IGLib 1.4
The IGLib base library for development of numerical, technical and business applications.

IG::Num::Func::WeightReciprocalPower Class Reference

A RealFunction class representing bell like polynomial weighting function with finite support, based on reciprocal power function (1/(1+|x|^p) where p>0 is an integer power). Reference function: bell like function with infinite support, 0 < |f(x)| <=1 f(0) = 1. More...

Inheritance diagram for IG::Num::Func::WeightReciprocalPower:
Collaboration diagram for IG::Num::Func::WeightReciprocalPower:

List of all members.

Public Member Functions

 WeightReciprocalPower (int power)
 WeightReciprocalPower (int power, double Kx, double Sx)
 WeightReciprocalPower (int power, double Kx, double Sx, double Ky, double Sy)
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.

Protected Member Functions

override double RefValue (double x)
 Returns the value of reference (untransformed) function.
override double RefDerivative (double x)
 Returns the first derivative of reference (untransformed) function.
override double RefSecondDerivative (double x)
 Returns the second derivative of the given order of reference (untransformed) function.
override double RefDerivative (double x, int order)
 Returns the derivative of the given order of reference (untransformed) function.
internal override void setHighestDerivativeDefined (int order)
 Sets the internal variable that specifies which is the highest order derivative devined (-1 for unlimited).
override double RefIntegral (double x)
 Returns definite integral of reference (untransformed) function from 0 to the function argument.
override double RefInverse (double x)
 Returns inverse of the reference (untransformed) function.

Protected Attributes

int _p = 0
 Power p in expression 1/(1+|x|^p) for function value.

Properties

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).
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).
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).
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).
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).

Detailed Description

A RealFunction class representing bell like polynomial weighting function with finite support, based on reciprocal power function (1/(1+|x|^p) where p>0 is an integer power). Reference function: bell like function with infinite support, 0 < |f(x)| <=1 f(0) = 1.


Constructor & Destructor Documentation

IG::Num::Func::WeightReciprocalPower::WeightReciprocalPower ( int  power) [inline]
IG::Num::Func::WeightReciprocalPower::WeightReciprocalPower ( int  power,
double  Kx,
double  Sx 
) [inline]
IG::Num::Func::WeightReciprocalPower::WeightReciprocalPower ( int  power,
double  Kx,
double  Sx,
double  Ky,
double  Sy 
) [inline]

Member Function Documentation

override double IG::Num::Func::WeightReciprocalPower::RefValue ( double  x) [inline, protected, virtual]

Returns the value of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::WeightReciprocalPower::RefDerivative ( double  x) [inline, protected, virtual]

Returns the first derivative of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::WeightReciprocalPower::RefSecondDerivative ( double  x) [inline, protected, virtual]

Returns the second derivative of the given order of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::WeightReciprocalPower::RefDerivative ( double  x,
int  order 
) [inline, protected, virtual]

Returns the derivative of the given order of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::WeightReciprocalPower::HigherDerivativeDefined ( int  order) [inline]

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.

Reimplemented from IG::Num::RealFunction.

internal override void IG::Num::Func::WeightReciprocalPower::setHighestDerivativeDefined ( int  order) [inline, protected, virtual]

Sets the internal variable that specifies which is the highest order derivative devined (-1 for unlimited).

Parameters:
orderHighest order for which derivative is defined. -1 means that all derivatives are defined.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::WeightReciprocalPower::RefIntegral ( double  x) [inline, protected, virtual]

Returns definite integral of reference (untransformed) function from 0 to the function argument.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::WeightReciprocalPower::RefInverse ( double  y) [inline, protected, virtual]

Returns inverse of the reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.


Member Data Documentation

Power p in expression 1/(1+|x|^p) for function value.


Property Documentation

override bool IG::Num::Func::WeightReciprocalPower::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::WeightReciprocalPower::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::WeightReciprocalPower::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::WeightReciprocalPower::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::WeightReciprocalPower::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).

Reimplemented from IG::Num::RealFunction.


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