#include <RBFBasis_fwd.hpp>

Detailed Description

template<class RBFType, class vec_t>
class mm::RBFBasis< RBFType, vec_t >

Represents a basis of Radial Basis Functions over a local neighbourhood.

Template Parameters

RBFType	Type of the RBF used. Must satisfy the Radial Basis Function concept.
vec_t	Vector type used in calculations.

This class satisfies the Basis function concept.

Usage example:

    Gaussian<double> g(1.3);
    RBFBasis<Gaussian<double>, Vec2d> basis(3, g);  // construct
    std::cout << basis << std::endl;
    Range<Vec2d> support = {{0.1, 2.3}, {0.2, 2.2}, {0.0, 2.25}};
    double val = basis.eval(1, 0.05, support);  // evaluate
    double der = basis.evalOp(1, 0.05, Lap<2>(), support);  // evaluate derivative

Definition at line 30 of file RBFBasis_fwd.hpp.

Public Member Functions
	RBFBasis (int basis_size)
	Construct a basis of `basis_size` with default construction of RBF. More...

	RBFBasis (int basis_size, const rbf_t &rbf)
	Construct a basis of `basis_size` with given RBF. More...

int	size () const
	Returns basis size. More...

const rbf_t &	rbf () const
	Returns underlying RBF object. More...

rbf_t &	rbf ()
	Returns modifiable underlying RBF object. More...

scalar_t	eval (int index, const vector_t &point, const std::vector< vector_t > &support) const
	Evaluates `index`-th RBF's at `point`. More...

template<typename operator_t >
scalar_t	evalOp (int index, const vector_t &point, operator_t op, const std::vector< vector_t > &support, scalar_t scale=1) const
	Apply an operator at a given point. More...

scalar_t	evalOp (int index, const vector_t &point, Lap< dim > op, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate Laplacian. More...

scalar_t	evalOp (int index, const vector_t &point, Der1< dim > op, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate 1st derivative. More...

scalar_t	evalOp (int index, const vector_t &point, Der2< dim > op, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate 2nd derivative. More...

scalar_t	evalAt0 (int index, const std::vector< vector_t > &support) const
	Evaluate `index`-th function at zero. More...

template<typename operator_t >
scalar_t	evalOpAt0 (int index, const operator_t&op, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate general operator `op` at zero. More...

scalar_t	evalOpAt0 (int index, const Lap< dim > &lap, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate Laplacian `lap` at zero. More...

scalar_t	evalOpAt0 (int index, const Der1< dim > &der1, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate first derivative operator `der1` at zero. More...

scalar_t	evalOpAt0 (int index, const Der2< dim > &der2, const std::vector< vector_t > &support, scalar_t scale=1) const
	Evaluate second derivative operator `der2` at zero. More...

Public Types
enum	{ dim = vec_t::dim }
	Store dimension of the domain. More...

typedef RBFType	rbf_t
	Radial basis function type. More...

typedef vec_t	vector_t
	Vector type. More...

typedef vector_t::scalar_t	scalar_t
	Scalar type. More...

Friends
template<typename V , typename R >
std::ostream &	operator<< (std::ostream &os, const RBFBasis< V, R > &m)
	Output basic info about given basis. More...

Private Attributes
int	size_
	Basis size. More...

rbf_t	rbf_
	RBF function. More...

Member Enumeration Documentation

◆ anonymous enum

template<class RBFType , class vec_t >

anonymous enum

Store dimension of the domain.

Enumerator
dim	Dimensionality of the function domain.

Definition at line 38 of file RBFBasis_fwd.hpp.

Constructor & Destructor Documentation

◆ RBFBasis() [1/2]

template<class RBFType , class vec_t >

mm::RBFBasis< RBFType, vec_t >::RBFBasis ( int basis_size )

inlineexplicit

Construct a basis of basis_size with default construction of RBF.

Definition at line 46 of file RBFBasis_fwd.hpp.

◆ RBFBasis() [2/2]

template<class RBFType , class vec_t >

mm::RBFBasis< RBFType, vec_t >::RBFBasis	(	int	basis_size,
		const rbf_t &	rbf
	)

inline

Construct a basis of basis_size with given RBF.

Definition at line 48 of file RBFBasis_fwd.hpp.

Member Function Documentation

◆ eval()

template<class RBFType , class vec_t >

scalar_t mm::RBFBasis< RBFType, vec_t >::eval	(	int	index,
		const vector_t &	point,
		const std::vector< vector_t > &	support
	)		const

Evaluates index-th RBF's at point.

Parameters

index	A number in `[0, size())` specifying the index of RBF to evaluate.
point	Point in which to evaluate the RBF.
support	Points in local neighbourhood used as centers for RBFs.

Returns: Value of requested monomial at given point.

Exceptions

Assertion fails if index is out of range or if an invalid derivative is requested.

Note: Derivatives only up to combined order of 2 are currently supported.

◆ evalAt0()

template<class vec_t , class RBFType >

RBFBasis< vec_t, RBFType >::scalar_t mm::RBFBasis< vec_t, RBFType >::evalAt0	(	int	index,
		const std::vector< vector_t > &	support
	)		const

Evaluate index-th function at zero.

Definition at line 74 of file RBFBasis.hpp.

◆ evalOp() [1/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOp	(	int	index,
		const vector_t &	point,
		Der1< dim >	op,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate 1st derivative.

See also: evalOp

Definition at line 45 of file RBFBasis.hpp.

◆ evalOp() [2/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOp	(	int	index,
		const vector_t &	point,
		Der2< dim >	op,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate 2nd derivative.

See also: evalOp

Definition at line 57 of file RBFBasis.hpp.

◆ evalOp() [3/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOp	(	int	index,
		const vector_t &	point,
		Lap< dim >	op,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate Laplacian.

See also: evalOp

Definition at line 34 of file RBFBasis.hpp.

◆ evalOp() [4/4]

template<class RBFType , class vec_t >

template<typename operator_t >

scalar_t mm::RBFBasis< RBFType, vec_t >::evalOp	(	int	index,
		const vector_t &	point,
		operator_t	op,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Apply an operator at a given point.

For \(\frac{d}{dx}\), the function computes \( \frac{d}{dx} p_i(x_s), x_s = \frac{x - c}{s} \).

Parameters

index	A number in `[0, size())` specifying the index of a monomial to evaluate.
point	Translated and scaled point \(x_s\) at which the basis function is evaluated.
op	The differential operator.
support	Translated and scaled values of nodes in the support domain.
scale	The scaling factor \(s\).

Returns: Value of the operator applied to index-th basis function at point point.

Exceptions

Assertion fails if index is out of range.

See also: Operator, Lap, Der1, Der2

◆ evalOpAt0() [1/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOpAt0	(	int	index,
		const Der1< dim > &	der1,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate first derivative operator der1 at zero.

Definition at line 95 of file RBFBasis.hpp.

◆ evalOpAt0() [2/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOpAt0	(	int	index,
		const Der2< dim > &	der2,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate second derivative operator der2 at zero.

Definition at line 114 of file RBFBasis.hpp.

◆ evalOpAt0() [3/4]

template<class RBFType , class vec_t >

vec_t::scalar_t mm::RBFBasis< RBFType, vec_t >::evalOpAt0	(	int	index,
		const Lap< dim > &	lap,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

Evaluate Laplacian lap at zero.

Definition at line 85 of file RBFBasis.hpp.

◆ evalOpAt0() [4/4]

template<class RBFType , class vec_t >

template<typename operator_t >

scalar_t mm::RBFBasis< RBFType, vec_t >::evalOpAt0	(	int	index,
		const operator_t&	op,
		const std::vector< vector_t > &	support,
		scalar_t	scale = `1`
	)		const

inline

Evaluate general operator op at zero.

Parameters

index	A number in `[0, size())` specifying the index of RBF to evaluate.
op	Evaluated operator.
support	Points in local neighbourhood used as centers for RBFs.
scale	Scaling factor.

Returns: Value of requested monomial at given point.

Exceptions

Assertion fails if index is out of range or if an invalid derivative is requested.

Definition at line 115 of file RBFBasis_fwd.hpp.

◆ rbf() [1/2]

template<class RBFType , class vec_t >

rbf_t& mm::RBFBasis< RBFType, vec_t >::rbf ( )

inline

Returns modifiable underlying RBF object.

Definition at line 57 of file RBFBasis_fwd.hpp.

◆ rbf() [2/2]

template<class RBFType , class vec_t >

const rbf_t& mm::RBFBasis< RBFType, vec_t >::rbf ( ) const

inline

Returns underlying RBF object.

Definition at line 54 of file RBFBasis_fwd.hpp.

◆ size()

template<class RBFType , class vec_t >

int mm::RBFBasis< RBFType, vec_t >::size ( ) const

inline

Returns basis size.

Definition at line 51 of file RBFBasis_fwd.hpp.

Friends And Related Function Documentation

◆ operator<<

template<class RBFType , class vec_t >

template<typename V , typename R >

std::ostream& operator<<	(	std::ostream &	os,
		const RBFBasis< V, R > &	m
	)

friend

Output basic info about given basis.

Definition at line 139 of file RBFBasis.hpp.

Member Data Documentation

◆ rbf_

template<class RBFType , class vec_t >

rbf_t mm::RBFBasis< RBFType, vec_t >::rbf_

private

RBF function.

Definition at line 42 of file RBFBasis_fwd.hpp.

◆ size_

template<class RBFType , class vec_t >

int mm::RBFBasis< RBFType, vec_t >::size_

private

Basis size.

Definition at line 41 of file RBFBasis_fwd.hpp.

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

include/medusa/bits/approximations/RBFBasis_fwd.hpp
include/medusa/bits/approximations/RBFBasis.hpp

Detailed Description

template<class RBFType, class vec_t> class mm::RBFBasis< RBFType, vec_t >

Public Member Functions

Public Types

Friends

Private Attributes

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ RBFBasis() [1/2]

◆ RBFBasis() [2/2]

Member Function Documentation

◆ eval()

◆ evalAt0()

◆ evalOp() [1/4]

◆ evalOp() [2/4]

◆ evalOp() [3/4]

◆ evalOp() [4/4]

◆ evalOpAt0() [1/4]

◆ evalOpAt0() [2/4]

◆ evalOpAt0() [3/4]

◆ evalOpAt0() [4/4]

◆ rbf() [1/2]

◆ rbf() [2/2]

◆ size()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ rbf_

◆ size_

template<class RBFType, class vec_t>
class mm::RBFBasis< RBFType, vec_t >