LagrangeBase Class Reference

#include <SupportValues.h>

Inheritance diagram for LagrangeBase:

Public Member Functions
	LagrangeBase (const Matrix< double > &X, const Matrix< double > &Y)
double	GetCoefficient (const double &xk, const size_t i) const
virtual Matrix< double >	Evaluate (const Matrix< double > &in) const
std::string	buildLx (size_t i) const
virtual std::string	Function () const
Public Member Functions inherited from PolynomialBase
	PolynomialBase (const Matrix< double > &X, const Matrix< double > &Y)
virtual Matrix< double >	Evaluate (const Matrix< double > &) const =0
virtual std::string	Function () const =0

Private Attributes
Matrix< double >	x
	$$x_i$$ Support values More...
Matrix< double >	y
	$$y_i$$ Support values evaluated with the function More...

Detailed Description

Lagrange-Base using lagrange coefficients to build the polynomial

https://wiki.godesteem.de/wiki/interpolation-and-approximation/#Lagrange-Base

Examples

numerics/analysis/TestSupportValues.cpp, and plot/TestPlot.cpp.

Constructor & Destructor Documentation

LagrangeBase()

LagrangeBase::LagrangeBase ( const Matrix< double > &  X, const Matrix< double > &  Y  )

inline

Default constructor

Parameters

X	$$x_i$$
Y	$$y_i$$

Member Function Documentation

buildLx()

std::string LagrangeBase::buildLx ( size_t  i ) const

inline

builds lagrange coefficient $$L_i$$ string representation

Parameters

i

index

Returns

coefficient representation

Evaluate()

virtual Matrix< double > LagrangeBase::Evaluate ( const Matrix< double > &  in ) const

inlinevirtual

Evaluates the lagrange base

Parameters

in	values to evaluate

Returns

interpolated values

Implements PolynomialBase.

Examples

plot/TestPlot.cpp.

Function()

virtual std::string LagrangeBase::Function ( ) const

inlinevirtual

Builds string representation in lagrange base

Returns

representational string

Implements PolynomialBase.

GetCoefficient()

double LagrangeBase::GetCoefficient ( const double &  xk, const size_t  i  ) const

inline

Computes i-th coefficient

$$L_i(x) = \prod_{j=0, j\neq i}^{n} \frac{x-x_j}{x_i-x_j}, \forall i=0, \dots, n$$

Parameters

xk	current value $$x_k$$
i	index i

Returns

coefficient value

Member Data Documentation

x

Matrix<double> LagrangeBase::x

private

$$x_i$$ Support values

y

Matrix<double> LagrangeBase::y

private

$$y_i$$ Support values evaluated with the function

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

• include/math/numerics/analysis/SupportValues.h