Polynomial real functions of one variable. More...

Inheritance diagram for IG.Num.FunctionPolynomial:

Collaboration diagram for IG.Num.FunctionPolynomial:

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

Public Member Functions inherited from IG.Num.RealFunction
	RealFunction (DlgFunctionValue valueDelegate)
	Constructs a new function where delegates are provided for calculation of function valu. More...

	RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate)
	Constructs a new function where delegates are provided for calculation of function valu and first derivative. More...

	RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate)

	RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionValue integralDelegate)
	Constructs a new function where delegates are provided for calculation of function value, derivatives and integral. More...

	RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionValue integralDelegate, DlgFunctionValue inverseDelegate)
	Constructs a new function where delegates are provided for calculation of function value, derivatives, integral and inverse. More...

	RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionHigherDerivative higherDerivativeDelegate, DlgFunctionValue integralDelegate, DlgFunctionValue inverseDelegate)
	Constructs a new function where delegates are provided for calculation of function value, derivatives, integral and inverse. More...

RealFunction	CloneFunction ()

object	Clone ()

double	TransformedArgument (double t)

double	InverseTransformedArgument (double x)

virtual void	SetTransformationParameters (double kx, double sx, double ky, double sy)
	Sets parameters of the affine transformation parameters for both co-ordinates. More...

virtual void	SetXTransformationParameters (double kx, double sx)
	Sets parameters of the affine transformation parameters for independent variable. More...

override double	Value (double x)
	Returns the value of this function at the specified parameter. More...

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

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

override bool	HigherDerivativeDefined (int order)
	Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically). Returns true if either the internal variable indicates true or the appropriate delegate is non-null. More...

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

override double	Integral (double x)
	Returns definite integral of the current function from 0 to the function argument. More...

override double	Inverse (double y)
	Returns value of the inverse of the current function at the specified value of dependent variable. More...

Public Member Functions inherited from IG.Num.RealFunctionBase
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 ()

Properties
int	Order `[get]`
	Returns order of the polynomial. More...

override bool	ValueDefined `[get]`

override bool	DerivativeDefined `[get]`

override bool	SecondDerivativeDefined `[get]`

override bool	IntegralDefined `[get]`

override bool	InverseDefined `[get]`

Properties inherited from IG.Num.RealFunction
override RealFunctionBase	DerivativeFunction `[get]`
	Returns a function that represents a derivative of the current function. More...

override RealFunctionBase	InverseFunction `[get]`
	Returns a function that represents inverse of the current function. More...

override RealFunctionBase	IntegralFunction `[get]`
	Returns a function that represents definite integral of the current function from 0 to function argument. More...

bool	DoTransform `[get, private set]`
	Whether or not transformation (stretch/shift) is applied to the reference function, either in x or to y. Setter sets value both for transformation in X and Y direction. More...

bool	TransformX `[get, private set]`
	Whether or not reference function is stretched/shifted in x direction. More...

bool	TransformY `[get, private set]`
	Whether or not reference function is stretched/shifted in x direction. More...

double	ScaleX `[get, set]`
	Gets or sets the scaling factor for independent variable. More...

double	ShiftX `[get, set]`
	Gets or sets the shift of independent variable. More...

double	ScaleY `[get, set]`
	Gets or sets the scaling factor for function value. More...

double	ShiftY `[get, set]`
	Gets or sets the shift for function value. More...

override bool	ValueDefined `[get, set]`
	Tells whether value of the function is defined by implementation. Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...

override bool	DerivativeDefined `[get, set]`
	Tells whether the first derivative is defined for this function (by implementation, not mathematically). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...

override bool	SecondDerivativeDefined `[get, set]`
	Tells whether the second derivative is defined for this function (by implementation, not mathematically). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...

override bool	IntegralDefined `[get, set]`
	Indicates whether integral is defined for this function (w.r. implementation). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...

override bool	InverseDefined `[get, set]`
	Indicates whether inverse is defined for this function (w.r. implementation). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...

Properties inherited from IG.Num.RealFunctionBase
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...

Private Member Functions
	FunctionPolynomial (double[] coefficients)

void	Init ()

double	ReferenceValue (double x)

double	ReferencDerivative (double x)

double	DerivativeMonomial (double x, int power, int order)

double	ReferenceHigherDerivative (double x, int order)

double	ReferenceSecondDerivative (double x)

double	ReferenceIntegral (double x)

double	ReferenceInverse (double y)

Private Attributes
double[]	_coefficients = null

Additional Inherited Members
Static Public Member Functions inherited from IG.Num.RealFunction
static void	TestSpeed ()
	Compares calculation times of three ways of evaluations of exponential function: directly by Math.Exp(), through a delegate initialized by this function, and through a Function object initialized by this function. The number of repetitions is pre-defined. More...

static void	TestSpeed (long numiterations)
	Compares calculation times of three ways of evaluations of exponential function: directly by Math.Exp(), through a delegate initialized by this function, and through a Function object initialized by this function. More...

Static Public Member Functions inherited from IG.Num.RealFunctionBase
static void	ExampleTests ()

Protected Member Functions inherited from IG.Num.RealFunction
	RealFunction ()

virtual double	RefValue (double x)
	Returns the value of reference (untransformed) function. More...

virtual double	RefDerivative (double x)
	Returns the first derivative of reference (untransformed) function. More...

virtual double	RefDerivative (double x, int order)
	Returns the derivative of the given order of reference (untransformed) function. More...

virtual double	RefSecondDerivative (double x)
	Returns the second derivative of the given order of reference (untransformed) function. More...

virtual double	RefIntegral (double x)
	Returns definite integral of reference (untransformed) function from 0 to the function argument. More...

virtual double	RefInverse (double y)
	Returns inverse of the reference (untransformed) function. More...

Protected Attributes inherited from IG.Num.RealFunction
bool	_valueDefined = false

bool	_derivativeDefined = false

int	_highestDerivativeDefined = 0

bool	_secondDerivativeDefined = false

bool	_integralDefined = false

bool	_inverseDefined = false

Protected Attributes inherited from IG.Num.RealFunctionBase
string	_name

string	_description

Detailed Description

Polynomial real functions of one variable.

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Constructor & Destructor Documentation

IG.Num.FunctionPolynomial.FunctionPolynomial ( double[] coefficients )

inlineprivate

Member Function Documentation

void IG.Num.FunctionPolynomial.Init ( )

inlineprivate

double IG.Num.FunctionPolynomial.ReferenceValue ( double x )

inlineprivate

double IG.Num.FunctionPolynomial.ReferencDerivative ( double x )

inlineprivate

double IG.Num.FunctionPolynomial.DerivativeMonomial	(	double	x,
		int	power,
		int	order
	)

inlineprivate

double IG.Num.FunctionPolynomial.ReferenceHigherDerivative	(	double	x,
		int	order
	)

inlineprivate

double IG.Num.FunctionPolynomial.ReferenceSecondDerivative ( double x )

inlineprivate

double IG.Num.FunctionPolynomial.ReferenceIntegral ( double x )

inlineprivate

double IG.Num.FunctionPolynomial.ReferenceInverse ( double y )

inlineprivate

override bool IG.Num.FunctionPolynomial.HigherDerivativeDefined ( int order )

inline

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

Implements IG.Num.IRealFunction.

Member Data Documentation

double [] IG.Num.FunctionPolynomial._coefficients = null

private

Property Documentation

int IG.Num.FunctionPolynomial.Order

get

Returns order of the polynomial.

override bool IG.Num.FunctionPolynomial.ValueDefined

get

override bool IG.Num.FunctionPolynomial.DerivativeDefined

get

override bool IG.Num.FunctionPolynomial.SecondDerivativeDefined

get

override bool IG.Num.FunctionPolynomial.IntegralDefined

get

override bool IG.Num.FunctionPolynomial.InverseDefined

get

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

igbase/numeric/FunctionReal.cs

Public Member Functions

Properties

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation