Generalized Moving Least Squares (GMLS) More...

Detailed Description

Generalized Moving Least Squares (GMLS)

This class sets up a batch of GMLS problems from a given set of neighbor lists, target sites, and source sites. GMLS requires a target functional, reconstruction space, and sampling functional to be specified. For a given choice of reconstruction space and sampling functional, multiple targets can be generated with very little additional computation, which is why this class allows for multiple target functionals to be specified.

Definition at line 40 of file Compadre_GMLS.hpp.

#include <Compadre_GMLS.hpp>

Public Types
typedef PointConnections < Kokkos::View< double , layout_right > , Kokkos::View< double , layout_right > , NeighborLists< Kokkos::View < int * > > >	point_connections_type

typedef NeighborLists < Kokkos::View< int * > >	neighbor_lists_type

typedef Kokkos::View< double **, layout_right >	coordinates_type

Public Member Functions
Instantiation / Destruction
	GMLS (ReconstructionSpace reconstruction_space, const SamplingFunctional polynomial_sampling_strategy, const SamplingFunctional data_sampling_strategy, const int poly_order, const int dimensions, const DenseSolverType dense_solver_type, const ProblemType problem_type, const ConstraintType constraint_type, const int manifold_curvature_poly_order)
	Maximal constructor, not intended for users. More...

	GMLS (ReconstructionSpace reconstruction_space, const SamplingFunctional polynomial_sampling_strategy, const SamplingFunctional data_sampling_strategy, const int poly_order, const int dimensions=3, const std::string dense_solver_type=std::string("QR"), const std::string problem_type=std::string("STANDARD"), const std::string constraint_type=std::string("NO_CONSTRAINT"), const int manifold_curvature_poly_order=2)
	Maximal constructor, but with string arguments. More...

	GMLS (const int poly_order, const int dimensions=3, const std::string dense_solver_type=std::string("QR"), const std::string problem_type=std::string("STANDARD"), const std::string constraint_type=std::string("NO_CONSTRAINT"), const int manifold_curvature_poly_order=2)
	Constructor for the case when the data sampling functional does not match the polynomial sampling functional. More...

	GMLS (ReconstructionSpace reconstruction_space, SamplingFunctional dual_sampling_strategy, const int poly_order, const int dimensions=3, const std::string dense_solver_type=std::string("QR"), const std::string problem_type=std::string("STANDARD"), const std::string constraint_type=std::string("NO_CONSTRAINT"), const int manifold_curvature_poly_order=2)
	Constructor for the case when nonstandard sampling functionals or reconstruction spaces are to be used. More...

Accessors
Retrieve member variables through public member functions
host_managed_local_index_type	getPolynomialCoefficientsDomainRangeSize () const
	Returns (size of the basis used in instance's polynomial reconstruction) x (data input dimension) More...

int	getPolynomialCoefficientsSize () const
	Returns size of the basis used in instance's polynomial reconstruction. More...

host_managed_local_index_type	getPolynomialCoefficientsMemorySize () const
	Returns 2D array size in memory on which coefficients are stored. More...

int	getDimensions () const
	Dimension of the GMLS problem, set only at class instantiation. More...

int	getGlobalDimensions () const
	Dimension of the GMLS problem's point data (spatial description of points in ambient space), set only at class instantiation. More...

int	getLocalDimensions () const
	Local dimension of the GMLS problem (less than global dimension if on a manifold), set only at class instantiation. More...

DenseSolverType	getDenseSolverType () const
	Get dense solver type. More...

ProblemType	getProblemType () const
	Get problem type. More...

ConstraintType	getConstraintType () const
	Get constraint type. More...

int	getPolynomialOrder () const
	Get basis order used for reconstruction. More...

int	getCurvaturePolynomialOrder () const
	Get basis order used for curvature reconstruction. More...

WeightingFunctionType	getWeightingType () const
	Type for weighting kernel for GMLS problem. More...

WeightingFunctionType	getManifoldWeightingType () const
	Type for weighting kernel for curvature. More...

int	getWeightingParameter (const int index=0) const
	Get parameter for weighting kernel for GMLS problem. More...

int	getManifoldWeightingParameter (const int index=0) const
	Get parameter for weighting kernel for curvature. More...

int	getNumberOfQuadraturePoints () const
	Number of quadrature points. More...

int	getOrderOfQuadraturePoints () const
	Order of quadrature points. More...

int	getDimensionOfQuadraturePoints () const
	Dimensions of quadrature points. More...

std::string	getQuadratureType () const
	Type of quadrature points. More...

neighbor_lists_type *	getNeighborLists () const
	Get neighbor list accessor. More...

decltype(_pc)*	getPointConnections ()
	Get a view (device) of all point connection info. More...

neighbor_lists_type *	getAdditionalEvaluationIndices () const
	(OPTIONAL) Get additional evaluation sites neighbor list-like accessor More...

decltype(_additional_pc)*	getAdditionalPointConnections ()
	(OPTIONAL) Get a view (device) of all additional evaluation point connection info More...

decltype(_epsilons)*	getWindowSizes ()
	Get a view (device) of all window sizes. More...

decltype(_T)*	getTangentDirections ()
	Get a view (device) of all tangent direction bundles. More...

decltype(_ref_N)*	getReferenceNormalDirections ()
	Get a view (device) of all reference outward normal directions. More...

double	getTangentBundle (const int target_index, const int direction, const int component) const
	Get component of tangent or normal directions for manifold problems. More...

double	getReferenceNormalDirection (const int target_index, const int component) const
	Get component of tangent or normal directions for manifold problems. More...

decltype(_prestencil_weights)	getPrestencilWeights () const
	Get a view (device) of all rank 2 preprocessing tensors This is a rank 5 tensor that is able to provide data transformation into a form that GMLS is able to operate on. More...

decltype(_RHS)	getFullPolynomialCoefficientsBasis () const
	Get a view (device) of all polynomial coefficients basis. More...

SamplingFunctional	getPolynomialSamplingFunctional () const
	Get the polynomial sampling functional specified at instantiation. More...

SamplingFunctional	getDataSamplingFunctional () const
	Get the data sampling functional specified at instantiation (often the same as the polynomial sampling functional) More...

ReconstructionSpace	getReconstructionSpace () const
	Get the reconstruction space specified at instantiation. More...

double	getPreStencilWeight (SamplingFunctional sro, const int target_index, const int neighbor_index, bool for_target, const int output_component=0, const int input_component=0) const
	Returns a stencil to transform data from its existing state into the input expected for some sampling functionals. More...

decltype(_h_ss)*	getSolutionSetHost (bool alpha_validity_check=true)
	Get solution set on host. More...

decltype(_d_ss)*	getSolutionSetDevice (bool alpha_validity_check=true)
	Get solution set on device. More...

bool	containsValidAlphas () const
	Check if GMLS solution set contains valid alpha values (has generateAlphas been called) More...

const GMLSSolutionData	extractSolutionData () const
	Get GMLS solution data. More...

const GMLSBasisData	extractBasisData () const
	Get GMLS basis data. More...

Modifiers
Changed member variables through public member functions
void	resetCoefficientData ()

template<typename view_type_1 , typename view_type_2 , typename view_type_3 , typename view_type_4 >
void	setProblemData (view_type_1 neighbor_lists, view_type_2 source_coordinates, view_type_3 target_coordinates, view_type_4 epsilons)
	Sets basic problem data (neighbor lists, source coordinates, and target coordinates) More...

template<typename view_type_1 , typename view_type_2 , typename view_type_3 , typename view_type_4 >
void	setProblemData (view_type_1 cr_neighbor_lists, view_type_1 number_of_neighbors_list, view_type_2 source_coordinates, view_type_3 target_coordinates, view_type_4 epsilons)
	Sets basic problem data (neighbor lists data, number of neighbors list, source coordinates, and target coordinates) More...

template<typename view_type_1 , typename view_type_2 >
void	setAdditionalEvaluationSitesData (view_type_1 additional_evaluation_indices, view_type_2 additional_evaluation_coordinates)
	(OPTIONAL) Sets additional evaluation sites for each target site More...

template<typename view_type_1 , typename view_type_2 >
void	setAdditionalEvaluationSitesData (view_type_1 cr_additional_evaluation_indices, view_type_1 number_of_additional_evaluation_indices, view_type_2 additional_evaluation_coordinates)
	(OPTIONAL) Sets additional evaluation sites for each target site More...

template<typename view_type >
std::enable_if < view_type::rank==1 &&std::is_same < neighbor_lists_type::internal_view_type, view_type >::value==1, void > ::type	setNeighborLists (view_type neighbor_lists, view_type number_of_neighbors_list)
	Sets neighbor list information from compressed row neighborhood lists data (if same view_type). More...

template<typename view_type >
std::enable_if < view_type::rank==1 &&std::is_same < neighbor_lists_type::internal_view_type, view_type >::value==0, void > ::type	setNeighborLists (view_type neighbor_lists, view_type number_of_neighbors_list)
	Sets neighbor list information from compressed row neighborhood lists data (if different view_type). More...

template<typename view_type >
std::enable_if < view_type::rank==2, void > ::type	setNeighborLists (view_type neighbor_lists)
	Sets neighbor list information. More...

template<typename view_type >
void	setSourceSites (view_type source_coordinates)
	Sets source coordinate information. More...

template<typename view_type >
void	setSourceSites (coordinates_type source_coordinates)
	Sets source coordinate information. More...

template<typename view_type >
void	setTargetSites (view_type target_coordinates)
	Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists. More...

template<typename view_type >
void	setTargetSites (coordinates_type target_coordinates)
	Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists. More...

template<typename view_type >
void	setWindowSizes (view_type epsilons)
	Sets window sizes, also called the support of the kernel. More...

template<typename view_type >
void	setWindowSizes (decltype(_epsilons) epsilons)
	Sets window sizes, also called the support of the kernel (device) More...

template<typename view_type >
void	setTangentBundle (view_type tangent_directions)
	(OPTIONAL) Sets orthonormal tangent directions for reconstruction on a manifold. More...

template<typename view_type >
void	setReferenceOutwardNormalDirection (view_type outward_normal_directions, bool use_to_orient_surface=true)
	(OPTIONAL) Sets outward normal direction. More...

template<typename view_type >
void	setSourceExtraData (view_type extra_data)
	(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances. More...

template<typename view_type >
void	setSourceExtraData (decltype(_source_extra_data) extra_data)
	(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances. More...

template<typename view_type >
void	setTargetExtraData (view_type extra_data)
	(OPTIONAL) Sets extra data to be used by target operations in certain instances. More...

template<typename view_type >
void	setTargetExtraData (decltype(_target_extra_data) extra_data)
	(OPTIONAL) Sets extra data to be used by target operations in certain instances. More...

void	setDenseSolverType (const DenseSolverType dst)
	Set dense solver type type. More...

void	setConstraintType (const ConstraintType ct)
	Set constraint type. More...

void	setWeightingType (const std::string &wt)
	Type for weighting kernel for GMLS problem. More...

void	setWeightingType (const WeightingFunctionType wt)
	Type for weighting kernel for GMLS problem. More...

void	setCurvatureWeightingType (const std::string &wt)
	Type for weighting kernel for curvature. More...

void	setCurvatureWeightingType (const WeightingFunctionType wt)
	Type for weighting kernel for curvature. More...

void	setPolynomialOrder (const int poly_order)
	Sets basis order to be used when reconstructing any function. More...

void	setCurvaturePolynomialOrder (const int curvature_poly_order)
	Sets basis order to be used when reconstruction curvature. More...

void	setWeightingParameter (int wp, int index=0)
	Parameter for weighting kernel for GMLS problem index = 0 sets p paramater for weighting kernel index = 1 sets n paramater for weighting kernel. More...

void	setCurvatureWeightingParameter (int wp, int index=0)
	Parameter for weighting kernel for curvature index = 0 sets p paramater for weighting kernel index = 1 sets n paramater for weighting kernel. More...

void	setOrderOfQuadraturePoints (int order)
	Number quadrature points to use. More...

void	setDimensionOfQuadraturePoints (int dim)
	Dimensions of quadrature points to use. More...

void	setQuadratureType (std::string quadrature_type)
	Type of quadrature points. More...

void	addTargets (TargetOperation lro)
	Adds a target to the vector of target functional to be applied to the reconstruction. More...

void	addTargets (std::vector< TargetOperation > lro)
	Adds a vector of target functionals to the vector of target functionals already to be applied to the reconstruction. More...

void	clearTargets ()
	Empties the vector of target functionals to apply to the reconstruction. More...

bool	verifyPointConnections (bool assert_valid=false)
	Verify whether _pc is valid. More...

bool	verifyAdditionalPointConnections (bool assert_valid=false)
	Verify whether _additional_pc is valid. More...

void	generatePolynomialCoefficients (const int number_of_batches=1, const bool keep_coefficients=false, const bool clear_cache=true)
	Generates polynomial coefficients by setting up and solving least squares problems Sets up the batch of GMLS problems to be solved for. Provides alpha values that can later be contracted against data or degrees of freedom to form a global linear system. More...

void	generateAlphas (const int number_of_batches=1, const bool keep_coefficients=false, const bool clear_cache=true)
	Meant to calculate target operations and apply the evaluations to the previously constructed polynomial coefficients. But now that is inside of generatePolynomialCoefficients because it must be to handle number_of_batches>1. Effectively, this just calls generatePolynomialCoefficients. More...

Static Public Member Functions
Public Utility
static KOKKOS_INLINE_FUNCTION int	getNP (const int m, const int dimension=3, const ReconstructionSpace r_space=ReconstructionSpace::ScalarTaylorPolynomial)
	Returns size of the basis for a given polynomial order and dimension General to dimension 1..3 and polynomial order m The divfree options will return the divergence-free basis if true. More...

static KOKKOS_INLINE_FUNCTION int	getNN (const int m, const int dimension=3, const ReconstructionSpace r_space=ReconstructionSpace::ScalarTaylorPolynomial)
	Returns number of neighbors needed for unisolvency for a given basis order and dimension. More...

static KOKKOS_INLINE_FUNCTION double	Wab (const double r, const double h, const WeightingFunctionType &weighting_type, const int p, const int n)
	Evaluates the weighting kernel. More...

Private Member Functions
Private Modifiers
Private function because information lives on the device
template<typename view_type >
void	setAuxiliaryEvaluationCoordinates (view_type evaluation_coordinates)
	(OPTIONAL) Sets additional points for evaluation of target operation on polynomial reconstruction. More...

template<typename view_type >
void	setAuxiliaryEvaluationCoordinates (coordinates_type evaluation_coordinates)
	(OPTIONAL) Sets additional points for evaluation of target operation on polynomial reconstruction. More...

template<typename view_type >
std::enable_if < view_type::rank==1 &&std::is_same < neighbor_lists_type::internal_view_type, view_type >::value==1, void > ::type	setAuxiliaryEvaluationIndicesLists (view_type additional_evaluation_indices, view_type number_of_neighbors_list)
	(OPTIONAL) Sets the additional target evaluation indices list information from compressed row format (if same view_type) More...

template<typename view_type >
std::enable_if < view_type::rank==1 &&std::is_same < neighbor_lists_type::internal_view_type, view_type >::value==0, void > ::type	setAuxiliaryEvaluationIndicesLists (view_type additional_evaluation_indices, view_type number_of_neighbors_list)
	(OPTIONAL) Sets the additional target evaluation indices list information from compressed row format (if different view_type) More...

template<typename view_type >
std::enable_if < view_type::rank==2, void > ::type	setAuxiliaryEvaluationIndicesLists (view_type additional_evaluation_indices)
	(OPTIONAL) Sets the additional target evaluation indices list information. More...

Static Private Member Functions
Private Utility
static DenseSolverType	parseSolverType (const std::string &dense_solver_type)
	Parses a string to determine solver type. More...

static ProblemType	parseProblemType (const std::string &problem_type)
	Parses a string to determine problem type. More...

static ConstraintType	parseConstraintType (const std::string &constraint_type)
	Parses a string to determine constraint type. More...

Private Attributes
Kokkos::View< double * >	_w
	contains weights for all problems More...

Kokkos::View< double * >	_P
	P*sqrt(w) matrix for all problems. More...

Kokkos::View< double * >	_RHS
	sqrt(w)*Identity matrix for all problems, later holds polynomial coefficients for all problems More...

Kokkos::View< double * >	_Z
	stores evaluations of targets applied to basis More...

Kokkos::View< double * >	_T
	Rank 3 tensor for high order approximation of tangent vectors for all problems. More...

Kokkos::View< double * >	_ref_N
	Rank 2 tensor for high order approximation of tangent vectors for all problems. More...

Kokkos::View< double * > ::HostMirror	_host_T
	tangent vectors information (host) More...

Kokkos::View< double * > ::HostMirror	_host_ref_N
	reference outward normal vectors information (host) More...

Kokkos::View< double * >	_manifold_metric_tensor_inverse
	metric tensor inverse for all problems More...

Kokkos::View< double * >	_manifold_curvature_coefficients
	curvature polynomial coefficients for all problems More...

Kokkos::View< double * >	_manifold_curvature_gradient
	_dimension-1 gradient values for curvature for all problems More...

Kokkos::View< double **, layout_right >	_source_extra_data
	Extra data available to basis functions (optional) More...

Kokkos::View< double **, layout_right >	_target_extra_data
	Extra data available to target operations (optional) More...

point_connections_type	_pc
	connections between points and neighbors More...

Kokkos::View< double * >	_epsilons
	h supports determined through neighbor search (device) More...

Kokkos::View< double *****, layout_right >	_prestencil_weights
	generated weights for nontraditional samples required to transform data into expected sampling functional form (device). More...

Kokkos::View< const double *****, layout_right > ::HostMirror	_host_prestencil_weights
	generated weights for nontraditional samples required to transform data into expected sampling functional form (host) More...

point_connections_type	_additional_pc
	(OPTIONAL) connections between additional points and neighbors More...

SolutionSet< host_memory_space >	_h_ss
	Solution Set (contains all alpha values from solution and alpha layout methods) More...

SolutionSet< device_memory_space >	_d_ss

int	_poly_order
	order of basis for polynomial reconstruction More...

int	_curvature_poly_order
	order of basis for curvature reconstruction More...

int	_NP
	dimension of basis for polynomial reconstruction More...

int	_global_dimensions
	spatial dimension of the points, set at class instantiation only More...

int	_local_dimensions
	dimension of the problem, set at class instantiation only. For manifolds, generally _global_dimensions-1 More...

int	_dimensions
	dimension of the problem, set at class instantiation only More...

ReconstructionSpace	_reconstruction_space
	reconstruction space for GMLS problems, set at GMLS class instantiation More...

int	_reconstruction_space_rank
	actual rank of reconstruction basis More...

DenseSolverType	_dense_solver_type
	solver type for GMLS problem - can be QR, SVD or LU More...

ProblemType	_problem_type
	problem type for GMLS problem, can also be set to STANDARD for normal or MANIFOLD for manifold problems NOTE: can only be set at object instantiation More...

ConstraintType	_constraint_type
	constraint type for GMLS problem More...

SamplingFunctional	_polynomial_sampling_functional
	polynomial sampling functional used to construct P matrix, set at GMLS class instantiation NOTE: can only be set at object instantiation More...

SamplingFunctional	_data_sampling_functional
	generally the same as _polynomial_sampling_functional, but can differ if specified at More...

Kokkos::View< TargetOperation * >	_curvature_support_operations
	vector containing target functionals to be applied for curvature More...

Kokkos::View< TargetOperation * >	_operations
	vector containing target functionals to be applied for reconstruction problem (device) More...

Kokkos::View< TargetOperation * > ::HostMirror	_host_operations
	vector containing target functionals to be applied for reconstruction problem (host) More...

WeightingFunctionType	_weighting_type
	weighting kernel type for GMLS More...

WeightingFunctionType	_curvature_weighting_type
	weighting kernel type for curvature problem More...

int	_weighting_p
	first parameter to be used for weighting kernel More...

int	_weighting_n
	second parameter to be used for weighting kernel More...

int	_curvature_weighting_p
	first parameter to be used for weighting kernel for curvature More...

int	_curvature_weighting_n
	second parameter to be used for weighting kernel for curvature More...

int	_basis_multiplier
	dimension of the reconstructed function e.g. More...

int	_sampling_multiplier
	actual dimension of the sampling functional e.g. More...

int	_data_sampling_multiplier
	effective dimension of the data sampling functional e.g. More...

bool	_orthonormal_tangent_space_provided
	whether or not the orthonormal tangent directions were provided by the user. More...

bool	_reference_outward_normal_direction_provided
	whether or not the reference outward normal directions were provided by the user. More...

bool	_use_reference_outward_normal_direction_provided_to_orient_surface
	whether or not to use reference outward normal directions to orient the surface in a manifold problem. More...

bool	_entire_batch_computed_at_once
	whether entire calculation was computed at once the alternative is that it was broken up over many smaller groups, in which case this is false, and so the _RHS matrix can not be stored or requested More...

bool	_store_PTWP_inv_PTW
	whether polynomial coefficients were requested to be stored (in a state not yet applied to data) More...

int	_initial_index_for_batch
	initial index for current batch More...

ParallelManager	_pm
	determines scratch level spaces and is used to call kernels More...

int	_order_of_quadrature_points
	order of exact polynomial integration for quadrature rule More...

int	_dimension_of_quadrature_points
	dimension of quadrature rule More...

std::string	_quadrature_type
	quadrature rule type More...

Quadrature	_qm
	manages and calculates quadrature More...

Friends
class	Evaluator

Member Typedef Documentation

typedef Kokkos::View<double**, layout_right> Compadre::GMLS::coordinates_type

Definition at line 53 of file Compadre_GMLS.hpp.

typedef NeighborLists<Kokkos::View<int*> > Compadre::GMLS::neighbor_lists_type

Definition at line 51 of file Compadre_GMLS.hpp.

typedef PointConnections<Kokkos::View<double**, layout_right>, Kokkos::View<double**, layout_right>, NeighborLists<Kokkos::View<int*> > > Compadre::GMLS::point_connections_type

Definition at line 49 of file Compadre_GMLS.hpp.

Constructor & Destructor Documentation

Compadre::GMLS::GMLS	(	ReconstructionSpace	reconstruction_space,
		const SamplingFunctional	polynomial_sampling_strategy,
		const SamplingFunctional	data_sampling_strategy,
		const int	poly_order,
		const int	dimensions,
		const DenseSolverType	dense_solver_type,
		const ProblemType	problem_type,
		const ConstraintType	constraint_type,
		const int	manifold_curvature_poly_order
	)

inline

Maximal constructor, not intended for users.

Definition at line 389 of file Compadre_GMLS.hpp.

Compadre::GMLS::GMLS	(	ReconstructionSpace	reconstruction_space,
		const SamplingFunctional	polynomial_sampling_strategy,
		const SamplingFunctional	data_sampling_strategy,
		const int	poly_order,
		const int	dimensions = `3`,
		const std::string	dense_solver_type = `std::string("QR")`,
		const std::string	problem_type = `std::string("STANDARD")`,
		const std::string	constraint_type = `std::string("NO_CONSTRAINT")`,
		const int	manifold_curvature_poly_order = `2`
	)

inline

Maximal constructor, but with string arguments.

Definition at line 468 of file Compadre_GMLS.hpp.

Compadre::GMLS::GMLS	(	const int	poly_order,
		const int	dimensions = `3`,
		const std::string	dense_solver_type = `std::string("QR")`,
		const std::string	problem_type = `std::string("STANDARD")`,
		const std::string	constraint_type = `std::string("NO_CONSTRAINT")`,
		const int	manifold_curvature_poly_order = `2`
	)

inline

Constructor for the case when the data sampling functional does not match the polynomial sampling functional.

Only case anticipated is staggered Laplacian.

Definition at line 481 of file Compadre_GMLS.hpp.

Compadre::GMLS::GMLS	(	ReconstructionSpace	reconstruction_space,
		SamplingFunctional	dual_sampling_strategy,
		const int	poly_order,
		const int	dimensions = `3`,
		const std::string	dense_solver_type = `std::string("QR")`,
		const std::string	problem_type = `std::string("STANDARD")`,
		const std::string	constraint_type = `std::string("NO_CONSTRAINT")`,
		const int	manifold_curvature_poly_order = `2`
	)

inline

Constructor for the case when nonstandard sampling functionals or reconstruction spaces are to be used.

Reconstruction space and sampling strategy can only be set at instantiation.

Definition at line 491 of file Compadre_GMLS.hpp.

Member Function Documentation

void Compadre::GMLS::addTargets ( TargetOperation lro )

inline

Adds a target to the vector of target functional to be applied to the reconstruction.

Definition at line 1286 of file Compadre_GMLS.hpp.

void Compadre::GMLS::addTargets ( std::vector< TargetOperation > lro )

inline

Adds a vector of target functionals to the vector of target functionals already to be applied to the reconstruction.

Definition at line 1292 of file Compadre_GMLS.hpp.

void Compadre::GMLS::clearTargets ( )

inline

Empties the vector of target functionals to apply to the reconstruction.

Definition at line 1298 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::containsValidAlphas ( ) const

inline

Check if GMLS solution set contains valid alpha values (has generateAlphas been called)

Definition at line 824 of file Compadre_GMLS.hpp.

const GMLSBasisData Compadre::GMLS::extractBasisData ( ) const

Get GMLS basis data.

Definition at line 529 of file Compadre_GMLS.cpp.

const GMLSSolutionData Compadre::GMLS::extractSolutionData ( ) const

Get GMLS solution data.

Definition at line 481 of file Compadre_GMLS.cpp.

void Compadre::GMLS::generateAlphas	(	const int	number_of_batches = `1`,
		const bool	keep_coefficients = `false`,
		const bool	clear_cache = `true`
	)

Meant to calculate target operations and apply the evaluations to the previously constructed polynomial coefficients. But now that is inside of generatePolynomialCoefficients because it must be to handle number_of_batches>1. Effectively, this just calls generatePolynomialCoefficients.

Parameters

number_of_batches	[in] - how many batches to break up the total workload into (for storage)
keep_coefficients	[in] - whether to store (P^T W P)^-1 * P^T * W
clear_cache	[in] - clear whatever temporary memory was used for calculations that keep_coefficients hasn't indicated needs to be saved

clear_cache should be false to be used for debugging as it will leave all data structures used to compute the solution intact. If clear_cache is set true and keep_coefficients is true, it will allow the polynomial coefficients to persist after calculation.

Definition at line 475 of file Compadre_GMLS.cpp.

void Compadre::GMLS::generatePolynomialCoefficients	(	const int	number_of_batches = `1`,
		const bool	keep_coefficients = `false`,
		const bool	clear_cache = `true`
	)

Generates polynomial coefficients by setting up and solving least squares problems Sets up the batch of GMLS problems to be solved for. Provides alpha values that can later be contracted against data or degrees of freedom to form a global linear system.

Parameters

number_of_batches	[in] - how many batches to break up the total workload into (for storage)
keep_coefficients	[in] - whether to store (P^T W P)^-1 * P^T * W
clear_cache	[in] - clear whatever temporary memory was used for calculations that keep_coefficients hasn't indicated needs to be saved

clear_cache should be false to be used for debugging as it will leave all data structures used to compute the solution intact. If clear_cache is set true and keep_coefficients is true, it will allow the polynomial coefficients to persist after calculation.

Definition at line 14 of file Compadre_GMLS.cpp.

neighbor_lists_type* Compadre::GMLS::getAdditionalEvaluationIndices ( ) const

inline

(OPTIONAL) Get additional evaluation sites neighbor list-like accessor

Definition at line 706 of file Compadre_GMLS.hpp.

decltype(_additional_pc) * Compadre::GMLS::getAdditionalPointConnections ( )

inline

(OPTIONAL) Get a view (device) of all additional evaluation point connection info

Definition at line 711 of file Compadre_GMLS.hpp.

ConstraintType Compadre::GMLS::getConstraintType ( ) const

inline

Get constraint type.

Definition at line 653 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getCurvaturePolynomialOrder ( ) const

inline

Get basis order used for curvature reconstruction.

Definition at line 659 of file Compadre_GMLS.hpp.

SamplingFunctional Compadre::GMLS::getDataSamplingFunctional ( ) const

inline

Get the data sampling functional specified at instantiation (often the same as the polynomial sampling functional)

Definition at line 775 of file Compadre_GMLS.hpp.

DenseSolverType Compadre::GMLS::getDenseSolverType ( ) const

inline

Get dense solver type.

Definition at line 647 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getDimensionOfQuadraturePoints ( ) const

inline

Dimensions of quadrature points.

Definition at line 692 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getDimensions ( ) const

inline

Dimension of the GMLS problem, set only at class instantiation.

Definition at line 638 of file Compadre_GMLS.hpp.

decltype(_RHS) Compadre::GMLS::getFullPolynomialCoefficientsBasis ( ) const

inline

Get a view (device) of all polynomial coefficients basis.

Definition at line 759 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getGlobalDimensions ( ) const

inline

Dimension of the GMLS problem's point data (spatial description of points in ambient space), set only at class instantiation.

Definition at line 641 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getLocalDimensions ( ) const

inline

Local dimension of the GMLS problem (less than global dimension if on a manifold), set only at class instantiation.

Definition at line 644 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getManifoldWeightingParameter ( const int index = 0 ) const

inline

Get parameter for weighting kernel for curvature.

Definition at line 677 of file Compadre_GMLS.hpp.

WeightingFunctionType Compadre::GMLS::getManifoldWeightingType ( ) const

inline

Type for weighting kernel for curvature.

Definition at line 665 of file Compadre_GMLS.hpp.

neighbor_lists_type* Compadre::GMLS::getNeighborLists ( ) const

inline

Get neighbor list accessor.

Definition at line 698 of file Compadre_GMLS.hpp.

static KOKKOS_INLINE_FUNCTION int Compadre::GMLS::getNN	(	const int	m,
		const int	dimension = `3`,
		const ReconstructionSpace	r_space = `ReconstructionSpace::ScalarTaylorPolynomial`
	)

inlinestatic

Returns number of neighbors needed for unisolvency for a given basis order and dimension.

Definition at line 524 of file Compadre_GMLS.hpp.

static KOKKOS_INLINE_FUNCTION int Compadre::GMLS::getNP	(	const int	m,
		const int	dimension = `3`,
		const ReconstructionSpace	r_space = `ReconstructionSpace::ScalarTaylorPolynomial`
	)

inlinestatic

Returns size of the basis for a given polynomial order and dimension General to dimension 1..3 and polynomial order m The divfree options will return the divergence-free basis if true.

Examples:: GMLS Tutorial, and Manifold GMLS Tutorial.

Definition at line 512 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getNumberOfQuadraturePoints ( ) const

inline

Number of quadrature points.

Definition at line 686 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getOrderOfQuadraturePoints ( ) const

inline

Order of quadrature points.

Definition at line 689 of file Compadre_GMLS.hpp.

decltype(_pc) * Compadre::GMLS::getPointConnections ( )

inline

Get a view (device) of all point connection info.

Definition at line 703 of file Compadre_GMLS.hpp.

host_managed_local_index_type Compadre::GMLS::getPolynomialCoefficientsDomainRangeSize ( ) const

inline

Returns (size of the basis used in instance's polynomial reconstruction) x (data input dimension)

Definition at line 608 of file Compadre_GMLS.hpp.

host_managed_local_index_type Compadre::GMLS::getPolynomialCoefficientsMemorySize ( ) const

inline

Returns 2D array size in memory on which coefficients are stored.

Definition at line 622 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getPolynomialCoefficientsSize ( ) const

inline

Returns size of the basis used in instance's polynomial reconstruction.

Definition at line 616 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getPolynomialOrder ( ) const

inline

Get basis order used for reconstruction.

Definition at line 656 of file Compadre_GMLS.hpp.

SamplingFunctional Compadre::GMLS::getPolynomialSamplingFunctional ( ) const

inline

Get the polynomial sampling functional specified at instantiation.

Definition at line 772 of file Compadre_GMLS.hpp.

double Compadre::GMLS::getPreStencilWeight	(	SamplingFunctional	sro,
		const int	target_index,
		const int	neighbor_index,
		bool	for_target,
		const int	output_component = `0`,
		const int	input_component = `0`
	)		const

inline

Returns a stencil to transform data from its existing state into the input expected for some sampling functionals.

Definition at line 782 of file Compadre_GMLS.hpp.

decltype(_prestencil_weights) Compadre::GMLS::getPrestencilWeights ( ) const

inline

Get a view (device) of all rank 2 preprocessing tensors This is a rank 5 tensor that is able to provide data transformation into a form that GMLS is able to operate on.

The ranks are as follows:

1 - Either size 2 if it operates on the target site and neighbor site (staggered schemes) or 1 if it operates only on the neighbor sites (almost every scheme)

2 - If the data transform varies with each target site (but could be the same for each neighbor of that target site), then this is the number of target sites

3 - If the data transform varies with each neighbor of each target site, then this is the number of neighbors for each respective target (max number of neighbors for all target sites is its uniform size)

4 - Data transform resulting in rank 1 data for the GMLS operator will have size _local_dimensions, otherwise 1

5 - Data transform taking in rank 1 data will have size _global_dimensions, otherwise 1

Definition at line 754 of file Compadre_GMLS.hpp.

ProblemType Compadre::GMLS::getProblemType ( ) const

inline

Get problem type.

Definition at line 650 of file Compadre_GMLS.hpp.

std::string Compadre::GMLS::getQuadratureType ( ) const

inline

Type of quadrature points.

Definition at line 695 of file Compadre_GMLS.hpp.

ReconstructionSpace Compadre::GMLS::getReconstructionSpace ( ) const

inline

Get the reconstruction space specified at instantiation.

Definition at line 778 of file Compadre_GMLS.hpp.

double Compadre::GMLS::getReferenceNormalDirection	(	const int	target_index,
		const int	component
	)		const

inline

Get component of tangent or normal directions for manifold problems.

Definition at line 732 of file Compadre_GMLS.hpp.

decltype(_ref_N) * Compadre::GMLS::getReferenceNormalDirections ( )

inline

Get a view (device) of all reference outward normal directions.

Definition at line 720 of file Compadre_GMLS.hpp.

decltype(_d_ss) * Compadre::GMLS::getSolutionSetDevice ( bool alpha_validity_check = true )

inline

Get solution set on device.

Definition at line 817 of file Compadre_GMLS.hpp.

decltype(_h_ss) * Compadre::GMLS::getSolutionSetHost ( bool alpha_validity_check = true )

inline

Get solution set on host.

Definition at line 805 of file Compadre_GMLS.hpp.

double Compadre::GMLS::getTangentBundle	(	const int	target_index,
		const int	direction,
		const int	component
	)		const

inline

Get component of tangent or normal directions for manifold problems.

Definition at line 723 of file Compadre_GMLS.hpp.

decltype(_T) * Compadre::GMLS::getTangentDirections ( )

inline

Get a view (device) of all tangent direction bundles.

Definition at line 717 of file Compadre_GMLS.hpp.

int Compadre::GMLS::getWeightingParameter ( const int index = 0 ) const

inline

Get parameter for weighting kernel for GMLS problem.

Definition at line 668 of file Compadre_GMLS.hpp.

WeightingFunctionType Compadre::GMLS::getWeightingType ( ) const

inline

Type for weighting kernel for GMLS problem.

Definition at line 662 of file Compadre_GMLS.hpp.

decltype(_epsilons) * Compadre::GMLS::getWindowSizes ( )

inline

Get a view (device) of all window sizes.

Definition at line 714 of file Compadre_GMLS.hpp.

static ConstraintType Compadre::GMLS::parseConstraintType ( const std::string & constraint_type )

inlinestaticprivate

Parses a string to determine constraint type.

Definition at line 367 of file Compadre_GMLS.hpp.

static ProblemType Compadre::GMLS::parseProblemType ( const std::string & problem_type )

inlinestaticprivate

Parses a string to determine problem type.

Definition at line 354 of file Compadre_GMLS.hpp.

static DenseSolverType Compadre::GMLS::parseSolverType ( const std::string & dense_solver_type )

inlinestaticprivate

Parses a string to determine solver type.

Definition at line 343 of file Compadre_GMLS.hpp.

void Compadre::GMLS::resetCoefficientData ( )

inline

Definition at line 840 of file Compadre_GMLS.hpp.

template<typename view_type_1 , typename view_type_2 >

void Compadre::GMLS::setAdditionalEvaluationSitesData	(	view_type_1	additional_evaluation_indices,
		view_type_2	additional_evaluation_coordinates
	)

inline

(OPTIONAL) Sets additional evaluation sites for each target site

Definition at line 876 of file Compadre_GMLS.hpp.

template<typename view_type_1 , typename view_type_2 >

void Compadre::GMLS::setAdditionalEvaluationSitesData	(	view_type_1	cr_additional_evaluation_indices,
		view_type_1	number_of_additional_evaluation_indices,
		view_type_2	additional_evaluation_coordinates
	)

inline

(OPTIONAL) Sets additional evaluation sites for each target site

Definition at line 885 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setAuxiliaryEvaluationCoordinates ( view_type evaluation_coordinates )

inlineprivate

(OPTIONAL) Sets additional points for evaluation of target operation on polynomial reconstruction.

If this is never called, then the target sites are the only locations where the target operations will be evaluated and applied to polynomial reconstructions.

Definition at line 257 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setAuxiliaryEvaluationCoordinates ( coordinates_type evaluation_coordinates )

inlineprivate

(OPTIONAL) Sets additional points for evaluation of target operation on polynomial reconstruction.

If this is never called, then the target sites are the only locations where the target operations will be evaluated and applied to polynomial reconstructions. (device)

Definition at line 287 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==1&&std::is_same<neighbor_lists_type::internal_view_type,view_type>::value==1, void>::type Compadre::GMLS::setAuxiliaryEvaluationIndicesLists	(	view_type	additional_evaluation_indices,
		view_type	number_of_neighbors_list
	)

inlineprivate

(OPTIONAL) Sets the additional target evaluation indices list information from compressed row format (if same view_type)

Definition at line 296 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==1&&std::is_same<neighbor_lists_type::internal_view_type,view_type>::value==0, void>::type Compadre::GMLS::setAuxiliaryEvaluationIndicesLists	(	view_type	additional_evaluation_indices,
		view_type	number_of_neighbors_list
	)

inlineprivate

(OPTIONAL) Sets the additional target evaluation indices list information from compressed row format (if different view_type)

Definition at line 308 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==2, void>::type Compadre::GMLS::setAuxiliaryEvaluationIndicesLists ( view_type additional_evaluation_indices )

inlineprivate

(OPTIONAL) Sets the additional target evaluation indices list information.

Should be # targets x maximum number of indices evaluation indices for any target + 1. first entry in every row should be the number of indices for the corresponding target.

Definition at line 326 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setConstraintType ( const ConstraintType ct )

inline

Set constraint type.

Definition at line 1165 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setCurvaturePolynomialOrder ( const int curvature_poly_order )

inline

Sets basis order to be used when reconstruction curvature.

Definition at line 1237 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setCurvatureWeightingParameter	(	int	wp,
		int	index = `0`
	)

inline

Parameter for weighting kernel for curvature index = 0 sets p paramater for weighting kernel index = 1 sets n paramater for weighting kernel.

Definition at line 1258 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setCurvatureWeightingType ( const std::string & wt )

inline

Type for weighting kernel for curvature.

Definition at line 1200 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setCurvatureWeightingType ( const WeightingFunctionType wt )

inline

Type for weighting kernel for curvature.

Definition at line 1223 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setDenseSolverType ( const DenseSolverType dst )

inline

Set dense solver type type.

Definition at line 1159 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setDimensionOfQuadraturePoints ( int dim )

inline

Dimensions of quadrature points to use.

Definition at line 1274 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==1&&std::is_same<neighbor_lists_type::internal_view_type,view_type>::value==1, void>::type Compadre::GMLS::setNeighborLists	(	view_type	neighbor_lists,
		view_type	number_of_neighbors_list
	)

inline

Sets neighbor list information from compressed row neighborhood lists data (if same view_type).

Definition at line 897 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==1&&std::is_same<neighbor_lists_type::internal_view_type,view_type>::value==0, void>::type Compadre::GMLS::setNeighborLists	(	view_type	neighbor_lists,
		view_type	number_of_neighbors_list
	)

inline

Sets neighbor list information from compressed row neighborhood lists data (if different view_type).

Definition at line 907 of file Compadre_GMLS.hpp.

template<typename view_type >

std::enable_if<view_type::rank==2, void>::type Compadre::GMLS::setNeighborLists ( view_type neighbor_lists )

inline

Sets neighbor list information.

Should be # targets x maximum number of neighbors for any target + 1. first entry in ever row should be the number of neighbors for the corresponding target.

Definition at line 923 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setOrderOfQuadraturePoints ( int order )

inline

Number quadrature points to use.

Definition at line 1268 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setPolynomialOrder ( const int poly_order )

inline

Sets basis order to be used when reconstructing any function.

Definition at line 1229 of file Compadre_GMLS.hpp.

template<typename view_type_1 , typename view_type_2 , typename view_type_3 , typename view_type_4 >

void Compadre::GMLS::setProblemData	(	view_type_1	neighbor_lists,
		view_type_2	source_coordinates,
		view_type_3	target_coordinates,
		view_type_4	epsilons
	)

inline

Sets basic problem data (neighbor lists, source coordinates, and target coordinates)

Definition at line 849 of file Compadre_GMLS.hpp.

template<typename view_type_1 , typename view_type_2 , typename view_type_3 , typename view_type_4 >

void Compadre::GMLS::setProblemData	(	view_type_1	cr_neighbor_lists,
		view_type_1	number_of_neighbors_list,
		view_type_2	source_coordinates,
		view_type_3	target_coordinates,
		view_type_4	epsilons
	)

inline

Sets basic problem data (neighbor lists data, number of neighbors list, source coordinates, and target coordinates)

Definition at line 862 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setQuadratureType ( std::string quadrature_type )

inline

Type of quadrature points.

Definition at line 1280 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setReferenceOutwardNormalDirection	(	view_type	outward_normal_directions,
		bool	use_to_orient_surface = `true`
	)

inline

(OPTIONAL) Sets outward normal direction.

For manifolds this may be used for orienting surface. It is also accessible for sampling operators that require a normal direction.

Definition at line 1085 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setSourceExtraData ( view_type extra_data )

inline

(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances.

Definition at line 1113 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setSourceExtraData ( decltype(_source_extra_data) extra_data )

inline

(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances.

(device)

Definition at line 1128 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setSourceSites ( view_type source_coordinates )

inline

Sets source coordinate information.

Rows of this 2D-array should correspond to neighbor IDs contained in the entries of the neighbor lists 2D array.

Definition at line 933 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setSourceSites ( coordinates_type source_coordinates )

inline

Sets source coordinate information.

Rows of this 2D-array should correspond to neighbor IDs contained in the entries of the neighbor lists 2D array.

Definition at line 962 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setTangentBundle ( view_type tangent_directions )

inline

(OPTIONAL) Sets orthonormal tangent directions for reconstruction on a manifold.

The first rank of this 2D array corresponds to the target indices, i.e., rows of the neighbor lists 2D array. The second rank is the ordinal of the tangent direction (spatial dimensions-1 are tangent, last one is normal), and the third rank is indices into the spatial dimension.

Definition at line 1048 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setTargetExtraData ( view_type extra_data )

inline

(OPTIONAL) Sets extra data to be used by target operations in certain instances.

Definition at line 1137 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setTargetExtraData ( decltype(_target_extra_data) extra_data )

inline

(OPTIONAL) Sets extra data to be used by target operations in certain instances.

(device)

Definition at line 1152 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setTargetSites ( view_type target_coordinates )

inline

Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists.

Definition at line 970 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setTargetSites ( coordinates_type target_coordinates )

inline

Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists.

Definition at line 1007 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setWeightingParameter	(	int	wp,
		int	index = `0`
	)

inline

Parameter for weighting kernel for GMLS problem index = 0 sets p paramater for weighting kernel index = 1 sets n paramater for weighting kernel.

Definition at line 1246 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setWeightingType ( const std::string & wt )

inline

Type for weighting kernel for GMLS problem.

Definition at line 1171 of file Compadre_GMLS.hpp.

void Compadre::GMLS::setWeightingType ( const WeightingFunctionType wt )

inline

Type for weighting kernel for GMLS problem.

Definition at line 1194 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setWindowSizes ( view_type epsilons )

inline

Sets window sizes, also called the support of the kernel.

Definition at line 1024 of file Compadre_GMLS.hpp.

template<typename view_type >

void Compadre::GMLS::setWindowSizes ( decltype(_epsilons) epsilons )

inline

Sets window sizes, also called the support of the kernel (device)

Definition at line 1036 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::verifyAdditionalPointConnections ( bool assert_valid = false )

inline

Verify whether _additional_pc is valid.

Definition at line 1320 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::verifyPointConnections ( bool assert_valid = false )

inline

Verify whether _pc is valid.

Definition at line 1304 of file Compadre_GMLS.hpp.

static KOKKOS_INLINE_FUNCTION double Compadre::GMLS::Wab	(	const double	r,
		const double	h,
		const WeightingFunctionType &	weighting_type,
		const int	p,
		const int	n
	)

inlinestatic

Evaluates the weighting kernel.

Parameters

r	[in] - Euclidean distance of relative vector. Euclidean distance of (target - neighbor) in some basis.
h	[in] - window size. Kernel is guaranteed to take on a value of zero if it exceeds h.
weighting_type	[in] - weighting type to be evaluated as the kernel. e,g. power, Gaussian, etc..
p	[in] - parameter to be given to the kernel (see Wab definition for context).
n	[in] - parameter to be given to the kernel (see Wab definition for context).

Definition at line 549 of file Compadre_GMLS.hpp.

Friends And Related Function Documentation

friend class Evaluator

friend

Definition at line 42 of file Compadre_GMLS.hpp.

Member Data Documentation

point_connections_type Compadre::GMLS::_additional_pc

private

(OPTIONAL) connections between additional points and neighbors

Definition at line 117 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_basis_multiplier

private

dimension of the reconstructed function e.g.

reconstruction of vector on a 2D manifold in 3D would have _basis_multiplier of 2

Definition at line 197 of file Compadre_GMLS.hpp.

ConstraintType Compadre::GMLS::_constraint_type

private

constraint type for GMLS problem

Definition at line 157 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_curvature_poly_order

private

order of basis for curvature reconstruction

Definition at line 129 of file Compadre_GMLS.hpp.

Kokkos::View<TargetOperation*> Compadre::GMLS::_curvature_support_operations

private

vector containing target functionals to be applied for curvature

Definition at line 169 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_curvature_weighting_n

private

second parameter to be used for weighting kernel for curvature

Definition at line 193 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_curvature_weighting_p

private

first parameter to be used for weighting kernel for curvature

Definition at line 190 of file Compadre_GMLS.hpp.

WeightingFunctionType Compadre::GMLS::_curvature_weighting_type

private

weighting kernel type for curvature problem

Definition at line 181 of file Compadre_GMLS.hpp.

SolutionSet<device_memory_space> Compadre::GMLS::_d_ss

private

Definition at line 123 of file Compadre_GMLS.hpp.

SamplingFunctional Compadre::GMLS::_data_sampling_functional

private

generally the same as _polynomial_sampling_functional, but can differ if specified at

GMLS class instantiation

Definition at line 166 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_data_sampling_multiplier

private

effective dimension of the data sampling functional e.g.

in 3D, a scalar will be 1, a vector will be 3, and a vector of reused scalars will be 3

Definition at line 206 of file Compadre_GMLS.hpp.

DenseSolverType Compadre::GMLS::_dense_solver_type

private

solver type for GMLS problem - can be QR, SVD or LU

Definition at line 150 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_dimension_of_quadrature_points

private

dimension of quadrature rule

Definition at line 237 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_dimensions

private

dimension of the problem, set at class instantiation only

Definition at line 141 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::_entire_batch_computed_at_once

private

whether entire calculation was computed at once the alternative is that it was broken up over many smaller groups, in which case this is false, and so the _RHS matrix can not be stored or requested

Definition at line 222 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_epsilons

private

h supports determined through neighbor search (device)

Definition at line 106 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_global_dimensions

private

spatial dimension of the points, set at class instantiation only

Definition at line 135 of file Compadre_GMLS.hpp.

SolutionSet<host_memory_space> Compadre::GMLS::_h_ss

private

Solution Set (contains all alpha values from solution and alpha layout methods)

Definition at line 122 of file Compadre_GMLS.hpp.

Kokkos::View<TargetOperation*>::HostMirror Compadre::GMLS::_host_operations

private

vector containing target functionals to be applied for reconstruction problem (host)

Definition at line 175 of file Compadre_GMLS.hpp.

Kokkos::View<const double*****, layout_right>::HostMirror Compadre::GMLS::_host_prestencil_weights

private

generated weights for nontraditional samples required to transform data into expected sampling functional form (host)

Definition at line 114 of file Compadre_GMLS.hpp.

Kokkos::View<double*>::HostMirror Compadre::GMLS::_host_ref_N

private

reference outward normal vectors information (host)

Definition at line 85 of file Compadre_GMLS.hpp.

Kokkos::View<double*>::HostMirror Compadre::GMLS::_host_T

private

tangent vectors information (host)

Definition at line 82 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_initial_index_for_batch

private

initial index for current batch

Definition at line 228 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_local_dimensions

private

dimension of the problem, set at class instantiation only. For manifolds, generally _global_dimensions-1

Definition at line 138 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_manifold_curvature_coefficients

private

curvature polynomial coefficients for all problems

Definition at line 91 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_manifold_curvature_gradient

private

_dimension-1 gradient values for curvature for all problems

Definition at line 94 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_manifold_metric_tensor_inverse

private

metric tensor inverse for all problems

Definition at line 88 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_NP

private

dimension of basis for polynomial reconstruction

Definition at line 132 of file Compadre_GMLS.hpp.

Kokkos::View<TargetOperation*> Compadre::GMLS::_operations

private

vector containing target functionals to be applied for reconstruction problem (device)

Definition at line 172 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_order_of_quadrature_points

private

order of exact polynomial integration for quadrature rule

Definition at line 234 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::_orthonormal_tangent_space_provided

private

whether or not the orthonormal tangent directions were provided by the user.

If they are not, then for the case of calculations on manifolds, a GMLS approximation of the tangent space will be made and stored for use.

Definition at line 211 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_P

private

P*sqrt(w) matrix for all problems.

Definition at line 64 of file Compadre_GMLS.hpp.

point_connections_type Compadre::GMLS::_pc

private

connections between points and neighbors

Definition at line 103 of file Compadre_GMLS.hpp.

ParallelManager Compadre::GMLS::_pm

private

determines scratch level spaces and is used to call kernels

Definition at line 231 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_poly_order

private

order of basis for polynomial reconstruction

Definition at line 126 of file Compadre_GMLS.hpp.

SamplingFunctional Compadre::GMLS::_polynomial_sampling_functional

private

polynomial sampling functional used to construct P matrix, set at GMLS class instantiation
NOTE: can only be set at object instantiation

Definition at line 161 of file Compadre_GMLS.hpp.

Kokkos::View<double*****, layout_right> Compadre::GMLS::_prestencil_weights

private

generated weights for nontraditional samples required to transform data into expected sampling functional form (device).

Definition at line 110 of file Compadre_GMLS.hpp.

ProblemType Compadre::GMLS::_problem_type

private

problem type for GMLS problem, can also be set to STANDARD for normal or MANIFOLD for manifold problems
NOTE: can only be set at object instantiation

Definition at line 154 of file Compadre_GMLS.hpp.

Quadrature Compadre::GMLS::_qm

private

manages and calculates quadrature

Definition at line 243 of file Compadre_GMLS.hpp.

std::string Compadre::GMLS::_quadrature_type

private

quadrature rule type

Definition at line 240 of file Compadre_GMLS.hpp.

ReconstructionSpace Compadre::GMLS::_reconstruction_space

private

reconstruction space for GMLS problems, set at GMLS class instantiation

Definition at line 144 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_reconstruction_space_rank

private

actual rank of reconstruction basis

Definition at line 147 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_ref_N

private

Rank 2 tensor for high order approximation of tangent vectors for all problems.

First rank is for the target index, the second is for the spatial dimension (_dimensions)

Definition at line 79 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::_reference_outward_normal_direction_provided

private

whether or not the reference outward normal directions were provided by the user.

Definition at line 214 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_RHS

private

sqrt(w)*Identity matrix for all problems, later holds polynomial coefficients for all problems

Definition at line 67 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_sampling_multiplier

private

actual dimension of the sampling functional e.g.

reconstruction of vector on a 2D manifold in 3D would have _basis_multiplier of 2 e.g. in 3D, a scalar will be 1, a vector will be 3, and a vector of reused scalars will be 1

Definition at line 202 of file Compadre_GMLS.hpp.

Kokkos::View<double**, layout_right> Compadre::GMLS::_source_extra_data

private

Extra data available to basis functions (optional)

Definition at line 97 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::_store_PTWP_inv_PTW

private

whether polynomial coefficients were requested to be stored (in a state not yet applied to data)

Definition at line 225 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_T

private

Rank 3 tensor for high order approximation of tangent vectors for all problems.

First rank is for the target index, the second is for the local direction to the manifolds 0..(_dimensions-1) are tangent, _dimensions is the normal, and the third is for the spatial dimension (_dimensions)

Definition at line 75 of file Compadre_GMLS.hpp.

Kokkos::View<double**, layout_right> Compadre::GMLS::_target_extra_data

private

Extra data available to target operations (optional)

Definition at line 100 of file Compadre_GMLS.hpp.

bool Compadre::GMLS::_use_reference_outward_normal_direction_provided_to_orient_surface

private

whether or not to use reference outward normal directions to orient the surface in a manifold problem.

Definition at line 217 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_w

private

contains weights for all problems

Definition at line 61 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_weighting_n

private

second parameter to be used for weighting kernel

Definition at line 187 of file Compadre_GMLS.hpp.

int Compadre::GMLS::_weighting_p

private

first parameter to be used for weighting kernel

Definition at line 184 of file Compadre_GMLS.hpp.

WeightingFunctionType Compadre::GMLS::_weighting_type

private

weighting kernel type for GMLS

Definition at line 178 of file Compadre_GMLS.hpp.

Kokkos::View<double*> Compadre::GMLS::_Z

private

stores evaluations of targets applied to basis

Definition at line 70 of file Compadre_GMLS.hpp.

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

http://docs.trilinos.org/dev/packages/compadre/src/Compadre_GMLS.hpp
http://docs.trilinos.org/dev/packages/compadre/src/Compadre_GMLS.cpp

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