Base class for real functions of real variable. More...

Inheritance diagram for IG.Num.RealFunctionBase:

Collaboration diagram for IG.Num.RealFunctionBase:

Public Member Functions
abstract double	Value (double x)
	Returns the value of this function at the specified parameter. More...

abstract double	Derivative (double x)
	Returns the first derivative of this function at the specified parameter. More...

abstract double	Derivative (double x, int order)
	Returns the derivative of the given order of this function at the specified parameter. More...

abstract bool	HigherDerivativeDefined (int order)
	Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically) More...

abstract double	SecondDerivative (double x)
	Returns the second derivative of the given order of this function at the specified arameter. More...

abstract double	Integral (double x)
	Returns integral from 0 to x of the function. Throws an exception if the integral is not defined. More...

abstract double	Inverse (double y)
	Returns Inverse of the current function applied to function argument. Throws an exception if the inverse function is not defined. More...

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. More...

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. More...

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. More...

virtual double	NumericalIntegral (double from, double to, int numintervals)
	Calculates numerical integral of this function. Simpson's formula is used. More...

virtual double	NumericalDerivative (double x, double stepsize)
	Calculates numerical derivative of this function. Central difference formula is used. More...

virtual double	NumericalSecondDerivative (double x, double stepsize)
	Calculates numerical second order derivative of this function. Central difference formula is used. More...

virtual void	Test ()
	Performs numerical tests with parameters adjusted for specific function. This function can be be overridden in derived classes, however its current implementation may be relatively well suited for most weighting and basic functions. More...

virtual void	Test (double from, double to, int numProbes, double stepSize, double tolerance)
	Performs some numerical tests on the current function, such as correctness of first and second derivatives, integral and inverse of the function. Results are written to the standard output. Whenever a numerical result does not match the corresponding analytical value calculated by the function, a visible notification is written. More...

override string	ToString ()

Static Public Member Functions
static void	ExampleTests ()

Protected Attributes
string	_name

string	_description

Properties
virtual string	Name `[get, set]`
	Returns a short name of thecurrent function. More...

virtual string	Description `[get, set]`
	Returns a short description of the current function. More...

virtual RealFunctionBase	DerivativeFunction `[get]`
	Returns a function object that represents a derivative of this function. Returns null if this is not implemented. More...

virtual RealFunctionBase	IntegralFunction `[get]`
	Returns a function object that represents a definite integral of this function from 0 to 1. Returns null if not implemented. More...

virtual RealFunctionBase	InverseFunction `[get]`
	Returns a function object that represents an inverse function of this function. Returns null if not implemented. More...

abstract bool	ValueDefined `[get, set]`
	Tells whether value of the function is defined by implementation. More...

abstract bool	DerivativeDefined `[get, set]`
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...

abstract bool	SecondDerivativeDefined `[get, set]`
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...

abstract bool	IntegralDefined `[get, set]`
	Tells whether analytical itegral of the function is defined or not. More...

abstract bool	InverseDefined `[get, set]`
	Tells whether analytical inverse function is defined or not. More...

Properties inherited from IG.Num.IRealFunction
string	Name `[get]`
	Returns a short name of the function. More...

string	Description `[get]`
	Returns a short description of the function. More...

bool	ValueDefined `[get]`
	Tells whether value of the function is defined by implementation. More...

bool	DerivativeDefined `[get]`
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...

bool	SecondDerivativeDefined `[get]`
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...

bool	IntegralDefined `[get]`
	Tells whether analytical itegral of the function is defined or not. More...

bool	InverseDefined `[get]`
	Tells whether analytical inverse function is defined or not. More...

Detailed Description

Base class for real functions of real variable.

A number of predefined functions can be bound in the class Func.

$A Igor xx;

Member Function Documentation

abstract double IG.Num.RealFunctionBase.Value ( double x )

pure virtual

Returns the value of this function at the specified parameter.

Implements IG.Num.IRealFunction.

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

abstract double IG.Num.RealFunctionBase.Derivative ( double x )

pure virtual

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

Implements IG.Num.IRealFunction.

Implemented in IG.Num.RealFunction.

abstract double IG.Num.RealFunctionBase.Derivative	(	double	x,
		int	order
	)

pure virtual

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

Implements IG.Num.IRealFunction.

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

abstract bool IG.Num.RealFunctionBase.HigherDerivativeDefined ( int order )

pure virtual

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

Implements IG.Num.IRealFunction.

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

abstract double IG.Num.RealFunctionBase.SecondDerivative ( double x )

pure virtual

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

Implements IG.Num.IRealFunction.

Implemented in IG.Num.RealFunction.

abstract double IG.Num.RealFunctionBase.Integral ( double x )

pure virtual

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.

Implements IG.Num.IRealFunction.

Implemented in IG.Num.RealFunction.

abstract double IG.Num.RealFunctionBase.Inverse ( double y )

pure virtual

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

Implements IG.Num.IRealFunction.

Implemented in IG.Num.RealFunction.

void IG.Num.RealFunctionBase.Tabulate	(	double	from,
		double	to,
		int	numPoints
	)

inline

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.

Implements IG.Num.IRealFunction.

void IG.Num.RealFunctionBase.Tabulate	(	double	from,
		double	to,
		int	numPoints,
		bool	printDerivatives
	)

inline

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.
printDerivatives	Whether to print the derivatives.

Implements IG.Num.IRealFunction.

void IG.Num.RealFunctionBase.Tabulate	(	double	from,
		double	to,
		int	numPoints,
		bool	printDerivatives,
		bool	printSecondDerivatives
	)

inline

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.

Implements IG.Num.IRealFunction.

virtual double IG.Num.RealFunctionBase.NumericalIntegral	(	double	from,
		double	to,
		int	numintervals
	)

inlinevirtual

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

Implements IG.Num.IRealFunction.

References IG.Num.Numeric.IntegralSimpson().

virtual double IG.Num.RealFunctionBase.NumericalDerivative	(	double	x,
		double	stepsize
	)

inlinevirtual

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.

Implements IG.Num.IRealFunction.

References IG.Num.Numeric.DerivativeCD().

virtual double IG.Num.RealFunctionBase.NumericalSecondDerivative	(	double	x,
		double	stepsize
	)

inlinevirtual

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.

Implements IG.Num.IRealFunction.

References IG.Num.Numeric.SecondDerivativeCD().

virtual void IG.Num.RealFunctionBase.Test ( )

inlinevirtual

Performs numerical tests with parameters adjusted for specific function. This function can be be overridden in derived classes, however its current implementation may be relatively well suited for most weighting and basic functions.

Referenced by IG.Num.RealFunctionBase.ExampleTests().

virtual void IG.Num.RealFunctionBase.Test	(	double	from,
		double	to,
		int	numProbes,
		double	stepSize,
		double	tolerance
	)

inlinevirtual

Performs some numerical tests on the current function, such as correctness of first and second derivatives, integral and inverse of the function. Results are written to the standard output. Whenever a numerical result does not match the corresponding analytical value calculated by the function, a visible notification is written.

Parameters

from	Lower bound of the interval where tests are performed.
to	Upper bound of the interval where tests are performed.
numProbes	Number of points for which evaluations and comparisons are performed.
stepSize	Step size used for numerical integration and differentiation.
tolerance	Absolute tolarence for match between analytical and numeriacl values (visible notification is launched whenever difference is larger than tolerance).

static void IG.Num.RealFunctionBase.ExampleTests ( )

inlinestatic

References IG.Num.Func.GetWeightGauss(), and IG.Num.RealFunctionBase.Test().

override string IG.Num.RealFunctionBase.ToString ( )

inline

Member Data Documentation

string IG.Num.RealFunctionBase._name

protected

string IG.Num.RealFunctionBase._description

protected

Property Documentation

virtual string IG.Num.RealFunctionBase.Name

getset

Returns a short name of thecurrent function.

virtual string IG.Num.RealFunctionBase.Description

getset

Returns a short description of the current function.

virtual RealFunctionBase IG.Num.RealFunctionBase.DerivativeFunction

get

Returns a function object that represents a derivative of this function. Returns null if this is not implemented.

virtual RealFunctionBase IG.Num.RealFunctionBase.IntegralFunction

get

Returns a function object that represents a definite integral of this function from 0 to 1. Returns null if not implemented.

virtual RealFunctionBase IG.Num.RealFunctionBase.InverseFunction

get

Returns a function object that represents an inverse function of this function. Returns null if not implemented.

abstract bool IG.Num.RealFunctionBase.ValueDefined

getset

Tells whether value of the function is defined by implementation.

abstract bool IG.Num.RealFunctionBase.DerivativeDefined

getset

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

abstract bool IG.Num.RealFunctionBase.SecondDerivativeDefined

getset

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

abstract bool IG.Num.RealFunctionBase.IntegralDefined

getset

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

abstract bool IG.Num.RealFunctionBase.InverseDefined

getset

Tells whether analytical inverse function is defined or not.

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

igbase/numeric/FunctionReal.cs

Public Member Functions

Static Public Member Functions

Protected Attributes

Properties

Detailed Description

Member Function Documentation

Member Data Documentation

Property Documentation