IG::Num::IRealFunction Interface Reference

Interface for real functions. More...

Inheritance diagram for IG::Num::IRealFunction:

List of all members.

Public Member Functions
double	Value (double x)
	Returns the value of this function at the specified parameter.
double	Derivative (double x)
	Returns the first derivative of this function at the specified parameter.
double	Derivative (double x, int order)
	Returns the derivative of the given order of this function at the specified parameter.
bool	HigherDerivativeDefined (int order)
	Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically)
double	SecondDerivative (double x)
	Returns the second derivative of the given order of this function at the specified arameter.
double	Integral (double x)
	Returns integral from 0 to x of the function. Throws an exception if the integral is not defined.
double	Inverse (double y)
	Returns Inverse of the current function applied to function argument. Throws an exception if the inverse function is not defined.
void	Tabulate (double from, double to, int numPoints)
	Tabulates the current function and its first and second derivatives (when available) on the specified interval, in the specified number of points.
void	Tabulate (double from, double to, int numPoints, bool printDerivatives)
	Tabulates the current function and its first and eventually second derivatives (when available) on the specified interval, in the specified number of points.
void	Tabulate (double from, double to, int numPoints, bool printDerivatives, bool printSecondDerivatives)
	Tabulates the current function and eventually its first and second derivatives (when available) on the specified interval, in the specified number of points.
double	NumericalIntegral (double from, double to, int numintervals)
	Calculates numerical integral of this function. Simpson's formula is usually used.
double	NumericalDerivative (double x, double stepsize)
	Calculates numerical derivative of this function. Central difference formula is used.
double	NumericalSecondDerivative (double x, double stepsize)
	Calculates numerical second order derivative of this function. Central difference formula is used.
Properties
string	Name [get]
	Returns a short name of the function.
string	Description [get]
	Returns a short description of the function.
bool	ValueDefined [get]
	Tells whether value of the function is defined by implementation.
bool	DerivativeDefined [get]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically)
bool	SecondDerivativeDefined [get]
	Tells whether the second derivative is defined for this function (by implementation, not mathematically)
bool	IntegralDefined [get]
	Tells whether analytical itegral of the function is defined or not.
bool	InverseDefined [get]
	Tells whether analytical inverse function is defined or not.

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Detailed Description

Interface for real functions.

$A Igor xx;

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Member Function Documentation

double IG::Num::IRealFunction::Value

(

double

x

)

Returns the value of this function at the specified parameter.

Implemented in IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Gr::PlotterZedGraph::ExampleSineFunctionForLissajous, IG::Gr3d::VtkPlotBase::ExampleSineFunctionForLissajous, and IG::Gr3d::VtkPlotBase::ExampleFunctionTorusKnot.

double IG::Num::IRealFunction::Derivative

(

double

x

)

Returns the first derivative of this function at the specified parameter.

Implemented in IG::Num::RealFunctionBase, and IG::Num::RealFunction.

double IG::Num::IRealFunction::Derivative	(	double	x,
		int	order
	)

Returns the derivative of the given order of this function at the specified parameter.

Implemented in IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::Func::Identity, and IG::Num::Func::Constant.

bool IG::Num::IRealFunction::HigherDerivativeDefined

(

int

order

)

Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically)

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

double IG::Num::IRealFunction::SecondDerivative

(

double

x

)

Returns the second derivative of the given order of this function at the specified arameter.

Implemented in IG::Num::RealFunctionBase, and IG::Num::RealFunction.

double IG::Num::IRealFunction::Integral

(

double

x

)

Returns integral from 0 to x of the function. Throws an exception if the integral is not defined.

Parameters:

x	Upper bound of the integral.

Implemented in IG::Num::RealFunctionBase, and IG::Num::RealFunction.

double IG::Num::IRealFunction::Inverse

(

double

y

)

Returns Inverse of the current function applied to function argument. Throws an exception if the inverse function is not defined.

Implemented in IG::Num::RealFunctionBase, and IG::Num::RealFunction.

void IG::Num::IRealFunction::Tabulate	(	double	from,
		double	to,
		int	numPoints
	)

Tabulates the current function and its first and second derivatives (when available) on the specified interval, in the specified number of points.

Parameters:

from	Left interval bound.
to	Right interval bound.
numPoints	Number of points in which the function is calculated.

Implemented in IG::Num::RealFunctionBase.

void IG::Num::IRealFunction::Tabulate	(	double	from,
		double	to,
		int	numPoints,
		bool	printDerivatives
	)

Tabulates the current function and its first and eventually second derivatives (when available) on the specified interval, in the specified number of points.

Parameters:

from	Left interval bound.
to	Right interval bound.
numPoints	Number of points in which the function is calculated.
printSecondDerivatives	Whether to print the second derivatives.

Implemented in IG::Num::RealFunctionBase.

void IG::Num::IRealFunction::Tabulate	(	double	from,
		double	to,
		int	numPoints,
		bool	printDerivatives,
		bool	printSecondDerivatives
	)

Tabulates the current function and eventually its first and second derivatives (when available) on the specified interval, in the specified number of points.

Parameters:

from	Left interval bound.
to	Right interval bound.
numPoints	Number of points in which the function is calculated.
printDerivatives	Whether to print the derivatives.
printSecondDerivatives	Whether to print the second derivatives.

Implemented in IG::Num::RealFunctionBase.

double IG::Num::IRealFunction::NumericalIntegral	(	double	from,
		double	to,
		int	numintervals
	)

Calculates numerical integral of this function. Simpson's formula is usually used.

Parameters:

from	Lower integral limit.
to	Upper integral limit.
numintervals	Number of subintervals (1 less thatn the number of evaluation points)

Returns:

Numerical integral.

Implemented in IG::Num::RealFunctionBase.

double IG::Num::IRealFunction::NumericalDerivative	(	double	x,
		double	stepsize
	)

Calculates numerical derivative of this function. Central difference formula is used.

Parameters:

x	Point at which derivative is calculated.
stepsize	Step size.

Returns:

Numerical derivative.

Implemented in IG::Num::RealFunctionBase.

double IG::Num::IRealFunction::NumericalSecondDerivative	(	double	x,
		double	stepsize
	)

Calculates numerical second order derivative of this function. Central difference formula is used.

Parameters:

x	Point at which second order derivative is calculated.
stepsize	Step size.

Returns:

Numerical derivative.

Implemented in IG::Num::RealFunctionBase.

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Property Documentation

string IG::Num::IRealFunction::Name [get]

Returns a short name of the function.

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, and IG::Num::RealFunction.

string IG::Num::IRealFunction::Description [get]

Returns a short description of the function.

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, and IG::Num::RealFunction.

bool IG::Num::IRealFunction::ValueDefined [get]

Tells whether value of the function is defined by implementation.

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

bool IG::Num::IRealFunction::DerivativeDefined [get]

Tells whether the first derivative is defined for this function (by implementation, not mathematically)

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

bool IG::Num::IRealFunction::SecondDerivativeDefined [get]

Tells whether the second derivative is defined for this function (by implementation, not mathematically)

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

bool IG::Num::IRealFunction::IntegralDefined [get]

Tells whether analytical itegral of the function is defined or not.

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

bool IG::Num::IRealFunction::InverseDefined [get]

Tells whether analytical inverse function is defined or not.

Implemented in IG::Lib::LoadableRealFunctionBase, IG::Num::RealFunctionBase, IG::Num::RealFunction, IG::Num::FunctionPolynomial, IG::Num::Func::Exp, IG::Num::Func::ReciprocalPower, IG::Num::Func::Identity, IG::Num::Func::Constant, IG::Num::Func::Linear, IG::Num::Func::Quadratic, IG::Num::Func::Cubic, IG::Num::Func::PenaltyPower, IG::Num::Func::WeightGauss, IG::Num::Func::WeightReciprocalPower, IG::Num::Func::WeightPol3, IG::Num::Func::WeightPol4, IG::Num::Func::WeightPol5, and IG::Num::Func::WeightPol7.

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

• FunctionReal.cs