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IG.Num.Func.PenaltyPower Class Reference

Penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc. More...

+ Inheritance diagram for IG.Num.Func.PenaltyPower:
+ Collaboration diagram for IG.Num.Func.PenaltyPower:

Public Member Functions

 PenaltyPower (double length, double height, int power)
 Creates a new penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Transition pint where function starts to be non-zero is at negative characteristic length. More...
 
 PenaltyPower (double length, double height, double zeroEnd, int power)
 Creates a new penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. More...
 
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 ()
 

Protected Member Functions

override double RefValue (double x)
 Returns the value of reference (untransformed) function. More...
 
override double RefDerivative (double x)
 Returns the first derivative of reference (untransformed) function. More...
 
override double RefSecondDerivative (double x)
 Returns the second derivative of the given order of reference (untransformed) function. More...
 
override double RefDerivative (double x, int order)
 Returns the derivative of the given order of reference (untransformed) function. More...
 
override double RefIntegral (double x)
 Returns definite integral of reference (untransformed) function from 0 to the function argument. More...
 
override double RefInverse (double y)
 Returns inverse of the reference (untransformed) function. More...
 
- Protected Member Functions inherited from IG.Num.RealFunction
 RealFunction ()
 

Properties

bool IsFiniteSupport [get]
 Whether penalty function has finite support (meaning that it is 0 for all arguments less than some specific value). More...
 
bool IsAbsoluteDifferentiable [get]
 True if absolute value is differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints. More...
 
bool IsAbsoluteTwiceDifferentiable [get]
 True if absolute value is twoce differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints. More...
 
bool CanSetMaxZero [get]
 Whether maximal value for which penalty function is zero can be set. More...
 
bool CanSetBarrierLength [get]
 Whether the gap can be set. More...
 
bool CanSetBarrierHeight [get]
 Whether the height can be set. More...
 
double MaxZero [get, set]
 Maximal value for which penalty function is zero. More...
 
double BarrierLength [get, set]
 Gap - characteristic length of transition area on which penalty function grows for about (or sometimes exactly, especially in case of finite support) characteristic height. More...
 
double BarrierHeight [get, set]
 Characteristic heitht of transition area, usually value of the penalty function at the end of transition area. More...
 
override bool ValueDefined [get, set]
 
override bool DerivativeDefined [get, set]
 
override bool SecondDerivativeDefined [get, set]
 
override bool IntegralDefined [get, set]
 
override bool InverseDefined [get, set]
 
- Properties inherited from IG.Num.RealFunction
override string Name [get, set]
 Returns a code name of the function (not necessarily unique). More...
 
override string Description [get, set]
 Returns a short description of the function (not necessarily unique). More...
 
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...
 
- Properties inherited from IG.Num.IRealFunctionPenalty
bool IsFiniteSupport [get]
 Whether penalty function has finite support (meaning that it is 0 for all arguments less than some specific value). More...
 
bool IsAbsoluteDifferentiable [get]
 True if absolute value is differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints. More...
 
bool IsAbsoluteTwiceDifferentiable [get]
 True if absolute value is twoce differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints. More...
 
bool CanSetMaxZero [get]
 Whether maximal value for which penalty function is zero can be set. More...
 
bool CanSetBarrierLength [get]
 Whether the gap can be set. More...
 
bool CanSetBarrierHeight [get]
 Whether the height can be set. More...
 
double MaxZero [get, set]
 Maximal value for which penalty function is zero. More...
 
double BarrierLength [get, set]
 Gap - characteristic length of transition area on which penalty function grows for about (or sometimes exactly, especially in case of finite support) characteristic height. More...
 
double BarrierHeight [get, set]
 Characteristic heitht of transition area, usually value of the penalty function at the end of transition area. More...
 

Private Member Functions

double Int0 (double tt)
 Returns integral for the function where x0 = 0. More...
 

Private Attributes

double dd
 
double hh
 
double xx0
 
double pp
 

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 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

Penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

Constructor & Destructor Documentation

IG.Num.Func.PenaltyPower.PenaltyPower ( double  length,
double  height,
int  power 
)
inline

Creates a new penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Transition pint where function starts to be non-zero is at negative characteristic length.

Parameters
lengthCharacteristic barrier length. Length of the interval on which function grows from 0 to characteristic height.
heightCharacteristic barrier height. Value of the function at transition point plus characteristic length.
powerPower. Must be greater than 0, for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.
IG.Num.Func.PenaltyPower.PenaltyPower ( double  length,
double  height,
double  zeroEnd,
int  power 
)
inline

Creates a new penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent.

Parameters
lengthCharacteristic barrier length. Length of the interval on which function grows from 0 to characteristic height.
heightCharacteristic barrier height. Value of the function at transition point plus characteristic length.
zeroEndTransition point where function starts to be non-zero.
powerPower. Must be greater than 0, for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

Member Function Documentation

override double IG.Num.Func.PenaltyPower.RefValue ( double  x)
inlineprotectedvirtual

Returns the value of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.PenaltyPower.RefDerivative ( double  x)
inlineprotectedvirtual

Returns the first derivative of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.PenaltyPower.RefSecondDerivative ( double  x)
inlineprotectedvirtual

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

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.PenaltyPower.RefDerivative ( double  x,
int  order 
)
inlineprotectedvirtual

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

Reimplemented from IG.Num.RealFunction.

override bool IG.Num.Func.PenaltyPower.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.

double IG.Num.Func.PenaltyPower.Int0 ( double  tt)
inlineprivate

Returns integral for the function where x0 = 0.

override double IG.Num.Func.PenaltyPower.RefIntegral ( double  x)
inlineprotectedvirtual

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

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.PenaltyPower.RefInverse ( double  y)
inlineprotectedvirtual

Returns inverse of the reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

Member Data Documentation

double IG.Num.Func.PenaltyPower.dd
private
double IG.Num.Func.PenaltyPower.hh
private
double IG.Num.Func.PenaltyPower.xx0
private
double IG.Num.Func.PenaltyPower.pp
private

Property Documentation

bool IG.Num.Func.PenaltyPower.IsFiniteSupport
get

Whether penalty function has finite support (meaning that it is 0 for all arguments less than some specific value).

bool IG.Num.Func.PenaltyPower.IsAbsoluteDifferentiable
get

True if absolute value is differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints.

bool IG.Num.Func.PenaltyPower.IsAbsoluteTwiceDifferentiable
get

True if absolute value is twoce differentiable, false otherwise. Differentiability of absolute value at 0 is important for penalty functions used for equality constraints.

bool IG.Num.Func.PenaltyPower.CanSetMaxZero
get

Whether maximal value for which penalty function is zero can be set.

bool IG.Num.Func.PenaltyPower.CanSetBarrierLength
get

Whether the gap can be set.

bool IG.Num.Func.PenaltyPower.CanSetBarrierHeight
get

Whether the height can be set.

double IG.Num.Func.PenaltyPower.MaxZero
getset

Maximal value for which penalty function is zero.

double IG.Num.Func.PenaltyPower.BarrierLength
getset

Gap - characteristic length of transition area on which penalty function grows for about (or sometimes exactly, especially in case of finite support) characteristic height.

double IG.Num.Func.PenaltyPower.BarrierHeight
getset

Characteristic heitht of transition area, usually value of the penalty function at the end of transition area.

override bool IG.Num.Func.PenaltyPower.ValueDefined
getset
override bool IG.Num.Func.PenaltyPower.DerivativeDefined
getset
override bool IG.Num.Func.PenaltyPower.SecondDerivativeDefined
getset
override bool IG.Num.Func.PenaltyPower.IntegralDefined
getset
override bool IG.Num.Func.PenaltyPower.InverseDefined
getset

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