &scratch_data, CopyData &copy_data)
	Assembles the local contributions to the refined potential.

bool	is_simplex_element () const
	Checks if the finite element is a simplex element.

Private Attributes
MPI_Comm	mpi_communicator
	The MPI communicator.

const unsigned int	n_mpi_processes
	The number of MPI processes.

const unsigned int	this_mpi_process
	The rank of the current MPI process.

ConditionalOStream	pcout
	A conditional output stream for parallel printing.

std::function< double(const Point< spacedim > &, const Point< spacedim > &)>	distance_function
	The distance function.

const DoFHandler< dim, spacedim > &	dof_handler
	The DoF handler for the source mesh.

const Mapping< dim, spacedim > &	mapping
	The mapping for the source mesh.

const FiniteElement< dim, spacedim > &	fe
	The finite element for the source mesh.

const LinearAlgebra::distributed::Vector< double > &	source_density
	The density of the source measure.

const unsigned int	quadrature_order
	The order of the quadrature rule to use for integration.

RTree	target_points_rtree
	An R-tree for fast spatial queries on the target points.

double	current_lambda {0.0}
	The current regularization parameter.

const double	current_distance_threshold
	The current distance threshold.

const bool	use_log_sum_exp_trick
	Whether to use the log-sum-exp trick.

const std::vector< Point< spacedim > > *	current_target_points_fine {nullptr}
	The current fine target points.

const Vector< double > *	current_target_density_fine {nullptr}
	The current fine target density.

const std::vector< Point< spacedim > > *	current_target_points_coarse {nullptr}
	The current coarse target points.

const Vector< double > *	current_target_density_coarse {nullptr}
	The current coarse target density.

const Vector< double > *	current_potential_coarse {nullptr}
	The current coarse potential.

const std::vector< std::vector< std::vector< size_t > > > *	current_child_indices {nullptr}
	The current child indices.

int	current_level {0}
	The current level.

Detailed Description

template<int dim, int spacedim = dim>
class SoftmaxRefinement< dim, spacedim >

A class for refining the optimal transport potential using a softmax operation.

This class implements a method for refining the optimal transport potential from a coarser level to a finer level in a multilevel scheme. It uses a softmax-like operation to distribute the potential from the coarse points to their children in the finer level.

Template Parameters

dim	The dimension of the source mesh.
spacedim	The dimension of the space the mesh is embedded in.

Definition at line 43 of file SoftmaxRefinement.h.

Member Typedef Documentation

◆ IndexedPoint

template<int dim, int spacedim = dim>

using SoftmaxRefinement< dim, spacedim >::IndexedPoint = std::pair<Point<spacedim>, std::size_t>

private

Definition at line 147 of file SoftmaxRefinement.h.

◆ RTreeParams

template<int dim, int spacedim = dim>

using SoftmaxRefinement< dim, spacedim >::RTreeParams = boost::geometry::index::rstar<8>

private

Definition at line 148 of file SoftmaxRefinement.h.

◆ RTree

template<int dim, int spacedim = dim>

using SoftmaxRefinement< dim, spacedim >::RTree = boost::geometry::index::rtree<IndexedPoint, RTreeParams>

private

Definition at line 149 of file SoftmaxRefinement.h.

Constructor & Destructor Documentation

◆ SoftmaxRefinement()

template<int dim, int spacedim>

SoftmaxRefinement< dim, spacedim >::SoftmaxRefinement	(	MPI_Comm	mpi_comm,
		const DoFHandler< dim, spacedim > &	dof_handler,
		const Mapping< dim, spacedim > &	mapping,
		const FiniteElement< dim, spacedim > &	fe,
		const LinearAlgebra::distributed::Vector< double > &	source_density,
		unsigned int	quadrature_order,
		double	distance_threshold,
		bool	use_log_sum_exp_trick = `true`
	)

Constructor for the SoftmaxRefinement class.

Parameters

mpi_comm	The MPI communicator.
dof_handler	The DoF handler for the source mesh.
mapping	The mapping for the source mesh.
fe	The finite element for the source mesh.
source_density	The density of the source measure.
quadrature_order	The order of the quadrature rule to use for integration.
distance_threshold	The distance threshold for the R-tree search.
use_log_sum_exp_trick	Whether to use the log-sum-exp trick for numerical stability.

Definition at line 5 of file SoftmaxRefinement.cc.

Member Function Documentation

◆ set_distance_function()

template<int dim, int spacedim = dim>

void SoftmaxRefinement< dim, spacedim >::set_distance_function ( const std::function< double(const Point< spacedim > &, const Point< spacedim > &)> & dist )

inline

Sets the distance function to be used.

Parameters

dist	The distance function.

Definition at line 49 of file SoftmaxRefinement.h.

◆ compute_refinement()

template<int dim, int spacedim>

Vector< double > SoftmaxRefinement< dim, spacedim >::compute_refinement	(	const std::vector< Point< spacedim > > &	target_points_fine,
		const Vector< double > &	target_density_fine,
		const std::vector< Point< spacedim > > &	target_points_coarse,
		const Vector< double > &	target_density_coarse,
		const Vector< double > &	potential_coarse,
		double	regularization_param,
		int	current_level,
		const std::vector< std::vector< std::vector< size_t > > > &	child_indices
	)

Computes the refined potential.

Parameters

target_points_fine	The points of the fine target measure.
target_density_fine	The weights of the fine target measure.
target_points_coarse	The points of the coarse target measure.
target_density_coarse	The weights of the coarse target measure.
potential_coarse	The potential at the coarse level.
regularization_param	The regularization parameter.
current_level	The current level in the multilevel hierarchy.
child_indices	The indices of the children of each coarse point.

Returns: The refined potential.

Definition at line 201 of file SoftmaxRefinement.cc.

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◆ setup_rtree()

template<int dim, int spacedim>

void SoftmaxRefinement< dim, spacedim >::setup_rtree ( )

private

Sets up the R-tree.

Definition at line 30 of file SoftmaxRefinement.cc.

◆ find_nearest_target_points()

template<int dim, int spacedim>

std::vector< std::size_t > SoftmaxRefinement< dim, spacedim >::find_nearest_target_points ( const Point< spacedim > & query_point ) const

private

Finds the nearest target points to a query point.

Parameters

query_point The query point.

Returns: A vector of indices of the nearest target points.

Definition at line 44 of file SoftmaxRefinement.cc.

◆ local_assemble()

template<int dim, int spacedim>

void SoftmaxRefinement< dim, spacedim >::local_assemble	(	const typename DoFHandler< dim, spacedim >::active_cell_iterator &	cell,
		ScratchData &	scratch_data,
		CopyData &	copy_data
	)

private

Assembles the local contributions to the refined potential.

Parameters

cell	The current cell.
scratch_data	The scratch data.
copy_data	The copy data.

Definition at line 62 of file SoftmaxRefinement.cc.

◆ is_simplex_element()

template<int dim, int spacedim = dim>

bool SoftmaxRefinement< dim, spacedim >::is_simplex_element ( ) const

inlineprivate

Checks if the finite element is a simplex element.

Definition at line 189 of file SoftmaxRefinement.h.

Member Data Documentation

◆ mpi_communicator

template<int dim, int spacedim = dim>

MPI_Comm SoftmaxRefinement< dim, spacedim >::mpi_communicator

private

The MPI communicator.

Definition at line 131 of file SoftmaxRefinement.h.

◆ n_mpi_processes

template<int dim, int spacedim = dim>

const unsigned int SoftmaxRefinement< dim, spacedim >::n_mpi_processes

private

The number of MPI processes.

Definition at line 132 of file SoftmaxRefinement.h.

◆ this_mpi_process

template<int dim, int spacedim = dim>

const unsigned int SoftmaxRefinement< dim, spacedim >::this_mpi_process

private

The rank of the current MPI process.

Definition at line 133 of file SoftmaxRefinement.h.

◆ pcout

template<int dim, int spacedim = dim>

ConditionalOStream SoftmaxRefinement< dim, spacedim >::pcout

private

A conditional output stream for parallel printing.

Definition at line 134 of file SoftmaxRefinement.h.

◆ distance_function

template<int dim, int spacedim = dim>

std::function<double(const Point<spacedim>&, const Point<spacedim>&)> SoftmaxRefinement< dim, spacedim >::distance_function

private

The distance function.

Definition at line 137 of file SoftmaxRefinement.h.

◆ dof_handler

template<int dim, int spacedim = dim>

const DoFHandler<dim, spacedim>& SoftmaxRefinement< dim, spacedim >::dof_handler

private

The DoF handler for the source mesh.

Definition at line 140 of file SoftmaxRefinement.h.

◆ mapping

template<int dim, int spacedim = dim>

const Mapping<dim, spacedim>& SoftmaxRefinement< dim, spacedim >::mapping

private

The mapping for the source mesh.

Definition at line 141 of file SoftmaxRefinement.h.

◆ fe

template<int dim, int spacedim = dim>

const FiniteElement<dim, spacedim>& SoftmaxRefinement< dim, spacedim >::fe

private

The finite element for the source mesh.

Definition at line 142 of file SoftmaxRefinement.h.

◆ source_density

template<int dim, int spacedim = dim>

const LinearAlgebra::distributed::Vector<double>& SoftmaxRefinement< dim, spacedim >::source_density

private

The density of the source measure.

Definition at line 143 of file SoftmaxRefinement.h.

◆ quadrature_order

template<int dim, int spacedim = dim>

const unsigned int SoftmaxRefinement< dim, spacedim >::quadrature_order

private

The order of the quadrature rule to use for integration.

Definition at line 144 of file SoftmaxRefinement.h.

◆ target_points_rtree

template<int dim, int spacedim = dim>

RTree SoftmaxRefinement< dim, spacedim >::target_points_rtree

private

An R-tree for fast spatial queries on the target points.

Definition at line 150 of file SoftmaxRefinement.h.

◆ current_lambda

template<int dim, int spacedim = dim>

double SoftmaxRefinement< dim, spacedim >::current_lambda {0.0}

private

The current regularization parameter.

Definition at line 153 of file SoftmaxRefinement.h.

◆ current_distance_threshold

template<int dim, int spacedim = dim>

const double SoftmaxRefinement< dim, spacedim >::current_distance_threshold

private

The current distance threshold.

Definition at line 154 of file SoftmaxRefinement.h.

◆ use_log_sum_exp_trick

template<int dim, int spacedim = dim>

const bool SoftmaxRefinement< dim, spacedim >::use_log_sum_exp_trick

private

Whether to use the log-sum-exp trick.

Definition at line 155 of file SoftmaxRefinement.h.

◆ current_target_points_fine

template<int dim, int spacedim = dim>

const std::vector<Point<spacedim> >* SoftmaxRefinement< dim, spacedim >::current_target_points_fine {nullptr}

private

The current fine target points.

Definition at line 156 of file SoftmaxRefinement.h.

◆ current_target_density_fine

template<int dim, int spacedim = dim>

const Vector<double>* SoftmaxRefinement< dim, spacedim >::current_target_density_fine {nullptr}

private

The current fine target density.

Definition at line 157 of file SoftmaxRefinement.h.

◆ current_target_points_coarse

template<int dim, int spacedim = dim>

const std::vector<Point<spacedim> >* SoftmaxRefinement< dim, spacedim >::current_target_points_coarse {nullptr}

private

The current coarse target points.

Definition at line 158 of file SoftmaxRefinement.h.

◆ current_target_density_coarse

template<int dim, int spacedim = dim>

const Vector<double>* SoftmaxRefinement< dim, spacedim >::current_target_density_coarse {nullptr}

private

The current coarse target density.

Definition at line 159 of file SoftmaxRefinement.h.

◆ current_potential_coarse

template<int dim, int spacedim = dim>

const Vector<double>* SoftmaxRefinement< dim, spacedim >::current_potential_coarse {nullptr}

private

The current coarse potential.

Definition at line 160 of file SoftmaxRefinement.h.

◆ current_child_indices

template<int dim, int spacedim = dim>

const std::vector<std::vector<std::vector<size_t> > >* SoftmaxRefinement< dim, spacedim >::current_child_indices {nullptr}

private

The current child indices.

Definition at line 161 of file SoftmaxRefinement.h.

◆ current_level

template<int dim, int spacedim = dim>

int SoftmaxRefinement< dim, spacedim >::current_level {0}

private

The current level.

Definition at line 162 of file SoftmaxRefinement.h.

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

include/SemiDiscreteOT/solvers/SoftmaxRefinement.h
src/solvers/SoftmaxRefinement.cc

Classes

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ IndexedPoint

◆ RTreeParams

◆ RTree

Constructor & Destructor Documentation

◆ SoftmaxRefinement()

Member Function Documentation

◆ set_distance_function()

◆ compute_refinement()

◆ setup_rtree()

◆ find_nearest_target_points()

◆ local_assemble()

◆ is_simplex_element()

Member Data Documentation

◆ mpi_communicator

◆ n_mpi_processes

◆ this_mpi_process

◆ pcout

◆ distance_function

◆ dof_handler

◆ mapping

◆ fe

◆ source_density

◆ quadrature_order

◆ target_points_rtree

◆ current_lambda

◆ current_distance_threshold

◆ use_log_sum_exp_trick

◆ current_target_points_fine

◆ current_target_density_fine

◆ current_target_points_coarse

◆ current_target_density_coarse

◆ current_potential_coarse

◆ current_child_indices

◆ current_level