#include <WLSApproximant_fwd.hpp>

Detailed Description

template<typename basis_t>
class mm::WLSApproximant< basis_t >

Class representing the function that is a WLS approximant using some basis function over some points.

These must satisfy the Basis function concept.

Note: This class does not compute the approximant, that is done by WLS::getApproximant.

See also: WLS

Template Parameters

basis_t Basis function type.

Usage example:

    double h = 0.1, u1 = 3.23432, u2 = -2.3234, u3 = 0.12443498, u4 = 1.908432, u5 = -0.98742532;
    Vec2d c = {0.05, 0.05};
    std::vector<Vec2d> pts = {{0, 0}, {0, h}, {0, -h}, {h, 0}, {-h, 0}};
    Eigen::VectorXd values(pts.size()); values << u1, u2, u3, u4, u5;
    WLS<Monomials<Vec2d>, GaussianWeight<Vec2d>, ScaleToClosest> wls(1, 1.0);
    auto appr = wls.getApproximant(c, pts, values);
    double value = appr(0);
    double der = appr(0, Der1<2>(1));

Definition at line 27 of file WLSApproximant_fwd.hpp.

Public Member Functions
	WLSApproximant (const basis_t &basis, const vector_t &point, const std::vector< vector_t > &support, scalar_t scale, const Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 > &coefficients, scalar_t residual=NaN)
	Construct a WLS approximant with known coefficients. More...

scalar_t	operator() (const vector_t &point) const
	Evaluate the approximant 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 approximant at given `point`. More...

const basis_t &	basis () const
	Get the basis functions. 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...

scalar_t	residual () const
	Get the residual. More...

Public Types
typedef basis_t::scalar_t	scalar_t
	Scalar type. More...

typedef basis_t::vector_t	vector_t
	Vector type. More...

Private Attributes
basis_t	basis_
	Basis. 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...

scalar_t	residual_
	Store residual of the approximation. More...

Constructor & Destructor Documentation

◆ WLSApproximant()

template<typename basis_t >

mm::WLSApproximant< basis_t >::WLSApproximant	(	const basis_t &	basis,
		const vector_t &	point,
		const std::vector< vector_t > &	support,
		scalar_t	scale,
		const Eigen::Matrix< scalar_t, Eigen::Dynamic, 1 > &	coefficients,
		scalar_t	residual = `NaN`
	)

Construct a WLS approximant with known coefficients.

The approximant is of the form

\[ u(p) = \sum_{i=1}^m \alpha_i b_i\left(\frac{p - p_c}{s}\right), \]

where \(b_i\) may depend on the stencil nodes (e.g. RBF-s).

Parameters

basis	Basis functions \(b_i\) to be used, must satisfy the Basis function concept.
point	Center point \(p_c\) of the WLS approximation.
support	Nonscaled stencil of the WLS approximation.
scale	Scale \(s\) used in WLS computation, see Scale function concept.
coefficients	Coefficients \(\alpha_i\) of the approximation.
residual	The resudial of the weighted least squares approximation. If 0, this function is an interpolant.

Definition at line 15 of file WLSApproximant.hpp.

Member Function Documentation

◆ basis()

template<typename basis_t >

const basis_t& mm::WLSApproximant< basis_t >::basis ( ) const

inline

Get the basis functions.

Definition at line 66 of file WLSApproximant_fwd.hpp.

◆ coefficients()

template<typename basis_t >

const Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>& mm::WLSApproximant< basis_t >::coefficients ( ) const

inline

Get the coefficient vector.

Definition at line 72 of file WLSApproximant_fwd.hpp.

◆ operator()() [1/2]

template<typename basis_t >

WLSApproximant< basis_t >::scalar_t mm::WLSApproximant< basis_t >::operator() ( const vector_t & point ) const

Evaluate the approximant at given point.

Definition at line 30 of file WLSApproximant.hpp.

◆ operator()() [2/2]

template<typename basis_t >

template<typename operator_t >

WLSApproximant< basis_t >::scalar_t mm::WLSApproximant< basis_t >::operator()	(	const vector_t &	point,
		const operator_t&	op
	)		const

Evaluate an operator applied to approximant at given point.

Definition at line 43 of file WLSApproximant.hpp.

◆ point()

template<typename basis_t >

const vector_t& mm::WLSApproximant< basis_t >::point ( ) const

inline

Get the center point.

Definition at line 68 of file WLSApproximant_fwd.hpp.

◆ residual()

template<typename basis_t >

scalar_t mm::WLSApproximant< basis_t >::residual ( ) const

inline

Get the residual.

Definition at line 74 of file WLSApproximant_fwd.hpp.

◆ scale()

template<typename basis_t >

scalar_t mm::WLSApproximant< basis_t >::scale ( ) const

inline

Get the scale.

Definition at line 70 of file WLSApproximant_fwd.hpp.

Member Data Documentation

◆ basis_

template<typename basis_t >

basis_t mm::WLSApproximant< basis_t >::basis_

private

Basis.

Definition at line 33 of file WLSApproximant_fwd.hpp.

◆ coefficients_

template<typename basis_t >

Eigen::Matrix<scalar_t, Eigen::Dynamic, 1> mm::WLSApproximant< basis_t >::coefficients_

private

Coefficients (for scaled fn.)

Definition at line 37 of file WLSApproximant_fwd.hpp.

◆ point_

template<typename basis_t >

vector_t mm::WLSApproximant< basis_t >::point_

private

Center point.

Definition at line 34 of file WLSApproximant_fwd.hpp.

◆ residual_

template<typename basis_t >

scalar_t mm::WLSApproximant< basis_t >::residual_

private

Store residual of the approximation.

Definition at line 38 of file WLSApproximant_fwd.hpp.

◆ scale_

template<typename basis_t >

scalar_t mm::WLSApproximant< basis_t >::scale_

private

Scale.

Definition at line 36 of file WLSApproximant_fwd.hpp.

◆ support_

template<typename basis_t >

std::vector<vector_t> mm::WLSApproximant< basis_t >::support_

private

Local scaled stencil points.

Definition at line 35 of file WLSApproximant_fwd.hpp.

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

include/medusa/bits/approximations/WLSApproximant_fwd.hpp
include/medusa/bits/approximations/WLSApproximant.hpp

Detailed Description

template<typename basis_t> class mm::WLSApproximant< basis_t >

Public Member Functions

Public Types

Private Attributes

Constructor & Destructor Documentation

◆ WLSApproximant()

Member Function Documentation

◆ basis()

◆ coefficients()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ point()

◆ residual()

◆ scale()

Member Data Documentation

◆ basis_

◆ coefficients_

◆ point_

◆ residual_

◆ scale_

◆ support_

template<typename basis_t>
class mm::WLSApproximant< basis_t >