NumA::Chebyshev Class Reference

Chebyshev expansion class. More...

Public Member Functions
	Chebyshev (unsigned int N=50)
	Default Constructor with the order N of the expansion. More...
virtual	~Chebyshev ()
	Default destructor. More...
unsigned int	getN () const
	Get the order N of the expansion. More...
void	setN (unsigned int n)
	Set the order N of the expansion/. More...
const NumA::VectorD &	getRoots () const
const NumA::MatrixD &	getValuesToCoeffsMatrix () const
	Interpolation matrix. More...
const NumA::MatrixD &	getCoeffsToValuesMatrix () const
NumA::MatrixD	getCoeffsToValuesMatrix (const NumA::VectorD &points) const
NumA::VectorD	getCoeffsToValueVector (double x) const
NumA::MatrixD	getValuesToValuesMatrix (const NumA::VectorD &points) const
	Interpolation matrix. More...
NumA::VectorD	getValuesToValueVector (double x) const

Detailed Description

Chebyshev expansion class.

Interpolation \( f(x) = \sum_{i=0}^{N-1} c_i T_i \left( x \right) \) for \( x \in \left[ -1, 1 \right] \) , where \( N \) is the order of the expansion.

TODO: \( x \in \) any interval.

Constructor & Destructor Documentation

Chebyshev()

NumA::Chebyshev::Chebyshev

(

unsigned int

N = 50

)

Default Constructor with the order N of the expansion.

Parameters

N	Order of the expansion.

~Chebyshev()

NumA::Chebyshev::~Chebyshev ( )

virtual

Default destructor.

Member Function Documentation

getCoeffsToValuesMatrix() [1/2]

const NumA::MatrixD & NumA::Chebyshev::getCoeffsToValuesMatrix

(

)

const

Returns

Matrix which gives a vector of the values on Chebyshev nodes when applied to a vector of coefficients for the expansion.

getCoeffsToValuesMatrix() [2/2]

NumA::MatrixD NumA::Chebyshev::getCoeffsToValuesMatrix

(

const NumA::VectorD &

points

)

const

Parameters

points

Points where to evaluate the expansion.

Returns

Matrix which gives a vector of the values on given points when applied to a vector of coefficients for the expansion.

getCoeffsToValueVector()

NumA::VectorD NumA::Chebyshev::getCoeffsToValueVector

(

double

x

)

const

Parameters

x	Point where the expansion is evaluated.

Returns

Vector which gives the Chebyshev expansion on x when a scalar product is taken with a vector of coefficients for the expansion.

getN()

unsigned int NumA::Chebyshev::getN

(

)

const

Get the order N of the expansion.

Returns

N unsigned int

getRoots()

const NumA::VectorD & NumA::Chebyshev::getRoots

(

)

const

getValuesToCoeffsMatrix()

const NumA::MatrixD & NumA::Chebyshev::getValuesToCoeffsMatrix

(

)

const

Interpolation matrix.

Returns

Matrix which gives a vector of the coefficients for the expansion when applied to a vector of values on Chebyshev nodes.

getValuesToValuesMatrix()

NumA::MatrixD NumA::Chebyshev::getValuesToValuesMatrix

(

const NumA::VectorD &

points

)

const

Interpolation matrix.

Parameters

points

Points where to evaluate the expansion.

Returns

Matrix which gives a vector of values on given points when applied to a vector of values on Chebyshev nodes.

getValuesToValueVector()

NumA::VectorD NumA::Chebyshev::getValuesToValueVector

(

double

x

)

const

Parameters

x	Point where the expansion is evaluated.

Returns

Vector which gives the Chebyshev expansion on x when a scalar product is taken with a vector of values on Chebyshev nodes.

setN()

void NumA::Chebyshev::setN

(

unsigned int

n

)

Set the order N of the expansion/.

Parameters

n	unsigned int

---

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

• include/NumA/interpolation/Chebyshev.h
• src/NumA/interpolation/Chebyshev.cpp