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Compadre
1.2.0
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Compadre
1.2.0
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Generalized Moving Least Squares (GMLS) More...
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 25 of file Compadre_GMLS.hpp.
#include <Compadre_GMLS.hpp>
Classes | |
| struct | ApplyCurvatureTargets |
| Tag for functor to evaluate curvature targets and apply to coefficients of curvature reconstruction. More... | |
| struct | ApplyManifoldTargets |
| Tag for functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas. More... | |
| struct | ApplyStandardTargets |
| Tag for functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas. More... | |
| struct | AssembleCurvaturePsqrtW |
| Tag for functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity for curvature. More... | |
| struct | AssembleManifoldPsqrtW |
| Tag for functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity. More... | |
| struct | AssembleStandardPsqrtW |
| Tag for functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity. More... | |
| struct | ComputeCoarseTangentPlane |
| Tag for functor to create a coarse tangent approximation from a given neighborhood of points. More... | |
| struct | ComputePrestencilWeights |
| Tag for functor to calculate prestencil weights to apply to data to transform into a format expected by a GMLS stencil. More... | |
| struct | FixTangentDirectionOrdering |
| Tag for functor to determine if tangent directions need reordered, and to reorder them if needed. More... | |
| struct | GetAccurateTangentDirections |
| Tag for functor to evaluate curvature targets and construct accurate tangent direction approximation for manifolds. More... | |
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=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) | |
| Minimal constructor providing no data (neighbor lists, source sites, target sites) 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... | |
| ~GMLS () | |
| Destructor. More... | |
Functors | |
Member functions that perform operations on the entire batch | |
| KOKKOS_INLINE_FUNCTION void | operator() (const AssembleStandardPsqrtW &, const member_type &teamMember) const |
| Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const ApplyStandardTargets &, const member_type &teamMember) const |
| Functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const ComputeCoarseTangentPlane &, const member_type &teamMember) const |
| Functor to create a coarse tangent approximation from a given neighborhood of points. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const AssembleCurvaturePsqrtW &, const member_type &teamMember) const |
| Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity for curvature. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const GetAccurateTangentDirections &, const member_type &teamMember) const |
| Functor to evaluate curvature targets and construct accurate tangent direction approximation for manifolds. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const FixTangentDirectionOrdering &, const member_type &teamMember) const |
| Functor to determine if tangent directions need reordered, and to reorder them if needed We require that the normal is consistent with a right hand rule on the tangent vectors. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const ApplyCurvatureTargets &, const member_type &teamMember) const |
| Functor to evaluate curvature targets and apply to coefficients of curvature reconstruction. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const AssembleManifoldPsqrtW &, const member_type &teamMember) const |
| Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const ApplyManifoldTargets &, const member_type &teamMember) const |
| Functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas. More... | |
| KOKKOS_INLINE_FUNCTION void | operator() (const ComputePrestencilWeights &, const member_type &teamMember) const |
| Functor to calculate prestencil weights to apply to data to transform into a format expected by a GMLS stencil. 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 () |
| Get dense solver type. More... | |
| ProblemType | getProblemType () |
| Get problem type. More... | |
| ConstraintType | getConstraintType () |
| Get constraint type. More... | |
| WeightingFunctionType | getWeightingType () const |
| Type for weighting kernel for GMLS problem. More... | |
| WeightingFunctionType | getManifoldWeightingType () const |
| Type for weighting kernel for curvature. More... | |
| int | getWeightingPower () const |
| Power for weighting kernel for GMLS problem. More... | |
| int | getManifoldWeightingPower () const |
| Power 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... | |
| decltype(_neighbor_lists)* | getNeighborLists () |
| Get neighbor list accessor. More... | |
| decltype(_T) | getTangentDirections () const |
| Get a view (device) of all tangent direction bundles. More... | |
| decltype(_ref_N) | getReferenceNormalDirections () const |
| 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... | |
| int | getTargetOperationLocalIndex (TargetOperation lro) const |
| Get the local index (internal) to GMLS for a particular TargetOperation Every TargetOperation has a global index which can be readily found in Compadre::TargetOperation but this function returns the index used inside of the GMLS class. 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... | |
| int | getAlphaColumnOffset (TargetOperation lro, const int output_component_axis_1, const int output_component_axis_2, const int input_component_axis_1, const int input_component_axis_2, const int additional_evaluation_local_index=0) const |
| Retrieves the offset for an operator based on input and output component, generic to row (but still multiplied by the number of neighbors for each row and then needs a neighbor number added to this returned value to be meaningful) More... | |
| decltype(_alphas) | getAlphas () const |
| Get a view (device) of all alphas. 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 | getAlpha0TensorTo0Tensor (TargetOperation lro, const int target_index, const int neighbor_index, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for scalar reconstruction from scalar data. More... | |
| double | getAlpha0TensorTo1Tensor (TargetOperation lro, const int target_index, const int output_component, const int neighbor_index, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for vector reconstruction from scalar data. More... | |
| double | getAlpha0TensorTo2Tensor (TargetOperation lro, const int target_index, const int output_component_axis_1, const int output_component_axis_2, const int neighbor_index, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for matrix reconstruction from scalar data. More... | |
| double | getAlpha1TensorTo0Tensor (TargetOperation lro, const int target_index, const int neighbor_index, const int input_component, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for scalar reconstruction from vector data. More... | |
| double | getAlpha1TensorTo1Tensor (TargetOperation lro, const int target_index, const int output_component, const int neighbor_index, const int input_component, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for vector reconstruction from vector data. More... | |
| double | getAlpha1TensorTo2Tensor (TargetOperation lro, const int target_index, const int output_component_axis_1, const int output_component_axis_2, const int neighbor_index, const int input_component, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for matrix reconstruction from vector data. More... | |
| double | getAlpha2TensorTo0Tensor (TargetOperation lro, const int target_index, const int neighbor_index, const int input_component_axis_1, const int input_component_axis_2, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for scalar reconstruction from matrix data. More... | |
| double | getAlpha2TensorTo1Tensor (TargetOperation lro, const int target_index, const int output_component, const int neighbor_index, const int input_component_axis_1, const int input_component_axis_2, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for vector reconstruction from matrix data. More... | |
| double | getAlpha2TensorTo2Tensor (TargetOperation lro, const int target_index, const int output_component_axis_1, const int output_component_axis_2, const int neighbor_index, const int input_component_axis_1, const int input_component_axis_2, const int additional_evaluation_site=0) const |
| Helper function for getting alphas for matrix reconstruction from matrix data. More... | |
| KOKKOS_INLINE_FUNCTION global_index_type | getAlphaIndexDevice (const int target_index, const int alpha_column_offset) const |
| Gives index into alphas given two axes, which when incremented by the neighbor number transforms access into alphas from a rank 1 view into a rank 3 view. More... | |
| global_index_type | getAlphaIndexHost (const int target_index, const int alpha_column_offset) const |
| Gives index into alphas given two axes, which when incremented by the neighbor number transforms access into alphas from a rank 1 view into a rank 3 view. More... | |
| double | getAlpha (TargetOperation lro, const int target_index, const int output_component_axis_1, const int output_component_axis_2, const int neighbor_index, const int input_component_axis_1, const int input_component_axis_2, const int additional_evaluation_site=0) const |
| Underlying function all interface helper functions call to retrieve alpha values. 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... | |
| int | getOutputDimensionOfOperation (TargetOperation lro, bool ambient=false) const |
| Dimensions ^ output rank for target operation. More... | |
| int | getInputDimensionOfOperation (TargetOperation lro) const |
| Dimensions ^ input rank for target operation (always in local chart if on a manifold, never ambient space) More... | |
| int | getOutputDimensionOfSampling (SamplingFunctional sro) const |
| Dimensions ^ output rank for sampling operation (always in local chart if on a manifold, never ambient space) More... | |
| int | getInputDimensionOfSampling (SamplingFunctional sro) const |
| Dimensions ^ output rank for sampling operation (always in ambient space, never local chart on a manifold) More... | |
| int | calculateBasisMultiplier (const ReconstructionSpace rs) const |
| Calculate basis_multiplier. More... | |
| int | calculateSamplingMultiplier (const ReconstructionSpace rs, const SamplingFunctional sro) const |
| Calculate sampling_multiplier. 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 > | |
| std::enable_if < view_type::rank==1 &&std::is_same< decltype(_neighbor_lists)::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< decltype(_neighbor_lists)::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 (decltype(_source_coordinates) 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 (decltype(_target_coordinates) 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... | |
| 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 (decltype(_additional_evaluation_coordinates) evaluation_coordinates) |
| (OPTIONAL) Sets additional points for evaluation of target operation on polynomial reconstruction. More... | |
| template<typename view_type > | |
| void | setAuxiliaryEvaluationIndicesLists (view_type indices_lists) |
| (OPTIONAL) Sets the additional target evaluation coordinate indices list information. More... | |
| template<typename view_type > | |
| void | setAuxiliaryEvaluationIndicesLists (decltype(_additional_evaluation_indices) indices_lists) |
| (OPTIONAL) Sets the additional target evaluation coordinate indices list information. 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 reoncstructing any function. More... | |
| void | setCurvaturePolynomialOrder (const int manifold_poly_order) |
| Sets basis order to be used when reoncstructing curvature. More... | |
| void | setWeightingPower (int wp) |
| Power for weighting kernel for GMLS problem. More... | |
| void | setCurvatureWeightingPower (int wp) |
| Power for weighting kernel for curvature. 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... | |
| void | generatePolynomialCoefficients (const int number_of_batches=1, const bool keep_coefficients=false) |
| 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) |
| 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 power) |
| Evaluates the weighting kernel. More... | |
| static KOKKOS_INLINE_FUNCTION double | EuclideanVectorLength (const XYZ &delta_vector, const int dimension) |
| Returns Euclidean norm of a vector. More... | |
| static int | getTargetOutputIndex (const int operation_num, const int output_component_axis_1, const int output_component_axis_2, const int dimensions) |
| Helper function for finding alpha coefficients. More... | |
| static int | getSamplingOutputIndex (const SamplingFunctional sf, const int output_component_axis_1, const int output_component_axis_2) |
| Helper function for finding alpha coefficients. More... | |
| static int | getOutputRankOfSampling (SamplingFunctional sro) |
| Output rank for sampling operation. More... | |
| static int | getInputRankOfSampling (SamplingFunctional sro) |
| Input rank for sampling operation. More... | |
Protected Member Functions | |
Private Modifiers | |
Private function because information lives on the device | |
| KOKKOS_INLINE_FUNCTION void | calcPij (const member_type &teamMember, double *delta, double *thread_workspace, const int target_index, int neighbor_index, const double alpha, const int dimension, const int poly_order, bool specific_order_only=false, const scratch_matrix_right_type *V=NULL, const ReconstructionSpace reconstruction_space=ReconstructionSpace::ScalarTaylorPolynomial, const SamplingFunctional sampling_strategy=PointSample, const int additional_evaluation_local_index=0) const |
| Evaluates the polynomial basis under a particular sampling function. Generally used to fill a row of P. More... | |
| KOKKOS_INLINE_FUNCTION void | calcGradientPij (const member_type &teamMember, double *delta, double *thread_workspace, const int target_index, int neighbor_index, const double alpha, const int partial_direction, const int dimension, const int poly_order, bool specific_order_only, const scratch_matrix_right_type *V, const ReconstructionSpace reconstruction_space, const SamplingFunctional sampling_strategy, const int additional_evaluation_local_index=0) const |
| Evaluates the gradient of a polynomial basis under the Dirac Delta (pointwise) sampling function. More... | |
| KOKKOS_INLINE_FUNCTION void | calcHessianPij (const member_type &teamMember, double *delta, double *thread_workspace, const int target_index, int neighbor_index, const double alpha, const int partial_direction_1, const int partial_direction_2, const int dimension, const int poly_order, bool specific_order_only, const scratch_matrix_right_type *V, const ReconstructionSpace reconstruction_space, const SamplingFunctional sampling_strategy, const int additional_evaluation_local_index=0) const |
| Evaluates the Hessian of a polynomial basis under the Dirac Delta (pointwise) sampling function. More... | |
| KOKKOS_INLINE_FUNCTION void | createWeightsAndP (const member_type &teamMember, scratch_vector_type delta, scratch_vector_type thread_workspace, scratch_matrix_right_type P, scratch_vector_type w, const int dimension, int polynomial_order, bool weight_p=false, scratch_matrix_right_type *V=NULL, const ReconstructionSpace reconstruction_space=ReconstructionSpace::ScalarTaylorPolynomial, const SamplingFunctional sampling_strategy=PointSample) const |
| Fills the _P matrix with either P or P*sqrt(w) More... | |
| KOKKOS_INLINE_FUNCTION void | createWeightsAndPForCurvature (const member_type &teamMember, scratch_vector_type delta, scratch_vector_type thread_workspace, scratch_matrix_right_type P, scratch_vector_type w, const int dimension, bool only_specific_order, scratch_matrix_right_type *V=NULL) const |
| Fills the _P matrix with P*sqrt(w) for use in solving for curvature. More... | |
| KOKKOS_INLINE_FUNCTION void | computeTargetFunctionals (const member_type &teamMember, scratch_vector_type t1, scratch_vector_type t2, scratch_matrix_right_type P_target_row) const |
| Evaluates a polynomial basis with a target functional applied to each member of the basis. More... | |
| KOKKOS_INLINE_FUNCTION void | computeCurvatureFunctionals (const member_type &teamMember, scratch_vector_type t1, scratch_vector_type t2, scratch_matrix_right_type P_target_row, const scratch_matrix_right_type *V, const local_index_type local_neighbor_index=-1) const |
| Evaluates a polynomial basis for the curvature with a gradient target functional applied. More... | |
| KOKKOS_INLINE_FUNCTION void | computeTargetFunctionalsOnManifold (const member_type &teamMember, scratch_vector_type t1, scratch_vector_type t2, scratch_matrix_right_type P_target_row, scratch_matrix_right_type V, scratch_matrix_right_type G_inv, scratch_vector_type curvature_coefficients, scratch_vector_type curvature_gradients) const |
| Evaluates a polynomial basis with a target functional applied, using information from the manifold curvature. More... | |
| KOKKOS_INLINE_FUNCTION void | applyTargetsToCoefficients (const member_type &teamMember, scratch_vector_type t1, scratch_vector_type t2, scratch_matrix_right_type Q, scratch_vector_type w, scratch_matrix_right_type P_target_row, const int target_NP) const |
| Helper function for applying the evaluations from a target functional to the polynomial coefficients. More... | |
Private Accessors | |
Private function because information lives on the device | |
| KOKKOS_INLINE_FUNCTION int | getNNeighbors (const int target_index) const |
| Returns number of neighbors for a particular target. More... | |
| KOKKOS_INLINE_FUNCTION int | getNeighborIndex (const int target_index, const int neighbor_list_num) const |
| Mapping from [0,number of neighbors for a target] to the row that contains the source coordinates for that neighbor. More... | |
| KOKKOS_INLINE_FUNCTION int | getMaxNNeighbors () const |
| Returns the maximum neighbor lists size over all target sites. More... | |
| KOKKOS_INLINE_FUNCTION int | getMaxEvaluationSitesPerTarget () const |
| Returns the maximum number of evaluation sites over all target sites (target sites are included in total) More... | |
| KOKKOS_INLINE_FUNCTION int | getNEvaluationSitesPerTarget (const int target_index) const |
| (OPTIONAL) Returns number of additional evaluation sites for a particular target More... | |
| KOKKOS_INLINE_FUNCTION int | getAdditionalEvaluationIndex (const int target_index, const int additional_list_num) const |
| (OPTIONAL) Mapping from [0,number of additional evaluation sites for a target] to the row that contains the coordinates for that evaluation More... | |
| KOKKOS_INLINE_FUNCTION double | getTargetCoordinate (const int target_index, const int dim, const scratch_matrix_right_type *V=NULL) const |
| Returns one component of the target coordinate for a particular target. More... | |
| KOKKOS_INLINE_FUNCTION double | getTargetAuxiliaryCoordinate (const int target_index, const int additional_list_num, const int dim, const scratch_matrix_right_type *V=NULL) const |
| (OPTIONAL) Returns one component of the additional evaluation coordinates. More... | |
| KOKKOS_INLINE_FUNCTION double | getNeighborCoordinate (const int target_index, const int neighbor_list_num, const int dim, const scratch_matrix_right_type *V=NULL) const |
| Returns one component of the neighbor coordinate for a particular target. More... | |
| KOKKOS_INLINE_FUNCTION XYZ | getRelativeCoord (const int target_index, const int neighbor_list_num, const int dimension, const scratch_matrix_right_type *V=NULL) const |
| Returns the relative coordinate as a vector between the target site and the neighbor site. More... | |
| KOKKOS_INLINE_FUNCTION double | convertGlobalToLocalCoordinate (const XYZ global_coord, const int dim, const scratch_matrix_right_type *V) const |
| Returns a component of the local coordinate after transformation from global to local under the orthonormal basis V. More... | |
| KOKKOS_INLINE_FUNCTION double | convertLocalToGlobalCoordinate (const XYZ local_coord, const int dim, const scratch_matrix_right_type *V) const |
| Returns a component of the global coordinate after transformation from local to global under the orthonormal basis V^T. More... | |
| int | getTargetOffsetIndexHost (const int lro_num, const int input_component, const int output_component, const int additional_evaluation_local_index=0) const |
| Handles offset from operation input/output + extra evaluation sites. More... | |
| KOKKOS_INLINE_FUNCTION int | getTargetOffsetIndexDevice (const int lro_num, const int input_component, const int output_component, const int additional_evaluation_local_index=0) const |
| Handles offset from operation input/output + extra evaluation sites. More... | |
Static Protected 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... | |
Protected Attributes | |
| pool_type | _random_number_pool |
| 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 * > | _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... | |
| NeighborLists< Kokkos::View < int * > > | _neighbor_lists |
| Accessor to get neighbor list data, offset data, and number of neighbors per target. More... | |
| Kokkos::View< int *, host_memory_space > | _host_number_of_neighbors_list |
| convenient copy on host of number of neighbors More... | |
| Kokkos::View< double **, layout_right > | _source_coordinates |
| all coordinates for the source for which _neighbor_lists refers (device) More... | |
| Kokkos::View< double **, layout_right > | _target_coordinates |
| coordinates for target sites for reconstruction (device) More... | |
| Kokkos::View< double * > | _epsilons |
| h supports determined through neighbor search (device) More... | |
| Kokkos::View< double * > ::HostMirror | _host_epsilons |
| h supports determined through neighbor search (host) More... | |
| Kokkos::View< double *, layout_right > | _alphas |
| generated alpha coefficients (device) More... | |
| Kokkos::View< const double *, layout_right >::HostMirror | _host_alphas |
| generated alpha coefficients (host) 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... | |
| Kokkos::View< double **, layout_right > | _additional_evaluation_coordinates |
| (OPTIONAL) user provided additional coordinates for target operation evaluation (device) More... | |
| Kokkos::View< int **, layout_right > | _additional_evaluation_indices |
| (OPTIONAL) contains indices of entries in the _additional_evaluation_coordinates view (device) More... | |
| Kokkos::View< int **, layout_right >::HostMirror | _host_additional_evaluation_indices |
| (OPTIONAL) contains indices of entries in the _additional_evaluation_coordinates view (host) More... | |
| Kokkos::View< int * > | _number_of_additional_evaluation_indices |
| (OPTIONAL) contains the # of additional coordinate indices for each target More... | |
| 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 More... | |
| ConstraintType | _constraint_type |
| constraint type for GMLS problem More... | |
| const SamplingFunctional | _polynomial_sampling_functional |
| polynomial sampling functional used to construct P matrix, set at GMLS class instantiation More... | |
| const SamplingFunctional | _data_sampling_functional |
| generally the same as _polynomial_sampling_functional, but can differ if specified at GMLS class instantiation 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_power |
| power to be used for weighting kernel More... | |
| int | _curvature_weighting_power |
| power 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 | _nontrivial_nullspace |
| whether or not operator to be inverted for GMLS problem has a nontrivial nullspace (requiring SVD) 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... | |
| int | _max_num_neighbors |
| maximum number of neighbors over all target sites More... | |
| int | _max_evaluation_sites_per_target |
| maximum number of evaluation sites for each target (includes target site) More... | |
| std::vector< TargetOperation > | _lro |
| vector of user requested target operations More... | |
| std::vector< int > | _lro_lookup |
| vector containing a mapping from a target functionals enum value to the its place in the list of target functionals to be applied More... | |
| Kokkos::View< int * > | _lro_total_offsets |
| index for where this operation begins the for _alpha coefficients (device) More... | |
| Kokkos::View< int * >::HostMirror | _host_lro_total_offsets |
| index for where this operation begins the for _alpha coefficients (host) More... | |
| Kokkos::View< int * > | _lro_output_tile_size |
| dimensions ^ rank of tensor of output for each target functional (device) More... | |
| Kokkos::View< int * >::HostMirror | _host_lro_output_tile_size |
| dimensions ^ rank of tensor of output for each target functional (host) More... | |
| Kokkos::View< int * > | _lro_input_tile_size |
| dimensions ^ rank of tensor of output for each sampling functional (device) More... | |
| Kokkos::View< int * >::HostMirror | _host_lro_input_tile_size |
| dimensions ^ rank of tensor of output for each sampling functional (host) More... | |
| Kokkos::View< int * > | _lro_output_tensor_rank |
| tensor rank of target functional (device) More... | |
| Kokkos::View< int * >::HostMirror | _host_lro_output_tensor_rank |
| tensor rank of target functional (host) More... | |
| Kokkos::View< int * > | _lro_input_tensor_rank |
| tensor rank of sampling functional (device) More... | |
| Kokkos::View< int * >::HostMirror | _host_lro_input_tensor_rank |
| tensor rank of sampling functional (host) More... | |
| int | _total_alpha_values |
| used for sizing P_target_row and the _alphas view More... | |
| int | _added_alpha_size |
| additional alpha coefficients due to constraints 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... | |
|
inline |
Minimal constructor providing no data (neighbor lists, source sites, target sites)
Definition at line 625 of file Compadre_GMLS.hpp.
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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 705 of file Compadre_GMLS.hpp.
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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 715 of file Compadre_GMLS.hpp.
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Destructor.
Definition at line 726 of file Compadre_GMLS.hpp.
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Adds a target to the vector of target functional to be applied to the reconstruction.
Definition at line 1787 of file Compadre_GMLS.hpp.
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Adds a vector of target functionals to the vector of target functionals already to be applied to the reconstruction.
Definition at line 1794 of file Compadre_GMLS.hpp.
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Helper function for applying the evaluations from a target functional to the polynomial coefficients.
Definition at line 8 of file Compadre_GMLS_ApplyTargetEvaluations.hpp.
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Evaluates the gradient of a polynomial basis under the Dirac Delta (pointwise) sampling function.
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis. |
| target_index | [in] - target number |
| neighbor_index | [in] - index of neighbor for this target with respect to local numbering [0,...,number of neighbors for target] |
| alpha | [in] - double to determine convex combination of target and neighbor site at which to evaluate polynomials. (1-alpha)*neighbor + alpha*target |
| partial_direction | [in] - direction that partial is taken with respect to, e.g. 0 is x direction, 1 is y direction |
| dimension | [in] - spatial dimension of basis to evaluate. e.g. dimension two basis of order one is 1, x, y, whereas for dimension 3 it is 1, x, y, z |
| poly_order | [in] - polynomial basis degree |
| specific_order_only | [in] - boolean for only evaluating one degree of polynomial when true |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
| reconstruction_space | [in] - space of polynomial that a sampling functional is to evaluate |
| sampling_strategy | [in] - sampling functional specification |
| additional_evaluation_local_index | [in] - local index for evaluation sites |
Definition at line 468 of file Compadre_GMLS_Basis.hpp.
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protected |
Evaluates the Hessian of a polynomial basis under the Dirac Delta (pointwise) sampling function.
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis. |
| target_index | [in] - target number |
| neighbor_index | [in] - index of neighbor for this target with respect to local numbering [0,...,number of neighbors for target] |
| alpha | [in] - double to determine convex combination of target and neighbor site at which to evaluate polynomials. (1-alpha)*neighbor + alpha*target |
| partial_direction_1 | [in] - first direction that partial is taken with respect to, e.g. 0 is x direction, 1 is y direction |
| partial_direction_2 | [in] - second direction that partial is taken with respect to, e.g. 0 is x direction, 1 is y direction |
| dimension | [in] - spatial dimension of basis to evaluate. e.g. dimension two basis of order one is 1, x, y, whereas for dimension 3 it is 1, x, y, z |
| poly_order | [in] - polynomial basis degree |
| specific_order_only | [in] - boolean for only evaluating one degree of polynomial when true |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
| reconstruction_space | [in] - space of polynomial that a sampling functional is to evaluate |
| sampling_strategy | [in] - sampling functional specification |
| additional_evaluation_local_index | [in] - local index for evaluation sites |
Definition at line 531 of file Compadre_GMLS_Basis.hpp.
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Evaluates the polynomial basis under a particular sampling function. Generally used to fill a row of P.
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis. |
| target_index | [in] - target number |
| neighbor_index | [in] - index of neighbor for this target with respect to local numbering [0,...,number of neighbors for target] |
| alpha | [in] - double to determine convex combination of target and neighbor site at which to evaluate polynomials. (1-alpha)*neighbor + alpha*target |
| dimension | [in] - spatial dimension of basis to evaluate. e.g. dimension two basis of order one is 1, x, y, whereas for dimension 3 it is 1, x, y, z |
| poly_order | [in] - polynomial basis degree |
| specific_order_only | [in] - boolean for only evaluating one degree of polynomial when true |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
| reconstruction_space | [in] - space of polynomial that a sampling functional is to evaluate |
| sampling_strategy | [in] - sampling functional specification |
| additional_evaluation_local_index | [in] - local index for evaluation sites |
Definition at line 9 of file Compadre_GMLS_Basis.hpp.
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Calculate basis_multiplier.
Definition at line 1252 of file Compadre_GMLS.hpp.
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Calculate sampling_multiplier.
Definition at line 1259 of file Compadre_GMLS.hpp.
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Empties the vector of target functionals to apply to the reconstruction.
Definition at line 1879 of file Compadre_GMLS.hpp.
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protected |
Evaluates a polynomial basis for the curvature with a gradient target functional applied.
_operations is used by this function which is set through a modifier function
| teamMember | [in] - Kokkos::TeamPolicy member type (created by parallel_for) |
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _curvature_poly_order*the spatial dimension of the polynomial basis. |
| P_target_row | [out] - 1D Kokkos View where the evaluation of the polynomial basis is stored |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
Definition at line 951 of file Compadre_GMLS_Targets.hpp.
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protected |
Evaluates a polynomial basis with a target functional applied to each member of the basis.
| teamMember | [in] - Kokkos::TeamPolicy member type (created by parallel_for) |
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each team has its own copy. Must be at least as large is the _poly_order*_global_dimensions. |
| P_target_row | [out] - 1D Kokkos View where the evaluation of the polynomial basis is stored |
Definition at line 10 of file Compadre_GMLS_Targets.hpp.
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protected |
Evaluates a polynomial basis with a target functional applied, using information from the manifold curvature.
_operations is used by this function which is set through a modifier function
| teamMember | [in] - Kokkos::TeamPolicy member type (created by parallel_for) |
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _curvature_poly_order*the spatial dimension of the polynomial basis. |
| P_target_row | [out] - 1D Kokkos View where the evaluation of the polynomial basis is stored |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
| G_inv | [in] - (_dimensions-1)*(_dimensions-1) Kokkos View containing inverse of metric tensor |
| curvature_coefficients | [in] - polynomial coefficients for curvature |
| curvature_gradients | [in] - approximation of gradient of curvature, Kokkos View of size (_dimensions-1) |
Definition at line 1001 of file Compadre_GMLS_Targets.hpp.
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Returns a component of the local coordinate after transformation from global to local under the orthonormal basis V.
Definition at line 528 of file Compadre_GMLS.hpp.
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Returns a component of the global coordinate after transformation from local to global under the orthonormal basis V^T.
Definition at line 539 of file Compadre_GMLS.hpp.
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Fills the _P matrix with either P or P*sqrt(w)
| teamMember | [in] - Kokkos::TeamPolicy member type (created by parallel_for) |
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis. |
| P | [out] - 2D Kokkos View which will contain evaluation of sampling functional on polynomial basis for each neighbor the target has (stored column major) |
| w | [out] - 1D Kokkos View which will contain weighting kernel values for the target with each neighbor if weight_p = true |
| dimension | [in] - spatial dimension of basis to evaluate. e.g. dimension two basis of order one is 1, x, y, whereas for dimension 3 it is 1, x, y, z |
| polynomial_order | [in] - polynomial basis degree |
| weight_p | [in] - boolean whether to fill w with kernel weights |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
| reconstruction_space | [in] - space of polynomial that a sampling functional is to evaluate |
| sampling_strategy | [in] - sampling functional specification |
Definition at line 592 of file Compadre_GMLS_Basis.hpp.
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protected |
Fills the _P matrix with P*sqrt(w) for use in solving for curvature.
Uses _curvature_poly_order as the polynomial order of the basis
| teamMember | [in] - Kokkos::TeamPolicy member type (created by parallel_for) |
| delta | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large is the _basis_multipler*the dimension of the polynomial basis. |
| thread_workspace | [in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis. |
| P | [out] - 2D Kokkos View which will contain evaluation of sampling functional on polynomial basis for each neighbor the target has (stored column major) |
| w | [out] - 1D Kokkos View which will contain weighting kernel values for the target with each neighbor if weight_p = true |
| dimension | [in] - spatial dimension of basis to evaluate. e.g. dimension two basis of order one is 1, x, y, whereas for dimension 3 it is 1, x, y, z |
| only_specific_order | [in] - boolean for only evaluating one degree of polynomial when true |
| V | [in] - orthonormal basis matrix size _dimensions * _dimensions whose first _dimensions-1 columns are an approximation of the tangent plane |
Definition at line 667 of file Compadre_GMLS_Basis.hpp.
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inlinestatic |
Returns Euclidean norm of a vector.
Definition at line 873 of file Compadre_GMLS.hpp.
| void Compadre::GMLS::generateAlphas | ( | const int | number_of_batches = 1, |
| const bool | keep_coefficients = false |
||
| ) |
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. !
| 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 |
Definition at line 446 of file Compadre_GMLS.cpp.
| void Compadre::GMLS::generatePolynomialCoefficients | ( | const int | number_of_batches = 1, |
| const bool | keep_coefficients = false |
||
| ) |
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. !
| 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 |
Definition at line 11 of file Compadre_GMLS.cpp.
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(OPTIONAL) Mapping from [0,number of additional evaluation sites for a target] to the row that contains the coordinates for that evaluation
Definition at line 462 of file Compadre_GMLS.hpp.
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Underlying function all interface helper functions call to retrieve alpha values.
Definition at line 1173 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for scalar reconstruction from scalar data.
Definition at line 1092 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for vector reconstruction from scalar data.
Definition at line 1098 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for matrix reconstruction from scalar data.
Definition at line 1104 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for scalar reconstruction from vector data.
Definition at line 1109 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for vector reconstruction from vector data.
Definition at line 1115 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for matrix reconstruction from vector data.
Definition at line 1121 of file Compadre_GMLS.hpp.
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Helper function for getting alphas for scalar reconstruction from matrix data.
Definition at line 1127 of file Compadre_GMLS.hpp.
|
inline |
Helper function for getting alphas for vector reconstruction from matrix data.
Definition at line 1132 of file Compadre_GMLS.hpp.
|
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Helper function for getting alphas for matrix reconstruction from matrix data.
Definition at line 1137 of file Compadre_GMLS.hpp.
|
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Retrieves the offset for an operator based on input and output component, generic to row (but still multiplied by the number of neighbors for each row and then needs a neighbor number added to this returned value to be meaningful)
Definition at line 1049 of file Compadre_GMLS.hpp.
|
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Gives index into alphas given two axes, which when incremented by the neighbor number transforms access into alphas from a rank 1 view into a rank 3 view.
Definition at line 1144 of file Compadre_GMLS.hpp.
|
inline |
Gives index into alphas given two axes, which when incremented by the neighbor number transforms access into alphas from a rank 1 view into a rank 3 view.
Definition at line 1159 of file Compadre_GMLS.hpp.
Get a view (device) of all alphas.
Definition at line 1067 of file Compadre_GMLS.hpp.
|
inline |
Get constraint type.
Definition at line 968 of file Compadre_GMLS.hpp.
|
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Get the data sampling functional specified at instantiation (often the same as the polynomial sampling functional)
Definition at line 1086 of file Compadre_GMLS.hpp.
|
inline |
Get dense solver type.
Definition at line 962 of file Compadre_GMLS.hpp.
|
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Dimensions of quadrature points.
Definition at line 989 of file Compadre_GMLS.hpp.
|
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Dimension of the GMLS problem, set only at class instantiation.
Definition at line 953 of file Compadre_GMLS.hpp.
Get a view (device) of all polynomial coefficients basis.
Definition at line 1070 of file Compadre_GMLS.hpp.
|
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Dimension of the GMLS problem's point data (spatial description of points in ambient space), set only at class instantiation.
Definition at line 956 of file Compadre_GMLS.hpp.
|
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Dimensions ^ input rank for target operation (always in local chart if on a manifold, never ambient space)
Definition at line 1234 of file Compadre_GMLS.hpp.
|
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Dimensions ^ output rank for sampling operation (always in ambient space, never local chart on a manifold)
Definition at line 1247 of file Compadre_GMLS.hpp.
|
inlinestatic |
Input rank for sampling operation.
Definition at line 907 of file Compadre_GMLS.hpp.
|
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Local dimension of the GMLS problem (less than global dimension if on a manifold), set only at class instantiation.
Definition at line 959 of file Compadre_GMLS.hpp.
|
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Power for weighting kernel for curvature.
Definition at line 980 of file Compadre_GMLS.hpp.
|
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Type for weighting kernel for curvature.
Definition at line 974 of file Compadre_GMLS.hpp.
|
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Returns the maximum number of evaluation sites over all target sites (target sites are included in total)
Definition at line 447 of file Compadre_GMLS.hpp.
|
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Returns the maximum neighbor lists size over all target sites.
Definition at line 441 of file Compadre_GMLS.hpp.
|
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Returns one component of the neighbor coordinate for a particular target.
Whether global or local coordinates depends upon V being specified
Definition at line 503 of file Compadre_GMLS.hpp.
|
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Mapping from [0,number of neighbors for a target] to the row that contains the source coordinates for that neighbor.
Definition at line 435 of file Compadre_GMLS.hpp.
|
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Get neighbor list accessor.
Definition at line 995 of file Compadre_GMLS.hpp.
|
inlineprotected |
(OPTIONAL) Returns number of additional evaluation sites for a particular target
Definition at line 454 of file Compadre_GMLS.hpp.
|
inlinestatic |
Returns number of neighbors needed for unisolvency for a given basis order and dimension.
Definition at line 831 of file Compadre_GMLS.hpp.
|
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Returns number of neighbors for a particular target.
Definition at line 428 of file Compadre_GMLS.hpp.
|
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.
Definition at line 821 of file Compadre_GMLS.hpp.
|
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Number of quadrature points.
Definition at line 983 of file Compadre_GMLS.hpp.
|
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Order of quadrature points.
Definition at line 986 of file Compadre_GMLS.hpp.
|
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Dimensions ^ output rank for target operation.
Definition at line 1226 of file Compadre_GMLS.hpp.
|
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Dimensions ^ output rank for sampling operation (always in local chart if on a manifold, never ambient space)
Definition at line 1241 of file Compadre_GMLS.hpp.
|
inlinestatic |
Output rank for sampling operation.
Definition at line 902 of file Compadre_GMLS.hpp.
|
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Returns (size of the basis used in instance's polynomial reconstruction) x (data input dimension)
Definition at line 921 of file Compadre_GMLS.hpp.
|
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Returns 2D array size in memory on which coefficients are stored.
Definition at line 935 of file Compadre_GMLS.hpp.
|
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Returns size of the basis used in instance's polynomial reconstruction.
Definition at line 929 of file Compadre_GMLS.hpp.
|
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Get the polynomial sampling functional specified at instantiation.
Definition at line 1083 of file Compadre_GMLS.hpp.
|
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Returns a stencil to transform data from its existing state into the input expected for some sampling functionals.
Definition at line 1203 of file Compadre_GMLS.hpp.
|
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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 1042 of file Compadre_GMLS.hpp.
|
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Get problem type.
Definition at line 965 of file Compadre_GMLS.hpp.
|
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Type of quadrature points.
Definition at line 992 of file Compadre_GMLS.hpp.
|
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Get the reconstruction space specified at instantiation.
Definition at line 1089 of file Compadre_GMLS.hpp.
|
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Get component of tangent or normal directions for manifold problems.
Definition at line 1013 of file Compadre_GMLS.hpp.
Get a view (device) of all reference outward normal directions.
Definition at line 1001 of file Compadre_GMLS.hpp.
|
inlineprotected |
Returns the relative coordinate as a vector between the target site and the neighbor site.
Whether global or local coordinates depends upon V being specified
Definition at line 516 of file Compadre_GMLS.hpp.
|
inlinestatic |
Helper function for finding alpha coefficients.
Definition at line 896 of file Compadre_GMLS.hpp.
|
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Get component of tangent or normal directions for manifold problems.
Definition at line 1004 of file Compadre_GMLS.hpp.
Get a view (device) of all tangent direction bundles.
Definition at line 998 of file Compadre_GMLS.hpp.
|
inlineprotected |
(OPTIONAL) Returns one component of the additional evaluation coordinates.
Whether global or local coordinates depends upon V being specified
Definition at line 487 of file Compadre_GMLS.hpp.
|
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Returns one component of the target coordinate for a particular target.
Whether global or local coordinates depends upon V being specified
Definition at line 471 of file Compadre_GMLS.hpp.
|
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Handles offset from operation input/output + extra evaluation sites.
Definition at line 562 of file Compadre_GMLS.hpp.
|
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Handles offset from operation input/output + extra evaluation sites.
Definition at line 553 of file Compadre_GMLS.hpp.
|
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Get the local index (internal) to GMLS for a particular TargetOperation Every TargetOperation has a global index which can be readily found in Compadre::TargetOperation but this function returns the index used inside of the GMLS class.
Definition at line 1024 of file Compadre_GMLS.hpp.
|
inlinestatic |
Helper function for finding alpha coefficients.
Definition at line 890 of file Compadre_GMLS.hpp.
|
inline |
Power for weighting kernel for GMLS problem.
Definition at line 977 of file Compadre_GMLS.hpp.
|
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Type for weighting kernel for GMLS problem.
Definition at line 971 of file Compadre_GMLS.hpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const AssembleStandardPsqrtW & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity.
Definition at line 454 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const ApplyStandardTargets & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas.
Definition at line 533 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const ComputeCoarseTangentPlane & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to create a coarse tangent approximation from a given neighborhood of points.
Definition at line 586 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const AssembleCurvaturePsqrtW & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity for curvature.
Definition at line 640 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const GetAccurateTangentDirections & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to evaluate curvature targets and construct accurate tangent direction approximation for manifolds.
Definition at line 715 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const FixTangentDirectionOrdering & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to determine if tangent directions need reordered, and to reorder them if needed We require that the normal is consistent with a right hand rule on the tangent vectors.
Definition at line 868 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const ApplyCurvatureTargets & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to evaluate curvature targets and apply to coefficients of curvature reconstruction.
Definition at line 913 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const AssembleManifoldPsqrtW & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to assemble the P*sqrt(weights) matrix and construct sqrt(weights)*Identity.
Definition at line 1057 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const ApplyManifoldTargets & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to evaluate targets, apply target evaluation to polynomial coefficients to store in _alphas.
Definition at line 1128 of file Compadre_GMLS.cpp.
| KOKKOS_INLINE_FUNCTION void Compadre::GMLS::operator() | ( | const ComputePrestencilWeights & | , |
| const member_type & | teamMember | ||
| ) | const |
Functor to calculate prestencil weights to apply to data to transform into a format expected by a GMLS stencil.
Definition at line 1191 of file Compadre_GMLS.cpp.
|
inlinestaticprotected |
Parses a string to determine constraint type.
Definition at line 603 of file Compadre_GMLS.hpp.
|
inlinestaticprotected |
Parses a string to determine problem type.
Definition at line 590 of file Compadre_GMLS.hpp.
|
inlinestaticprotected |
Parses a string to determine solver type.
Definition at line 577 of file Compadre_GMLS.hpp.
|
inline |
Definition at line 1282 of file Compadre_GMLS.hpp.
|
inline |
(OPTIONAL) Sets additional evaluation sites for each target site
Definition at line 1316 of file Compadre_GMLS.hpp.
|
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(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 1594 of file Compadre_GMLS.hpp.
|
inline |
(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 1623 of file Compadre_GMLS.hpp.
|
inline |
(OPTIONAL) Sets the additional target evaluation coordinate 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 1632 of file Compadre_GMLS.hpp.
|
inline |
(OPTIONAL) Sets the additional target evaluation coordinate 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 1674 of file Compadre_GMLS.hpp.
|
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Sets basis order to be used when reoncstructing curvature.
Definition at line 1751 of file Compadre_GMLS.hpp.
|
inline |
Power for weighting kernel for curvature.
Definition at line 1763 of file Compadre_GMLS.hpp.
|
inline |
Type for weighting kernel for curvature.
Definition at line 1721 of file Compadre_GMLS.hpp.
|
inline |
Type for weighting kernel for curvature.
Definition at line 1738 of file Compadre_GMLS.hpp.
|
inline |
Dimensions of quadrature points to use.
Definition at line 1775 of file Compadre_GMLS.hpp.
|
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Sets neighbor list information from compressed row neighborhood lists data (if same view_type).
Definition at line 1326 of file Compadre_GMLS.hpp.
|
inline |
Sets neighbor list information from compressed row neighborhood lists data (if different view_type).
Definition at line 1342 of file Compadre_GMLS.hpp.
|
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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 1364 of file Compadre_GMLS.hpp.
|
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Number quadrature points to use.
Definition at line 1769 of file Compadre_GMLS.hpp.
|
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Sets basis order to be used when reoncstructing any function.
Definition at line 1744 of file Compadre_GMLS.hpp.
|
inline |
Sets basic problem data (neighbor lists, source coordinates, and target coordinates)
Definition at line 1289 of file Compadre_GMLS.hpp.
|
inline |
Sets basic problem data (neighbor lists data, number of neighbors list, source coordinates, and target coordinates)
Definition at line 1302 of file Compadre_GMLS.hpp.
|
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Type of quadrature points.
Definition at line 1781 of file Compadre_GMLS.hpp.
|
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(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 1516 of file Compadre_GMLS.hpp.
|
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(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances.
Definition at line 1544 of file Compadre_GMLS.hpp.
|
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(OPTIONAL) Sets extra data to be used by sampling functionals in certain instances.
(device)
Definition at line 1559 of file Compadre_GMLS.hpp.
|
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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 1380 of file Compadre_GMLS.hpp.
|
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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 1408 of file Compadre_GMLS.hpp.
|
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(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 1482 of file Compadre_GMLS.hpp.
|
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(OPTIONAL) Sets extra data to be used by target operations in certain instances.
Definition at line 1568 of file Compadre_GMLS.hpp.
|
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(OPTIONAL) Sets extra data to be used by target operations in certain instances.
(device)
Definition at line 1583 of file Compadre_GMLS.hpp.
|
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Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists.
Definition at line 1416 of file Compadre_GMLS.hpp.
|
inline |
Sets target coordinate information. Rows of this 2D-array should correspond to rows of the neighbor lists.
Definition at line 1445 of file Compadre_GMLS.hpp.
|
inline |
Power for weighting kernel for GMLS problem.
Definition at line 1757 of file Compadre_GMLS.hpp.
|
inline |
Type for weighting kernel for GMLS problem.
Definition at line 1698 of file Compadre_GMLS.hpp.
|
inline |
Type for weighting kernel for GMLS problem.
Definition at line 1715 of file Compadre_GMLS.hpp.
|
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Sets window sizes, also called the support of the kernel.
Definition at line 1456 of file Compadre_GMLS.hpp.
|
inline |
Sets window sizes, also called the support of the kernel (device)
Definition at line 1470 of file Compadre_GMLS.hpp.
|
inlinestatic |
Evaluates the weighting kernel.
| 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.. |
| power | [in] - power parameter to be given to the kernel. |
Definition at line 855 of file Compadre_GMLS.hpp.
|
protected |
additional alpha coefficients due to constraints
Definition at line 266 of file Compadre_GMLS.hpp.
|
protected |
(OPTIONAL) user provided additional coordinates for target operation evaluation (device)
Definition at line 106 of file Compadre_GMLS.hpp.
|
protected |
(OPTIONAL) contains indices of entries in the _additional_evaluation_coordinates view (device)
Definition at line 109 of file Compadre_GMLS.hpp.
|
protected |
generated alpha coefficients (device)
Definition at line 92 of file Compadre_GMLS.hpp.
|
protected |
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 183 of file Compadre_GMLS.hpp.
|
protected |
constraint type for GMLS problem
Definition at line 149 of file Compadre_GMLS.hpp.
|
protected |
order of basis for curvature reconstruction
Definition at line 122 of file Compadre_GMLS.hpp.
|
protected |
vector containing target functionals to be applied for curvature
Definition at line 159 of file Compadre_GMLS.hpp.
|
protected |
power to be used for weighting kernel for curvature
Definition at line 179 of file Compadre_GMLS.hpp.
|
protected |
weighting kernel type for curvature problem
Definition at line 173 of file Compadre_GMLS.hpp.
|
protected |
generally the same as _polynomial_sampling_functional, but can differ if specified at GMLS class instantiation
Definition at line 156 of file Compadre_GMLS.hpp.
|
protected |
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 192 of file Compadre_GMLS.hpp.
|
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solver type for GMLS problem - can be QR, SVD or LU
Definition at line 143 of file Compadre_GMLS.hpp.
|
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dimension of quadrature rule
Definition at line 275 of file Compadre_GMLS.hpp.
|
protected |
dimension of the problem, set at class instantiation only
Definition at line 134 of file Compadre_GMLS.hpp.
|
protected |
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 211 of file Compadre_GMLS.hpp.
|
protected |
h supports determined through neighbor search (device)
Definition at line 86 of file Compadre_GMLS.hpp.
|
protected |
spatial dimension of the points, set at class instantiation only
Definition at line 128 of file Compadre_GMLS.hpp.
|
protected |
(OPTIONAL) contains indices of entries in the _additional_evaluation_coordinates view (host)
Definition at line 112 of file Compadre_GMLS.hpp.
|
protected |
generated alpha coefficients (host)
Definition at line 95 of file Compadre_GMLS.hpp.
|
protected |
h supports determined through neighbor search (host)
Definition at line 89 of file Compadre_GMLS.hpp.
|
protected |
tensor rank of sampling functional (host)
Definition at line 260 of file Compadre_GMLS.hpp.
|
protected |
dimensions ^ rank of tensor of output for each sampling functional (host)
Definition at line 248 of file Compadre_GMLS.hpp.
|
protected |
tensor rank of target functional (host)
Definition at line 254 of file Compadre_GMLS.hpp.
|
protected |
dimensions ^ rank of tensor of output for each target functional (host)
Definition at line 242 of file Compadre_GMLS.hpp.
|
protected |
index for where this operation begins the for _alpha coefficients (host)
Definition at line 236 of file Compadre_GMLS.hpp.
|
protected |
convenient copy on host of number of neighbors
Definition at line 77 of file Compadre_GMLS.hpp.
|
protected |
vector containing target functionals to be applied for reconstruction problem (host)
Definition at line 165 of file Compadre_GMLS.hpp.
|
protected |
generated weights for nontraditional samples required to transform data into expected sampling functional form (host)
Definition at line 103 of file Compadre_GMLS.hpp.
|
protected |
reference outward normal vectors information (host)
Definition at line 56 of file Compadre_GMLS.hpp.
|
protected |
tangent vectors information (host)
Definition at line 53 of file Compadre_GMLS.hpp.
|
protected |
initial index for current batch
Definition at line 217 of file Compadre_GMLS.hpp.
|
protected |
dimension of the problem, set at class instantiation only. For manifolds, generally _global_dimensions-1
Definition at line 131 of file Compadre_GMLS.hpp.
|
protected |
vector of user requested target operations
Definition at line 226 of file Compadre_GMLS.hpp.
|
protected |
tensor rank of sampling functional (device)
Definition at line 257 of file Compadre_GMLS.hpp.
|
protected |
dimensions ^ rank of tensor of output for each sampling functional (device)
Definition at line 245 of file Compadre_GMLS.hpp.
|
protected |
vector containing a mapping from a target functionals enum value to the its place in the list of target functionals to be applied
Definition at line 230 of file Compadre_GMLS.hpp.
|
protected |
tensor rank of target functional (device)
Definition at line 251 of file Compadre_GMLS.hpp.
|
protected |
dimensions ^ rank of tensor of output for each target functional (device)
Definition at line 239 of file Compadre_GMLS.hpp.
|
protected |
index for where this operation begins the for _alpha coefficients (device)
Definition at line 233 of file Compadre_GMLS.hpp.
|
protected |
curvature polynomial coefficients for all problems
Definition at line 62 of file Compadre_GMLS.hpp.
|
protected |
_dimension-1 gradient values for curvature for all problems
Definition at line 65 of file Compadre_GMLS.hpp.
|
protected |
metric tensor inverse for all problems
Definition at line 59 of file Compadre_GMLS.hpp.
|
protected |
maximum number of evaluation sites for each target (includes target site)
Definition at line 223 of file Compadre_GMLS.hpp.
|
protected |
maximum number of neighbors over all target sites
Definition at line 220 of file Compadre_GMLS.hpp.
|
protected |
Accessor to get neighbor list data, offset data, and number of neighbors per target.
Definition at line 74 of file Compadre_GMLS.hpp.
|
protected |
whether or not operator to be inverted for GMLS problem has a nontrivial nullspace (requiring SVD)
Definition at line 195 of file Compadre_GMLS.hpp.
|
protected |
dimension of basis for polynomial reconstruction
Definition at line 125 of file Compadre_GMLS.hpp.
|
protected |
(OPTIONAL) contains the # of additional coordinate indices for each target
Definition at line 115 of file Compadre_GMLS.hpp.
|
protected |
vector containing target functionals to be applied for reconstruction problem (device)
Definition at line 162 of file Compadre_GMLS.hpp.
|
protected |
order of exact polynomial integration for quadrature rule
Definition at line 272 of file Compadre_GMLS.hpp.
|
protected |
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 200 of file Compadre_GMLS.hpp.
|
protected |
P*sqrt(w) matrix for all problems.
Definition at line 38 of file Compadre_GMLS.hpp.
|
protected |
determines scratch level spaces and is used to call kernels
Definition at line 269 of file Compadre_GMLS.hpp.
|
protected |
order of basis for polynomial reconstruction
Definition at line 119 of file Compadre_GMLS.hpp.
|
protected |
polynomial sampling functional used to construct P matrix, set at GMLS class instantiation
Definition at line 152 of file Compadre_GMLS.hpp.
|
protected |
generated weights for nontraditional samples required to transform data into expected sampling functional form (device).
Definition at line 99 of file Compadre_GMLS.hpp.
|
protected |
problem type for GMLS problem, can also be set to STANDARD for normal or MANIFOLD for manifold problems
Definition at line 146 of file Compadre_GMLS.hpp.
|
protected |
manages and calculates quadrature
Definition at line 281 of file Compadre_GMLS.hpp.
|
protected |
quadrature rule type
Definition at line 278 of file Compadre_GMLS.hpp.
|
protected |
Definition at line 29 of file Compadre_GMLS.hpp.
|
protected |
reconstruction space for GMLS problems, set at GMLS class instantiation
Definition at line 137 of file Compadre_GMLS.hpp.
|
protected |
actual rank of reconstruction basis
Definition at line 140 of file Compadre_GMLS.hpp.
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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 50 of file Compadre_GMLS.hpp.
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whether or not the reference outward normal directions were provided by the user.
Definition at line 203 of file Compadre_GMLS.hpp.
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sqrt(w)*Identity matrix for all problems, later holds polynomial coefficients for all problems
Definition at line 41 of file Compadre_GMLS.hpp.
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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 188 of file Compadre_GMLS.hpp.
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all coordinates for the source for which _neighbor_lists refers (device)
Definition at line 80 of file Compadre_GMLS.hpp.
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Extra data available to basis functions (optional)
Definition at line 68 of file Compadre_GMLS.hpp.
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whether polynomial coefficients were requested to be stored (in a state not yet applied to data)
Definition at line 214 of file Compadre_GMLS.hpp.
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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 46 of file Compadre_GMLS.hpp.
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coordinates for target sites for reconstruction (device)
Definition at line 83 of file Compadre_GMLS.hpp.
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Extra data available to target operations (optional)
Definition at line 71 of file Compadre_GMLS.hpp.
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used for sizing P_target_row and the _alphas view
Definition at line 263 of file Compadre_GMLS.hpp.
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whether or not to use reference outward normal directions to orient the surface in a manifold problem.
Definition at line 206 of file Compadre_GMLS.hpp.
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contains weights for all problems
Definition at line 35 of file Compadre_GMLS.hpp.
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power to be used for weighting kernel
Definition at line 176 of file Compadre_GMLS.hpp.
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weighting kernel type for GMLS
Definition at line 170 of file Compadre_GMLS.hpp.
1.8.5
