mm::RBFInterpolant< RBFType, vec_t > Class Template Reference

#include <RBFInterpolant_fwd.hpp>

Detailed Description

template<typename RBFType, typename vec_t>
class mm::RBFInterpolant< RBFType, vec_t >

Class representing a RBF Interpolant over a set of nodes of the form.

\[ u(p) = \sum_{i=1}^n \alpha_i \phi\left(\left\|\frac{p - p_i}{s}\right\|\right) + \sum_{i=1}^s \beta_i q_i\left(\frac{p - p_c}{s} \right), \]

where \(\phi\) is the RBF and \(q_i\) are monomials.

Note

This class does not compute the interpolant, that is done by RBFFD::getApproximant.

See also

RBFFD

Template Parameters

basis_t	Radial basis function used. Must satisfy the Radial Basis Function concept.
vec_t	Vector type used.

Usage example:

    double h = 0.1;
    std::vector<Vec2d> pts = {{0, 0}, {0, h}, {0, -h}, {h, 0}, {-h, 0}};
    Eigen::VectorXd values(pts.size()); values << 0.1, 0.1, 0.1, 0.2, 0.0;  // linear function in x
    RBFFD<Gaussian<double>, Vec2d, ScaleToFarthest> approx(1.0, 2);
    auto appr = approx.getApproximant({0, 0}, pts, values);
    double val = appr({h/2, 0});
    double lap = appr({h/2, 0}, Lap<2>());

Definition at line 34 of file RBFInterpolant_fwd.hpp.

Public Member Functions
	RBFInterpolant (const rbf_t &rbf, const Monomials< vec_t > &mon, const vector_t &point, const std::vector< vector_t > &support, scalar_t scale, const Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 > &coefficients)
	Construct a RBF interpolant with known coefficients. More...
scalar_t	operator() (const vector_t &point) const
	Evaluate the interpolant at given point. More...
template<typename operator_t >
scalar_t	operator() (const vector_t &point, const operator_t&op) const
	Evaluate an operator applied to the interpolant at given point. More...
const vector_t &	point () const
	Get the center point. More...
scalar_t	scale () const
	Get the scale. More...
const Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 > &	coefficients () const
	Get the coefficient vector. More...

Public Types
typedef vec_t::scalar_t	scalar_t
	Scalar type. More...
typedef vec_t	vector_t
	Vector type. More...
typedef RBFType	rbf_t
	Radial basis function type. More...

Private Attributes
rbf_t	rbf_
	RBF used for interpolation. More...
Monomials< vec_t >	mon_
	Augmenting monomials. More...
vector_t	point_
	Center point. More...
std::vector< vector_t >	support_
	Local scaled stencil points. More...
scalar_t	scale_
	Scale. More...
Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 >	coefficients_
	Coefficients (for scaled fn.) More...

Constructor & Destructor Documentation

RBFInterpolant()

template<typename RBFType , typename vec_t >

mm::RBFInterpolant< RBFType, vec_t >::RBFInterpolant	(	const rbf_t &	rbf,
		const Monomials< vec_t > &	mon,
		const vector_t &	point,
		const std::vector< vector_t > &	support,
		scalar_t	scale,
		const Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 > &	coefficients
	)

Construct a RBF interpolant with known coefficients.

The interpolant is of the form

\[ u(p) = \sum_{i=1}^n \alpha_i \phi\left(\left\|\frac{p - p_i}{s}\right\|\right) + \sum_{i=1}^s \beta_i q_i\left(\frac{p - p_c}{s} \right), \]

where \(\phi\) is the RBF and \(q_i\) are monomials.

Parameters

rbf	Radial basis function \(\phi\), must satisfy the Radial Basis Function concept.
mon	Monomial basis \(q_i\).
point	Center point \(p_c\) of the RBF interpolation (used for monomial shift).
support	Nonscaled stencil of the RBFFD approximation.
scale	Scale \(s\) used in RBFFD computation, see Scale function concept.
coefficients	The \(n+s\) coefficients \(\alpha_i, \beta_i\) of the approximation.

Definition at line 16 of file RBFInterpolant.hpp.

Member Function Documentation

coefficients()

template<typename RBFType , typename vec_t >

const Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>& mm::RBFInterpolant< RBFType, vec_t >::coefficients ( ) const

inline

Get the coefficient vector.

Definition at line 80 of file RBFInterpolant_fwd.hpp.

operator()() [1/2]

template<typename RBFType , typename vec_t >

vec_t::scalar_t mm::RBFInterpolant< RBFType, vec_t >::operator()

(

const vector_t &

point

)

const

Evaluate the interpolant at given point.

Definition at line 30 of file RBFInterpolant.hpp.

operator()() [2/2]

template<typename RBFType , typename vec_t >

template<typename operator_t >

scalar_t mm::RBFInterpolant< RBFType, vec_t >::operator()	(	const vector_t &	point,
		const operator_t&	op
	)		const

Evaluate an operator applied to the interpolant at given point.

point()

template<typename RBFType , typename vec_t >

const vector_t& mm::RBFInterpolant< RBFType, vec_t >::point ( ) const

inline

Get the center point.

Definition at line 76 of file RBFInterpolant_fwd.hpp.

scale()

template<typename RBFType , typename vec_t >

scalar_t mm::RBFInterpolant< RBFType, vec_t >::scale ( ) const

inline

Get the scale.

Definition at line 78 of file RBFInterpolant_fwd.hpp.

Member Data Documentation

coefficients_

template<typename RBFType , typename vec_t >

Eigen::Matrix<scalar_t, Eigen::Dynamic, 1> mm::RBFInterpolant< RBFType, vec_t >::coefficients_

private

Coefficients (for scaled fn.)

Definition at line 46 of file RBFInterpolant_fwd.hpp.

mon_

template<typename RBFType , typename vec_t >

Monomials<vec_t> mm::RBFInterpolant< RBFType, vec_t >::mon_

private

Augmenting monomials.

Definition at line 42 of file RBFInterpolant_fwd.hpp.

point_

template<typename RBFType , typename vec_t >

vector_t mm::RBFInterpolant< RBFType, vec_t >::point_

private

Center point.

Definition at line 43 of file RBFInterpolant_fwd.hpp.

rbf_

template<typename RBFType , typename vec_t >

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

private

RBF used for interpolation.

Definition at line 41 of file RBFInterpolant_fwd.hpp.

scale_

template<typename RBFType , typename vec_t >

scalar_t mm::RBFInterpolant< RBFType, vec_t >::scale_

private

Scale.

Definition at line 45 of file RBFInterpolant_fwd.hpp.

support_

template<typename RBFType , typename vec_t >

std::vector<vector_t> mm::RBFInterpolant< RBFType, vec_t >::support_

private

Local scaled stencil points.

Definition at line 44 of file RBFInterpolant_fwd.hpp.

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

• include/medusa/bits/approximations/RBFInterpolant_fwd.hpp
• include/medusa/bits/approximations/RBFInterpolant.hpp