The ChebfunBase class provides a base for function approximation with Chebyshev polynomials. More...

#include <ChebfunBase.h>

Public Member Functions
template<class FunctionType >
ChebfunBase_sptr	bestFitTempl (double start, double end, FunctionType f, std::vector< double > &p, std::vector< double > &a, double maxA, double tolerance, size_t maxSize)
	Fit a function until full convergence. More...

std::vector< double >	calcA (const std::vector< double > &p) const
	Calculate expansion coefficients. More...

std::vector< double >	calcP (const std::vector< double > &a) const
	Calculate function values. More...

	ChebfunBase (ChebfunBase &&) noexcept=default
	Move constructor. More...

	ChebfunBase (const ChebfunBase &)=default
	Copy constructor. More...

	ChebfunBase (size_t n, double start, double end, double tolerance=0.0)
	Constructor. More...

void	derivative (const std::vector< double > &a, std::vector< double > &aout) const
	Calculate the derivative. More...

double	endX () const
	End of the interval. More...

double	eval (double x, const std::vector< double > &p) const
	Evaluate a function. More...

std::vector< double >	evalVector (const std::vector< double > &x, const std::vector< double > &p) const
	Evaluate a function. More...

void	evalVector (const std::vector< double > &x, const std::vector< double > &p, std::vector< double > &res) const
	Evaluate a function. More...

std::vector< double >	fit (ChebfunFunctionType f) const
	Calculate function values at chebfun x-points. More...

std::vector< double >	fit (const API::IFunction &f) const
	Calculate function values at chebfun x-points. More...

std::shared_ptr< ChebfunBase >	integral (const std::vector< double > &a, std::vector< double > &aout) const
	Calculate the integral. More...

double	integrate (const std::vector< double > &p) const
	Calculate an integral. More...

const std::vector< double > &	integrationWeights () const
	Get a reference to the integration weights. More...

std::vector< double >	linspace (size_t n) const
	Create a vector of x values linearly spaced on the approximation interval. More...

size_t	order () const
	Get the polynomial order of this base. More...

std::vector< double >	roots (const std::vector< double > &a) const
	Find all roots of a function on this interval. More...

size_t	size () const
	Get the size of the base which is the number of x-points. More...

std::vector< double >	smooth (const std::vector< double > &xvalues, const std::vector< double > &yvalues) const
	Smooth some data. More...

double	startX () const
	Start of the interval. More...

double	tolerance ()
	Tolerance for comparing doubles. More...

double	width () const
	Get the width of the interval. More...

const std::vector< double > &	xPoints () const
	Get a reference to the x-points. More...

Static Public Member Functions
static std::shared_ptr< ChebfunBase >	bestFit (double start, double end, ChebfunFunctionType, std::vector< double > &p, std::vector< double > &a, double maxA=0.0, double tolerance=0.0, size_t maxSize=0)
	Fit a function until full convergence. More...

static std::shared_ptr< ChebfunBase >	bestFit (double start, double end, const API::IFunction &, std::vector< double > &p, std::vector< double > &a, double maxA=0.0, double tolerance=0.0, size_t maxSize=0)
	Fit a function until full convergence. More...

template<class FunctionType >
static std::shared_ptr< ChebfunBase >	bestFitAnyTolerance (double start, double end, FunctionType f, std::vector< double > &p, std::vector< double > &a, double maxA=0.0, double tolerance=0.0, size_t maxSize=0)
	Find best fit with highest possible tolerance (to be used with noisy data). More...

Private Member Functions
void	calcIntegrationWeights () const
	Calculate the integration weights. More...

void	calcX ()
	Calculate the x-values based on the (start,end) interval. More...

std::vector< double >	fitOdd (const API::IFunction &f, std::vector< double > &pEven) const
	Calculate function values at odd-valued indices of the base x-points. More...

std::vector< double >	fitOdd (const ChebfunFunctionType &f, std::vector< double > &p) const
	Calculate function values at odd-valued indices of the base x-points. More...

ChebfunBase &	operator= (ChebfunBase &&other)=delete

ChebfunBase &	operator= (const ChebfunBase &other)=delete
	Private assingment operator to stress the immutability of ChebfunBase. More...

Static Private Member Functions
template<class FunctionType >
static std::shared_ptr< ChebfunBase >	bestFitTempl (double start, double end, FunctionType f, std::vector< double > &p, std::vector< double > &a, double maxA, double tolerance, size_t maxSize)
	Templated implementation of bestFit method. More...

static bool	hasConverged (const std::vector< double > &a, double maxA, double tolerance, size_t shift=0)
	Test an array of Chebyshev coefficients for convergence. More...

Private Attributes
std::vector< double >	m_bw
	The barycentric weights. More...

double	m_end
	End of the interval. More...

std::vector< double >	m_integrationWeights
	The integration weights. More...

size_t	m_n
	Polynomial order. More...

double	m_start
	Start of the interval. More...

const double	m_tolerance
	Actual tolerance in comparing doubles. More...

std::vector< double >	m_x
	The x-points. More...

Static Private Attributes
static const size_t	g_maxNumberPoints = 1026
	Maximum number of (x) points in a base. More...

static const double	g_tolerance = 1e-15
	Maximum tolerance in comparing doubles. More...

Detailed Description

The ChebfunBase class provides a base for function approximation with Chebyshev polynomials.

A smooth function on a finite interval [a,b] can be approximated by a Chebyshev expansion of order n. Finding an approximation is very easy: the function needs to be evaluated at n+1 specific x- points. These n+1 values can be used to interpolate the function at any x-point in interval [a,b]. This is done by calling the fit(...) method.

Different functions require different polynomial orders to reach the same accuracy of approximation. Static method bestFit(...) tries to find the smallest value of n that provides the required accuracy. If it fails to find an n smaller than some maximum number it returns an empty shared pointer.

Knowing the vector of the function values (P) at the n+1 base x-points and the related vector of the Chebyshev expansion coefficients (A) (claculated by calcA(...) method) allows one to perform various manipulations on the approximation:

algebraic operations: +,-,*,/
applying a function
root finding
differentiation
integration
convolution
solving of (integro-)differential equations
etc

This calss doesn't represent a function approximation itself but keeps proerties that can be shared by multiple approximations.

This class is based on the ideas from the Chebfun matlab package (http://www.chebfun.org/).

Definition at line 66 of file ChebfunBase.h.

Constructor & Destructor Documentation

◆ ChebfunBase() [1/3]

Mantid::CurveFitting::Functions::ChebfunBase::ChebfunBase	(	size_t	n,
		double	start,
		double	end,
		double	tolerance = `0.0`
	)

Constructor.

Parameters

n	:: Polynomial order == number of points - 1.
start	:: The start (lower bound) of an interval on the x-axis.
end	:: The end (upper bound) of an interval on the x-axis.
tolerance	:: Tolerance in comparing the expansion coefficients. Setting this tolerance is a way to specify the accuracy of the approximation.

Definition at line 51 of file ChebfunBase.cpp.

References calcX(), m_bw, m_x, and n.

◆ ChebfunBase() [2/3]

Mantid::CurveFitting::Functions::ChebfunBase::ChebfunBase ( const ChebfunBase & )

default

Copy constructor.

◆ ChebfunBase() [3/3]

Mantid::CurveFitting::Functions::ChebfunBase::ChebfunBase ( ChebfunBase && )

defaultnoexcept

Move constructor.

Member Function Documentation

◆ bestFit() [1/2]

ChebfunBase_sptr Mantid::CurveFitting::Functions::ChebfunBase::bestFit	(	double	start,
		double	end,
		ChebfunFunctionType	f,
		std::vector< double > &	p,
		std::vector< double > &	a,
		double	maxA = `0.0`,
		double	tolerance = `0.0`,
		size_t	maxSize = `0`
	)

static

Fit a function until full convergence.

Template specialization for a generic function type.

Definition at line 445 of file ChebfunBase.cpp.

References bestFitTempl(), and tolerance().

Referenced by bestFitAnyTolerance().

◆ bestFit() [2/2]

ChebfunBase_sptr Mantid::CurveFitting::Functions::ChebfunBase::bestFit	(	double	start,
		double	end,
		const API::IFunction &	f,
		std::vector< double > &	p,
		std::vector< double > &	a,
		double	maxA = `0.0`,
		double	tolerance = `0.0`,
		size_t	maxSize = `0`
	)

static

Fit a function until full convergence.

Template specialization for IFunction.

Definition at line 451 of file ChebfunBase.cpp.

References tolerance().

◆ bestFitAnyTolerance()

template<class FunctionType >

std::shared_ptr< ChebfunBase > Mantid::CurveFitting::Functions::ChebfunBase::bestFitAnyTolerance	(	double	start,
		double	end,
		FunctionType	f,
		std::vector< double > &	p,
		std::vector< double > &	a,
		double	maxA = `0.0`,
		double	tolerance = `0.0`,
		size_t	maxSize = `0`
	)

static

Find best fit with highest possible tolerance (to be used with noisy data).

Definition at line 178 of file ChebfunBase.h.

References bestFit(), g_tolerance, and tolerance().

Referenced by Mantid::CurveFitting::Algorithms::ChiSlice::makeApprox().

◆ bestFitTempl() [1/2]

template<class FunctionType >

static std::shared_ptr< ChebfunBase > Mantid::CurveFitting::Functions::ChebfunBase::bestFitTempl	(	double	start,
		double	end,
		FunctionType	f,
		std::vector< double > &	p,
		std::vector< double > &	a,
		double	maxA,
		double	tolerance,
		size_t	maxSize
	)

staticprivate

Templated implementation of bestFit method.

Referenced by bestFit().

◆ bestFitTempl() [2/2]

template<class FunctionType >

ChebfunBase_sptr Mantid::CurveFitting::Functions::ChebfunBase::bestFitTempl	(	double	start,
		double	end,
		FunctionType	f,
		std::vector< double > &	p,
		std::vector< double > &	a,
		double	maxA,
		double	tolerance,
		size_t	maxSize
	)

Fit a function until full convergence.

Increases size of the base until full conversion or a size limit is reached. If size limit is reached returns an empty pointer. In this case the calling method can divide the interval and fit each part separately.

Parameters

start	:: Lower limit of the x-interval.
end	:: Upper limit of the x-interval.
f	:: Function to fit.
p	:: Function values at the found x-points.
a	:: Chebyshev expansion coefficients.
maxA	:: A maximum value of the coefficients to compare against.
tolerance	:: A tolerance for comparing values. Defines the accuracy of the approximation.
maxSize	:: A maximum size of the expansion. If a large base is required to reach the desired accuracy returns an empty pointer.

Returns: :: A ChebfunBase of the best fit if succeeded or empty pointer if failed.

Definition at line 358 of file ChebfunBase.cpp.

References calcA(), fabs, fit(), fitOdd(), g_maxNumberPoints, g_tolerance, hasConverged(), Mantid::Geometry::m, n, tmp, and tolerance().

◆ calcA()

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::calcA ( const std::vector< double > & p ) const

Calculate expansion coefficients.

Calculate the chebyshev expansion coefficients given function values at the x-points.

Parameters

p	:: Function values at chebyshev points.

Definition at line 478 of file ChebfunBase.cpp.

References m_n, Mantid::CurveFitting::HalfComplex::real(), tmp, wavetable, and workspace.

Referenced by bestFitTempl(), and smooth().

◆ calcIntegrationWeights()

void Mantid::CurveFitting::Functions::ChebfunBase::calcIntegrationWeights ( ) const

private

Calculate the integration weights.

Definition at line 124 of file ChebfunBase.cpp.

References m_end, m_integrationWeights, m_n, m_start, and n.

Referenced by integrate(), and integrationWeights().

◆ calcP()

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::calcP ( const std::vector< double > & a ) const

Calculate function values.

Calculate function values at chebyshev points given chebyshev expansion coefficiens (inverse of calcA()).

Parameters

a	:: Chebyshev expansion coefficients.

Returns: Function values.

Definition at line 538 of file ChebfunBase.cpp.

References Mantid::Geometry::d, m_n, Mantid::CurveFitting::HalfComplex::set(), tmp, wavetable, and workspace.

Referenced by smooth().

◆ calcX()

void Mantid::CurveFitting::Functions::ChebfunBase::calcX ( )

private

Calculate the x-values based on the (start,end) interval.

Definition at line 105 of file ChebfunBase.cpp.

References m_end, m_n, m_start, and m_x.

Referenced by ChebfunBase().

◆ derivative()

void Mantid::CurveFitting::Functions::ChebfunBase::derivative	(	const std::vector< double > &	a,
		std::vector< double > &	aout
	)		const

Calculate the derivative.

Calculate the first derivative of a function.

Parameters

a	:: Chebyshev coefficients of the diffientiated function.
aout	:: Output coeffs of the derivative.

Definition at line 287 of file ChebfunBase.cpp.

References m_end, m_n, m_start, and m_x.

◆ endX()

double Mantid::CurveFitting::Functions::ChebfunBase::endX ( ) const

inline

End of the interval.

Definition at line 80 of file ChebfunBase.h.

Referenced by roots().

◆ eval()

double Mantid::CurveFitting::Functions::ChebfunBase::eval	(	double	x,
		const std::vector< double > &	p
	)		const

Evaluate a function.

Parameters

x	:: Point of evaluation.
p	:: The function y-points

Returns: Value of the function.

Definition at line 192 of file ChebfunBase.cpp.

References m_bw, m_end, m_x, and Mantid::Geometry::x.

Referenced by roots().

◆ evalVector() [1/2]

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::evalVector	(	const std::vector< double > &	x,
		const std::vector< double > &	p
	)		const

Evaluate a function.

Evaluate function on a vector of x-values.

Parameters

x	:: A vector of x-values.
p	:: The y-points of a function.

Returns: :: Output result. res.size() == x.size()

Definition at line 276 of file ChebfunBase.cpp.

References evalVector(), and Mantid::Geometry::x.

◆ evalVector() [2/2]

void Mantid::CurveFitting::Functions::ChebfunBase::evalVector	(	const std::vector< double > &	x,
		const std::vector< double > &	p,
		std::vector< double > &	res
	)		const

Evaluate a function.

Evaluate function on a vector of x-values.

Parameters

x	:: A vector of x-values.
p	:: The y-points of a function.
res	:: Output result. res.size() == x.size()

Definition at line 222 of file ChebfunBase.cpp.

References m_bw, m_start, m_x, value, and Mantid::Geometry::x.

Referenced by evalVector().

◆ fit() [1/2]

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::fit ( ChebfunFunctionType f ) const

Calculate function values at chebfun x-points.

Approximate a function using this base.

Parameters

f	:: A function pointer.

Returns: Function values at the base x-points.

Definition at line 576 of file ChebfunBase.cpp.

References m_x, and size().

Referenced by bestFitTempl().

◆ fit() [2/2]

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::fit ( const API::IFunction & f ) const

Calculate function values at chebfun x-points.

Approximate a function using this base.

Parameters

f	:: A reference to an IFunction

Returns: Function values at the base x-points.

Definition at line 587 of file ChebfunBase.cpp.

References Mantid::API::IFunction::function(), m_x, Mantid::Geometry::x, and Mantid::Geometry::y.

◆ fitOdd() [1/2]

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::fitOdd	(	const API::IFunction &	f,
		std::vector< double > &	pEven
	)		const

private

Calculate function values at odd-valued indices of the base x-points.

This method is used by bestFit to minimize the number of calls to the approximated function.

Parameters

f	:: Function to calculate.
pEven	:: Values of function f at the even-valued indices of m_x.

Definition at line 625 of file ChebfunBase.cpp.

References Mantid::API::IFunction::function(), m_x, size(), Mantid::Geometry::x, and Mantid::Geometry::y.

◆ fitOdd() [2/2]

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::fitOdd	(	const ChebfunFunctionType &	f,
		std::vector< double > &	p
	)		const

private

Calculate function values at odd-valued indices of the base x-points.

This method is used by bestFit to minimize the number of calls to the approximated function.

Parameters

f	:: Function to calculate.
p	:: Values of function f at the even-valued indices of m_x.

Definition at line 601 of file ChebfunBase.cpp.

References size(), Mantid::Geometry::x, and xPoints().

Referenced by bestFitTempl().

◆ hasConverged()

bool Mantid::CurveFitting::Functions::ChebfunBase::hasConverged	(	const std::vector< double > &	a,
		double	maxA,
		double	tolerance,
		size_t	shift = `0`
	)

staticprivate

Test an array of Chebyshev coefficients for convergence.

Test if an array of Chebyshev expansion coefficients converged to the specified tolerance.

Parameters

a	:: A vector of coefficients.
maxA	:: A maximum value of the coefficients to compare against.
tolerance	:: Convergence tolerance.
shift	:: Displacement from the back of the coeffs vector (a) from which the coefficients are considered for testing.

Returns: :: True if converged or false otherwise.

Definition at line 161 of file ChebfunBase.cpp.

References fabs, tmp, and tolerance().

Referenced by bestFitTempl().

◆ integral()

ChebfunBase_sptr Mantid::CurveFitting::Functions::ChebfunBase::integral	(	const std::vector< double > &	a,
		std::vector< double > &	aout
	)		const

Calculate the integral.

Calculate the first integral of a function.

Parameters

a	:: Chebyshev coefficients of the integrated function.
aout	:: Output coeffs of the integral.

Returns: :: A base for the integral.

Definition at line 320 of file ChebfunBase.cpp.

References Mantid::Geometry::d, m_end, m_n, m_start, and m_x.

◆ integrate()

double Mantid::CurveFitting::Functions::ChebfunBase::integrate ( const std::vector< double > & p ) const

Calculate an integral.

Calculate an integral of a function given its values at the base x-points.

Parameters

p	:: Function values at the x-points.

Returns: :: The integral.

Definition at line 84 of file ChebfunBase.cpp.

References calcIntegrationWeights(), m_integrationWeights, m_x, and tmp.

◆ integrationWeights()

const std::vector< double > & Mantid::CurveFitting::Functions::ChebfunBase::integrationWeights ( ) const

Get a reference to the integration weights.

Return the integration weights that can be used in function manipulations involving integration.

Definition at line 72 of file ChebfunBase.cpp.

References calcIntegrationWeights(), m_integrationWeights, and m_x.

◆ linspace()

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::linspace ( size_t n ) const

Create a vector of x values linearly spaced on the approximation interval.

Return a vector of linearly spaced values in the domain interval m_start <= x <= m_end.

Parameters

n	:: Number of points in the output vector.

Definition at line 461 of file ChebfunBase.cpp.

References m_end, m_start, n, width(), and Mantid::Geometry::x.

◆ operator=() [1/2]

ChebfunBase & Mantid::CurveFitting::Functions::ChebfunBase::operator= ( ChebfunBase && other )

privatedelete

◆ operator=() [2/2]

ChebfunBase & Mantid::CurveFitting::Functions::ChebfunBase::operator= ( const ChebfunBase & other )

privatedelete

Private assingment operator to stress the immutability of ChebfunBase.

◆ order()

size_t Mantid::CurveFitting::Functions::ChebfunBase::order ( ) const

inline

Get the polynomial order of this base.

Definition at line 74 of file ChebfunBase.h.

Referenced by roots().

◆ roots()

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::roots ( const std::vector< double > & a ) const

Find all roots of a function on this interval.

Find all roots of this chebfun.

Parameters

a	:: A vector with the Chebyshev expansion coefficients.

Returns: A vector with root values, unordered. If empty function has no roots.

Definition at line 656 of file ChebfunBase.cpp.

References endX(), eval(), fabs, Mantid::CurveFitting::getGSLMatrixView(), Mantid::CurveFitting::EigenMatrix::mutator(), order(), Mantid::CurveFitting::EigenMatrix::set(), startX(), tmp, Mantid::CurveFitting::EigenMatrix::tr(), workspace, Mantid::Geometry::x, and Mantid::CurveFitting::EigenMatrix::zero().

◆ size()

size_t Mantid::CurveFitting::Functions::ChebfunBase::size ( ) const

inline

Get the size of the base which is the number of x-points.

Definition at line 76 of file ChebfunBase.h.

Referenced by fit(), fitOdd(), and smooth().

◆ smooth()

std::vector< double > Mantid::CurveFitting::Functions::ChebfunBase::smooth	(	const std::vector< double > &	xvalues,
		const std::vector< double > &	yvalues
	)		const

Smooth some data.

Parameters

xvalues	:: X-values of the data to smooth.
yvalues	:: Y-values of the data to smooth. xvalues.size() == yvalues.size()

Returns: :: Vector of y-points in this base.

Definition at line 730 of file ChebfunBase.cpp.

References calcA(), calcP(), g_tolerance, m_x, n, sigma, size(), tmp, Mantid::Geometry::x, and Mantid::Geometry::y.

◆ startX()

double Mantid::CurveFitting::Functions::ChebfunBase::startX ( ) const

inline

Start of the interval.

Definition at line 78 of file ChebfunBase.h.

Referenced by roots().

◆ tolerance()

double Mantid::CurveFitting::Functions::ChebfunBase::tolerance ( )

inline

Tolerance for comparing doubles.

Definition at line 120 of file ChebfunBase.h.

Referenced by bestFit(), bestFitAnyTolerance(), bestFitTempl(), and hasConverged().

◆ width()

double Mantid::CurveFitting::Functions::ChebfunBase::width ( ) const

inline

Get the width of the interval.

Definition at line 82 of file ChebfunBase.h.

Referenced by linspace().

◆ xPoints()

const std::vector< double > & Mantid::CurveFitting::Functions::ChebfunBase::xPoints ( ) const

inline

Get a reference to the x-points.

Definition at line 84 of file ChebfunBase.h.

Referenced by fitOdd().

Member Data Documentation

◆ g_maxNumberPoints

const size_t Mantid::CurveFitting::Functions::ChebfunBase::g_maxNumberPoints = 1026

staticprivate

Maximum number of (x) points in a base.

Definition at line 171 of file ChebfunBase.h.

Referenced by bestFitTempl().

◆ g_tolerance

const double Mantid::CurveFitting::Functions::ChebfunBase::g_tolerance = 1e-15

staticprivate

Maximum tolerance in comparing doubles.

Definition at line 169 of file ChebfunBase.h.

Referenced by bestFitAnyTolerance(), bestFitTempl(), and smooth().

◆ m_bw

std::vector<double> Mantid::CurveFitting::Functions::ChebfunBase::m_bw

private

The barycentric weights.

Definition at line 165 of file ChebfunBase.h.

Referenced by ChebfunBase(), eval(), and evalVector().

◆ m_end

double Mantid::CurveFitting::Functions::ChebfunBase::m_end

private

End of the interval.

Definition at line 161 of file ChebfunBase.h.

Referenced by calcIntegrationWeights(), calcX(), derivative(), eval(), integral(), and linspace().

◆ m_integrationWeights

std::vector<double> Mantid::CurveFitting::Functions::ChebfunBase::m_integrationWeights

mutableprivate

The integration weights.

Definition at line 167 of file ChebfunBase.h.

Referenced by calcIntegrationWeights(), integrate(), and integrationWeights().

◆ m_n

size_t Mantid::CurveFitting::Functions::ChebfunBase::m_n

private

Polynomial order.

Definition at line 157 of file ChebfunBase.h.

Referenced by calcA(), calcIntegrationWeights(), calcP(), calcX(), derivative(), and integral().

◆ m_start

double Mantid::CurveFitting::Functions::ChebfunBase::m_start

private

Start of the interval.

Definition at line 159 of file ChebfunBase.h.

Referenced by calcIntegrationWeights(), calcX(), derivative(), evalVector(), integral(), and linspace().

◆ m_tolerance

const double Mantid::CurveFitting::Functions::ChebfunBase::m_tolerance

private

Actual tolerance in comparing doubles.

Definition at line 155 of file ChebfunBase.h.

◆ m_x

std::vector<double> Mantid::CurveFitting::Functions::ChebfunBase::m_x

private

The x-points.

Definition at line 163 of file ChebfunBase.h.

Referenced by calcX(), ChebfunBase(), derivative(), eval(), evalVector(), fit(), fitOdd(), integral(), integrate(), integrationWeights(), and smooth().

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

Framework/CurveFitting/inc/MantidCurveFitting/Functions/ChebfunBase.h
Framework/CurveFitting/src/Functions/ChebfunBase.cpp

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ChebfunBase() [1/3]

◆ ChebfunBase() [2/3]

◆ ChebfunBase() [3/3]

Member Function Documentation

◆ bestFit() [1/2]

◆ bestFit() [2/2]

◆ bestFitAnyTolerance()

◆ bestFitTempl() [1/2]

◆ bestFitTempl() [2/2]

◆ calcA()

◆ calcIntegrationWeights()

◆ calcP()

◆ calcX()

◆ derivative()

◆ endX()

◆ eval()

◆ evalVector() [1/2]

◆ evalVector() [2/2]

◆ fit() [1/2]

◆ fit() [2/2]

◆ fitOdd() [1/2]

◆ fitOdd() [2/2]

◆ hasConverged()

◆ integral()

◆ integrate()

◆ integrationWeights()

◆ linspace()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ order()

◆ roots()

◆ size()

◆ smooth()

◆ startX()

◆ tolerance()

◆ width()

◆ xPoints()

Member Data Documentation

◆ g_maxNumberPoints

◆ g_tolerance

◆ m_bw

◆ m_end

◆ m_integrationWeights

◆ m_n

◆ m_start

◆ m_tolerance

◆ m_x