Namespace of RBF interpolation. More...

Namespaces
namespace	concepts
	Namespace of C++ concepts.

namespace	distance_functions
	Namespace of distance functions for RBF interpolation.

namespace	impl
	Namespace of internal implementations.

namespace	length_parameter_calculators
	Namespace of calculators of length parameters.

namespace	rbfs
	Namespace of RBFs.

Classes
class	gaussian_process_interpolator
	Class to interpolate using Gaussian process. More...

class	polynomial_calculator
	Class to calculate polynomials used with RBF interpolation. More...

class	polynomial_calculator< Variable, PolynomialDegree >
	Class to calculate polynomials used with RBF interpolation. More...

class	rbf_interpolator
	Class to interpolate using RBF. More...

class	rbf_interpolator< FunctionValue(Variable), RBF, KernelMatrixType, DistanceFunction, LengthParameterCalculator >
	Class to interpolate using RBF. More...

class	rbf_polynomial_interpolator
	Class to interpolate using RBF and polynomials. More...

class	rbf_polynomial_interpolator< FunctionValue(Variable), RBF, PolynomialDegree, KernelMatrixType, DistanceFunction, LengthParameterCalculator >
	Class to interpolate using RBF and polynomials. More...

Typedefs
template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>
using	global_rbf_interpolator
	Class to interpolate using RBF with globally fixed length parameters.

template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, index_type PolynomialDegree = 1, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>
using	global_rbf_polynomial_interpolator
	Class to interpolate using RBF and polynomials with globally fixed length parameters.

template<typename FunctionSignature , concepts::rbf RBF = rbfs::wendland_csrbf< impl::get_default_scalar_type<FunctionSignature>, 3, 1>, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>
using	local_csrbf_interpolator
	Class to interpolate using compactly supported RBF with length parameters localized for sample points.

template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>
using	local_rbf_interpolator
	Class to interpolate using RBF with length parameters localized for sample points.

Enumerations
enum class	kernel_matrix_type : std::uint8_t { dense , sparse }
	Enumeration of types of kernel matrices. More...

Functions
template<concepts::distance_function DistanceFunction, concepts::rbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::dense_matrix KernelMatrix> requires LengthParameterCalculator::uses_global_length_parameter
void	compute_kernel_matrix (const DistanceFunction &distance_function, const RBF &rbf, LengthParameterCalculator &length_parameter_calculator, const std::vector< typename DistanceFunction::variable_type > &variables, KernelMatrix &kernel_matrix)
	Compute a kernel matrix.

template<concepts::distance_function DistanceFunction, concepts::rbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::dense_matrix KernelMatrix> requires std::is_same_v< typename LengthParameterCalculator::distance_function_type, DistanceFunction> && std::is_same_v<typename DistanceFunction::value_type, typename RBF::scalar_type> && std::is_same_v<typename DistanceFunction::value_type, typename KernelMatrix::Scalar> && (!LengthParameterCalculator::uses_global_length_parameter)
void	compute_kernel_matrix (const DistanceFunction &distance_function, const RBF &rbf, LengthParameterCalculator &length_parameter_calculator, const std::vector< typename DistanceFunction::variable_type > &variables, KernelMatrix &kernel_matrix)
	Compute a kernel matrix.

template<concepts::distance_function DistanceFunction, concepts::csrbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::sparse_matrix_of< typename DistanceFunction::value_type > KernelMatrix> requires std::is_same_v< typename LengthParameterCalculator::distance_function_type, DistanceFunction> && std::is_same_v<typename DistanceFunction::value_type, typename RBF::scalar_type> && std::is_same_v<typename DistanceFunction::value_type, typename KernelMatrix::Scalar>
void	compute_kernel_matrix (const DistanceFunction &distance_function, const RBF &rbf, LengthParameterCalculator &length_parameter_calculator, const std::vector< typename DistanceFunction::variable_type > &variables, KernelMatrix &kernel_matrix)
	Compute a kernel matrix.

template<index_type PolynomialDegree, base::concepts::real_scalar Variable, base::concepts::dense_matrix_of< Variable > Matrix> requires (PolynomialDegree >= 0)
void	compute_polynomial_term_matrix (const std::vector< Variable > &variables, Matrix &matrix)
	Compute a matrix of polynomial terms in RBF interpolation.

template<base::concepts::real_scalar Scalar>
auto	generate_1d_halton_nodes (index_type num_nodes) -> std::vector< Scalar >
	Generate Halton nodes in 1 dimension [6].

template<base::concepts::real_scalar Scalar, index_type Dimensions>
auto	generate_halton_nodes (index_type num_nodes) -> std::vector< Eigen::Vector< Scalar, Dimensions > >
	Generate Halton nodes [6].

Variables
constexpr auto	rbf_interpolator_tag
	Tag of rbf_interpolator.

constexpr auto	rbf_polynomial_interpolator_tag
	Tag of rbf_polynomial_interpolator.

Detailed Description

Namespace of RBF interpolation.

Typedef Documentation

◆ global_rbf_interpolator

template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>

using num_collect::rbf::global_rbf_interpolator

Initial value:

 
    rbf_interpolator<FunctionSignature, RBF, KernelMatrixType, DistanceFunction,
        length_parameter_calculators::global_length_parameter_calculator<
            DistanceFunction>>

Class to interpolate using RBF with globally fixed length parameters.

Template Parameters

FunctionSignature	Signature of the function to interpolate. (Example: `double(double)`, `double(Eigen::Vector3d)`, ...)
RBF	Type of the RBF.
KernelMatrixType	Type of kernel matrices.
DistanceFunction	Type of the distance function.

Definition at line 388 of file rbf_interpolator.h.

◆ global_rbf_polynomial_interpolator

template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, index_type PolynomialDegree = 1, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>

using num_collect::rbf::global_rbf_polynomial_interpolator

Initial value:

 
    rbf_polynomial_interpolator<FunctionSignature, RBF, PolynomialDegree,
        KernelMatrixType, DistanceFunction,
        length_parameter_calculators::global_length_parameter_calculator<
            DistanceFunction>>

Class to interpolate using RBF and polynomials with globally fixed length parameters.

Template Parameters

FunctionSignature	Signature of the function to interpolate. (Example: `double(double)`, `double(Eigen::Vector3d)`, ...)
RBF	Type of the RBF.
PolynomialDegree	Degree of the polynomial.
KernelMatrixType	Type of kernel matrices.
DistanceFunction	Type of the distance function.

Definition at line 391 of file rbf_polynomial_interpolator.h.

◆ local_csrbf_interpolator

template<typename FunctionSignature , concepts::rbf RBF = rbfs::wendland_csrbf< impl::get_default_scalar_type<FunctionSignature>, 3, 1>, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>

using num_collect::rbf::local_csrbf_interpolator

Initial value:

 rbf_interpolator<FunctionSignature, RBF,
    kernel_matrix_type::sparse, DistanceFunction,
    length_parameter_calculators::local_length_parameter_calculator<
        DistanceFunction>>

Class to interpolate using compactly supported RBF with length parameters localized for sample points.

Template Parameters

FunctionSignature	Signature of the function to interpolate. (Example: `double(double)`, `double(Eigen::Vector3d)`, ...)
RBF	Type of the RBF.
DistanceFunction	Type of the distance function.

Definition at line 408 of file rbf_interpolator.h.

◆ local_rbf_interpolator

template<typename FunctionSignature , concepts::rbf RBF = rbfs::gaussian_rbf<impl::get_default_scalar_type<FunctionSignature>>, kernel_matrix_type KernelMatrixType = kernel_matrix_type::dense, concepts::distance_function DistanceFunction = distance_functions::euclidean_distance_function< impl::get_variable_type_t<FunctionSignature>>>

using num_collect::rbf::local_rbf_interpolator

Initial value:

 
    rbf_interpolator<FunctionSignature, RBF, KernelMatrixType, DistanceFunction,
        length_parameter_calculators::local_length_parameter_calculator<
            DistanceFunction>>

Class to interpolate using RBF with length parameters localized for sample points.

Template Parameters

FunctionSignature	Signature of the function to interpolate. (Example: `double(double)`, `double(Eigen::Vector3d)`, ...)
RBF	Type of the RBF.
KernelMatrixType	Type of kernel matrices.
DistanceFunction	Type of the distance function.

Definition at line 367 of file rbf_interpolator.h.

Enumeration Type Documentation

◆ kernel_matrix_type

enum class num_collect::rbf::kernel_matrix_type : std::uint8_t

strong

Enumeration of types of kernel matrices.

Enumerator
dense	Dense matrix.
sparse	Sparse matrix.

Definition at line 29 of file kernel_matrix_type.h.

Function Documentation

◆ compute_kernel_matrix() [1/3]

template<concepts::distance_function DistanceFunction, concepts::rbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::dense_matrix KernelMatrix>
requires LengthParameterCalculator::uses_global_length_parameter

void num_collect::rbf::compute_kernel_matrix	(	const DistanceFunction &	distance_function,
		const RBF &	rbf,
		LengthParameterCalculator &	length_parameter_calculator,
		const std::vector< typename DistanceFunction::variable_type > &	variables,
		KernelMatrix &	kernel_matrix )

inline

Compute a kernel matrix.

Template Parameters

DistanceFunction	Type of the distance function.
RBF	Type of the RBF.
LengthParameterCalculator	Type of the calculator of length parameters.
KernelMatrix	Type of the kernel matrix.

Parameters

[in]	distance_function	Distance function.
[in]	rbf	RBF.
[in,out]	length_parameter_calculator	Calculator of length parameters.
[in]	variables	Variables.
[out]	kernel_matrix	Kernel matrix.

Definition at line 66 of file compute_kernel_matrix.h.

◆ compute_kernel_matrix() [2/3]

template<concepts::distance_function DistanceFunction, concepts::rbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::dense_matrix KernelMatrix>
requires std::is_same_v< typename LengthParameterCalculator::distance_function_type, DistanceFunction> && std::is_same_v<typename DistanceFunction::value_type, typename RBF::scalar_type> && std::is_same_v<typename DistanceFunction::value_type, typename KernelMatrix::Scalar> && (!LengthParameterCalculator::uses_global_length_parameter)

void num_collect::rbf::compute_kernel_matrix	(	const DistanceFunction &	distance_function,
		const RBF &	rbf,
		LengthParameterCalculator &	length_parameter_calculator,
		const std::vector< typename DistanceFunction::variable_type > &	variables,
		KernelMatrix &	kernel_matrix )

inline

Compute a kernel matrix.

Template Parameters

DistanceFunction	Type of the distance function.
RBF	Type of the RBF.
LengthParameterCalculator	Type of the calculator of length parameters.
KernelMatrix	Type of the kernel matrix.

Parameters

[in]	distance_function	Distance function.
[in]	rbf	RBF.
[in,out]	length_parameter_calculator	Calculator of length parameters.
[in]	variables	Variables.
[out]	kernel_matrix	Kernel matrix.

Definition at line 125 of file compute_kernel_matrix.h.

◆ compute_kernel_matrix() [3/3]

template<concepts::distance_function DistanceFunction, concepts::csrbf RBF, concepts::length_parameter_calculator LengthParameterCalculator, base::concepts::sparse_matrix_of< typename DistanceFunction::value_type > KernelMatrix>
requires std::is_same_v< typename LengthParameterCalculator::distance_function_type, DistanceFunction> && std::is_same_v<typename DistanceFunction::value_type, typename RBF::scalar_type> && std::is_same_v<typename DistanceFunction::value_type, typename KernelMatrix::Scalar>

void num_collect::rbf::compute_kernel_matrix	(	const DistanceFunction &	distance_function,
		const RBF &	rbf,
		LengthParameterCalculator &	length_parameter_calculator,
		const std::vector< typename DistanceFunction::variable_type > &	variables,
		KernelMatrix &	kernel_matrix )

inline

Compute a kernel matrix.

Template Parameters

DistanceFunction	Type of the distance function.
RBF	Type of the RBF.
LengthParameterCalculator	Type of the calculator of length parameters.
KernelMatrix	Type of the kernel matrix.

Parameters

[in]	distance_function	Distance function.
[in]	rbf	RBF.
[in,out]	length_parameter_calculator	Calculator of length parameters.
[in]	variables	Variables.
[out]	kernel_matrix	Kernel matrix.

Definition at line 178 of file compute_kernel_matrix.h.

◆ compute_polynomial_term_matrix()

template<index_type PolynomialDegree, base::concepts::real_scalar Variable, base::concepts::dense_matrix_of< Variable > Matrix>
requires (PolynomialDegree >= 0)

void num_collect::rbf::compute_polynomial_term_matrix	(	const std::vector< Variable > &	variables,
		Matrix &	matrix )

inline

Compute a matrix of polynomial terms in RBF interpolation.

Template Parameters

PolynomialDegree	Degree of polynomials.
Variable	Type of variables.
Matrix	Type of the matrix.

Parameters

[in]	variables	Variables.
[out]	matrix	Matrix.

Definition at line 47 of file compute_polynomial_term_matrix.h.

◆ generate_1d_halton_nodes()

template<base::concepts::real_scalar Scalar>

auto num_collect::rbf::generate_1d_halton_nodes ( index_type num_nodes ) -> std::vector<Scalar>

nodiscard

Generate Halton nodes in 1 dimension [6].

Template Parameters

Scalar Type of scalars.

Parameters

[in] num_nodes Number of nodes.

Returns: Generated nodes.

Definition at line 122 of file generate_halton_nodes.h.

◆ generate_halton_nodes()

template<base::concepts::real_scalar Scalar, index_type Dimensions>

auto num_collect::rbf::generate_halton_nodes ( index_type num_nodes ) -> std::vector<Eigen::Vector<Scalar, Dimensions>>

nodiscard

Generate Halton nodes [6].

Template Parameters

Scalar	Type of scalars.
Dimensions	Number of dimensions of the space in which nodes are generated.

Parameters

[in] num_nodes Number of nodes.

Returns: Generated nodes.

Definition at line 90 of file generate_halton_nodes.h.

Variable Documentation

◆ rbf_interpolator_tag

auto num_collect::rbf::rbf_interpolator_tag

constexpr

Initial value:

=

logging::log_tag_view("num_collect::rbf::rbf_interpolator")

Tag of rbf_interpolator.

Definition at line 52 of file rbf_interpolator.h.

◆ rbf_polynomial_interpolator_tag

auto num_collect::rbf::rbf_polynomial_interpolator_tag

constexpr

Initial value:

=

logging::log_tag_view("num_collect::rbf::rbf_polynomial_interpolator")

Tag of rbf_polynomial_interpolator.

Definition at line 54 of file rbf_polynomial_interpolator.h.

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ global_rbf_interpolator

◆ global_rbf_polynomial_interpolator

◆ local_csrbf_interpolator

◆ local_rbf_interpolator

Enumeration Type Documentation

◆ kernel_matrix_type

Function Documentation

◆ compute_kernel_matrix() [1/3]

◆ compute_kernel_matrix() [2/3]

◆ compute_kernel_matrix() [3/3]

◆ compute_polynomial_term_matrix()

◆ generate_1d_halton_nodes()

◆ generate_halton_nodes()

Variable Documentation

◆ rbf_interpolator_tag

◆ rbf_polynomial_interpolator_tag