IG.Num.ScalarFunctionRadialOneParametric Class Reference

Base class for one parametric families of radial scalar functions with affine transformation of co-ordinates. Parameters that completely define the function out of parametric family of functions can be queried or set. Affine transformation of coordinates is included: the reference function evaluation must be defined while the actual function is defined as that reference function of transformed coordinates. If transformation is not specified then function reduces to the reference one. More...

Inheritance diagram for IG.Num.ScalarFunctionRadialOneParametric:

Collaboration diagram for IG.Num.ScalarFunctionRadialOneParametric:

Public Member Functions
	ScalarFunctionRadialOneParametric (IRealFunctionOneParametric function, IVector parameters, IAffineTransformation transf)
	Constructor. Creates a new radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialOneParametric (IRealFunctionOneParametric function, IAffineTransformation transf)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialOneParametric (IRealFunctionOneParametric function, IVector parameters)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialOneParametric (IRealFunctionOneParametric function)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation or parameters. More...
override double[]	GetParameters ()
	Returns parameters of the current parametric function as an array. Since this class is for one parametric family of functions, an array of length 1 is always returned. More...
override void	SetParameters (double[] parameters)
	Sets parameters of the current parametric functions, where parameters are specified as array. More...
override double	GetParameter (int which)
	Returns value of the specified parameter of the parameterized function. More...
override void	SetParameter (int which, double value)
	Sets the specific parameters of the parameterized function. More...
Public Member Functions inherited from IG.Num.ScalarFunctionRadialParametric
	ScalarFunctionRadialParametric (IRealFunctionParametric function, IVector parameters, IAffineTransformation transf)
	Constructor. Creates a new radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialParametric (IRealFunctionParametric function, IAffineTransformation transf)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialParametric (IRealFunctionParametric function, IVector parameters)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation. More...
	ScalarFunctionRadialParametric (IRealFunctionOneParametric function)
	Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation or parameters. More...
Public Member Functions inherited from IG.Num.ScalarFunctionRadial
	ScalarFunctionRadial (IRealFunction function, IAffineTransformation transf)
	Constructor. Creates a new radial function without specifying coordinate transformation. More...
	ScalarFunctionRadial (IRealFunction function)
	Constructor. Creates a new radial function without specifying coordinate transformation. More...
virtual void	SetFunction (IRealFunction function1d)
	Changes the 1D function that defines the current radial function. More...
override double	ReferenceValue (IVector x)
	Returns the value of this function at the specified parameter. More...
override void	ReferenceGradientPlain (IVector x, IVector gradient)
	Returns the first derivative of this function at the specified parameter. More...
override void	ReferenceHessianPlain (IVector x, IMatrix hessian)
	Returns the second derivative (Hessian) of this function at the specified arameter. More...
Public Member Functions inherited from IG.Num.ScalarFunctionBase
	ScalarFunctionBase (IAffineTransformation transf)
	Constructs a scalar function that is identical to some reference funciton acting on affine transformed parameters. More...
override double	Value (IVector x)
	Returns the value of this function at the specified parameter. More...
override void	GradientPlain (IVector x, IVector gradient)
	Returns the first derivative of this function at the specified parameter. More...
override void	HessianPlain (IVector x, IMatrix hessian)
	Returns the second derivative (Hessian) of this function at the specified arameter. More...
Public Member Functions inherited from IG.Num.ScalarFunctionUntransformedBase
virtual void	Evaluate (IScalarFunctionResults data)
	Evaluates whatever needs to be evaluated and stores the results on the specified storage object. More...
virtual void	Gradient (IVector parameters, ref IVector gradient)
	Calculates first order derivatives (gradient) of this function at the specified parameters. More...
virtual void	Hessian (IVector parameters, ref IMatrix hessian)
	Calculates the second derivative (Hessian matrix) of this function at the specified parameters. More...
virtual void	NumericalGradientForwardPlain (IVector x, IVector stepSizes, IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
void	NumericalGradientForward (IVector x, IVector stepSizes, ref IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
void	NumericalGradientForward (IVector x, double stepSize, ref IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is used. More...
virtual void	NumericalGradientCentralPlain (IVector x, IVector stepSizes, IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
void	NumericalGradientCentral (IVector x, IVector stepSizes, ref IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
void	NumericalGradientCentral (IVector x, double stepSize, ref IVector gradient)
	Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
virtual void	NumericalHessianForwardPlain (IVector x, IVector stepSizes, IVector aux, IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianForward (IVector x, IVector stepSizes, ref IVector aux, ref IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianForward (IVector x, double stepSize, ref IVector aux, ref IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentralPlain (IVector x, IVector stepSizes, IVector aux1, IVector aux2, IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentral (IVector x, IVector stepSizes, ref IVector aux1, ref IVector aux2, ref IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentral (IVector x, double stepSize, ref IVector aux1, ref IVector aux2, ref IMatrix hessian)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentralPlain (IVector x, IVector stepSizes, IVector aux1, IVector aux2, IMatrix hessian, bool useAnalyticalGradient)
	Calculates numerical second derivatives (Hessian) of this function by the central difference formula. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentral (IVector x, IVector stepSizes, ref IVector aux1, ref IVector aux2, ref IMatrix hessian, bool useAnalyticalGradient)
	Calculates numerical second derivatives (Hessian) of this function by the central difference formula. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
virtual void	NumericalHessianCentral (IVector x, double stepSize, ref IVector aux1, ref IVector aux2, ref IMatrix hessian, bool useAnalyticalGradient)
	Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
void	TestSpeed (IVector parameters, int numEvaluations, bool randomPerturbations, double relativePerturbationSize, bool calcValue, bool calcGradient, bool calcHessian, bool writeLastResult)
	Tests speed of evaluation of the current scalar function and writes results to the console. More...
void	TestGradient (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeGradientComponents)
	Tests the calculation of gradients of the current scalar function. More...
void	TestGradient (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeGradientComponents, bool useCentralDifference)
	Tests the calculation of gradients of the current scalar function. More...
void	TestHessian (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeHessianComponents)
	Tests the calculation of Hessians of the current scalar function. More...
void	TestHessian (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeHessianComponents, bool useCentralDifference)
	Tests the calculation of Hessians of the current scalar function. More...
void	Test (IVector from, IVector to, int numProbes, IVector stepSizes, double tolerance, bool testDerivatives, bool testSecondDerivatives, bool printDifferences, bool printResults)
	Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...
void	Test (IVector from, IVector to, int numProbes, IVector stepSizes, double tolerance)
	Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. This method tests first and second order derivatives, prints differences between analytical and numerical values to the console, and prints reports where absolute differences exceed rolerance. More...
void	Test (IVector from, IVector to, int numProbes, double stepSize, double tolerance, bool testDerivatives, bool testSecondDerivatives, bool printDifferences, bool printResults)
	Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...
void	Test (IVector from, IVector to, int numProbes, double stepSize, double tolerance)
	Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...

Static Protected Attributes
static Vector	_parAux = new Vector(1)
	Auxiliary vector whose only function is to enable calling base constructors with parameters specified as vector. More...

Properties
virtual IRealFunctionOneParametric	FunctionOneParametric [get, protected set]
	Gets or sets the parametrivc real-valued function of one variable that defines the current radial function. More...
override IRealFunctionParametric	FunctionParametric [get, protected set]
	Gets or sets the oneparametric real-valued function of one variable that defines the current radial function. When setting, the argument must be of appropriate type (IRealFunctionOneParametric). More...
override IRealFunction	Function [get, protected set]
	Gets or sets a real-valued function of one variable that defines the current radial function. When setting, the argument must be of appropriate type (IRealFunctionOneParametric). More...
override IVector	Parameters [get, set]
	Gets or sets parameters that define the specific function out of parametric familiy of scalar functions. More...
virtual double	Parameter [get, set]
	Gets or sets the (only) parameter that defines the current function out of parametric family of functions. More...
override int	NumParameters [get]
	Gets number of parameters that define the current function out of parametric family of scalar functions. Always evaluates to 1 because this is a one parametric family of functions. More...
Properties inherited from IG.Num.ScalarFunctionRadialParametric
virtual IRealFunctionParametric	FunctionParametric [get, protected set]
	Gets or sets the parametrivc real-valued function of one variable that defines the current radial function. More...
override IRealFunction	Function [get, protected set]
	Gets or sets a real-valued function of one variable that defines the current radial function. When setting, the argument must be of appropriate type (IRealFunctionParametric). More...
virtual IVector	Parameters [get, set]
	Parameters that define the specific function out of parametric familiy of scalar functions. More...
virtual int	NumParameters [get]
	Gets number of parameters that define the current function out of parametric family of scalar functions. More...
Properties inherited from IG.Num.ScalarFunctionRadial
virtual IRealFunction	Function [get, protected set]
	Gets or sets a real-valued function of one variable that defines the current radial function. More...
double	Epsilon [get, set]
	Gets or sets a small number used as criteria of where to calculate things (especially derivatives) in a special way in order to overcome singularities in expressions. For example, some expressions contain divisions by vector norm. When vector norm is close to 0, this results in nearly singular terms, which must be replaced by suitable limits. More...
override string	Name [get]
	Returns a short name of the function. More...
override string	Description [get]
	Returns a short description of the function. More...
override bool	ValueDefined [get, protected set]
	Tells whether value of the function is defined by implementation. More...
override bool	GradientDefined [get, protected set]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
override bool	HessianDefined [get, protected set]
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
Properties inherited from IG.Num.ScalarFunctionBase
virtual IAffineTransformation	Transformation [get, set]
	Transformation of parameters. Actual function is evaluated as some reference function evaluated at inverse affine-transformed parameters. More...
Properties inherited from IG.Num.ScalarFunctionUntransformedBase
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...
abstract bool	ValueDefined [get, protected set]
	Tells whether value of the function is defined by implementation. More...
abstract bool	GradientDefined [get, protected set]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
abstract bool	HessianDefined [get, protected set]
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
Properties inherited from IG.Num.IScalarFunctionUntransformed
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	GradientDefined [get]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
bool	HessianDefined [get]
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
Properties inherited from IG.Num.IScalarFunction
IAffineTransformation	Transformation [get, set]
	Affine transformation of parameters. Actual function is evaluated as reference function evaluated at inverse affine transformed parameters. More...
Properties inherited from IG.Num.IScalarFunctionParametric
IVector	Parameters [get, set]
	Parameters that define the specific function out of parametric familiy of scalar functions. More...
int	NumParameters [get]
	Gets number of parameters that define the specific function out of parametric family of scalar functions. More...
Properties inherited from IG.Num.IScalarFunctionOneParametric
double	Parameter [get, set]
	Gets or sets the (only) parameter that defines the current function out of parametric family of functions. More...

Private Member Functions
	ScalarFunctionRadialOneParametric ()
	Default constructor is inaccessible because it has no meaning. More...

Private Attributes
IRealFunctionOneParametric	_functionOneParametric

Additional Inherited Members
Protected Member Functions inherited from IG.Num.ScalarFunctionBase
	ScalarFunctionBase ()
	Default constructor for scalar functions of affine transformed parameters. Constructs untransformed reference function. More...
Protected Attributes inherited from IG.Num.ScalarFunctionBase
IVector	_refParam
IVector	_refGrad
IMatrix	_refHess
Protected Attributes inherited from IG.Num.ScalarFunctionUntransformedBase
string	_name
string	_description

Detailed Description

Base class for one parametric families of radial scalar functions with affine transformation of co-ordinates. Parameters that completely define the function out of parametric family of functions can be queried or set. Affine transformation of coordinates is included: the reference function evaluation must be defined while the actual function is defined as that reference function of transformed coordinates. If transformation is not specified then function reduces to the reference one.

This base class does not implement data containing parameters. This enables to derive base classes with different representations of parameters, e.g. with only one number for one parametric functions.

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Constructor & Destructor Documentation

IG.Num.ScalarFunctionRadialOneParametric.ScalarFunctionRadialOneParametric ( )

inlineprivate

Default constructor is inaccessible because it has no meaning.

IG.Num.ScalarFunctionRadialOneParametric.ScalarFunctionRadialOneParametric ( IRealFunctionOneParametric  function, IVector  parameters, IAffineTransformation  transf  )

inline

Constructor. Creates a new radial scalar function without specifying coordinate transformation.

Parameters

function	A real-valued function of one parameter that defined the radial function.
parameters	Parameters that define the function out of a parametric family of functions.
transf	Affine transformation of coordinates. Actual function is calculated as some reference function evaluated at inverse affine transformed parameters. If null then transformation is not applied.

IG.Num.ScalarFunctionRadialOneParametric.ScalarFunctionRadialOneParametric ( IRealFunctionOneParametric  function, IAffineTransformation  transf  )

inline

Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation.

Parameters

function	A real-valued function of one parameter that defined the radial function.
transf	Affine transformation of coordinates. Actual function is calculated as some reference function evaluated at inverse affine transformed parameters. If null then transformation is not applied.

IG.Num.ScalarFunctionRadialOneParametric.ScalarFunctionRadialOneParametric ( IRealFunctionOneParametric  function, IVector  parameters  )

inline

Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation.

Parameters

function	A real-valued function of one parameter that defined the radial function.
parameters	Parameters that define the function out of a parametric family of functions.

IG.Num.ScalarFunctionRadialOneParametric.ScalarFunctionRadialOneParametric ( IRealFunctionOneParametric  function )

inline

Constructor. Creates a new parameterized radial scalar function without specifying coordinate transformation or parameters.

Parameters

function

A real-valued function of one parameter that defined the radial function.

Member Function Documentation

override double [] IG.Num.ScalarFunctionRadialOneParametric.GetParameters ( )

inline

Returns parameters of the current parametric function as an array. Since this class is for one parametric family of functions, an array of length 1 is always returned.

Implements IG.Num.IScalarFunctionParametric.

override void IG.Num.ScalarFunctionRadialOneParametric.SetParameters ( double[]  parameters )

inline

Sets parameters of the current parametric functions, where parameters are specified as array.

Parameters

parameters

Array of parameters. Array length must be 1 because this class represents a one parametric family..

Implements IG.Num.IScalarFunctionParametric.

override double IG.Num.ScalarFunctionRadialOneParametric.GetParameter ( int  which )

inline

Returns value of the specified parameter of the parameterized function.

Parameters

which

Specifies which parameter is returned, must be 0 because this class represents a one parametric family of functions.

Implements IG.Num.IScalarFunctionParametric.

override void IG.Num.ScalarFunctionRadialOneParametric.SetParameter ( int  which, double  value  )

inline

Sets the specific parameters of the parameterized function.

Parameters

which	Specifies which parameter is set, must be 0 because this class represents a one parametric family of functions.
value	Value of the specified parameter.

Implements IG.Num.IScalarFunctionParametric.

Member Data Documentation

Vector IG.Num.ScalarFunctionRadialOneParametric._parAux = new Vector(1)

staticprotected

Auxiliary vector whose only function is to enable calling base constructors with parameters specified as vector.

IRealFunctionOneParametric IG.Num.ScalarFunctionRadialOneParametric._functionOneParametric

private

Property Documentation

virtual IRealFunctionOneParametric IG.Num.ScalarFunctionRadialOneParametric.FunctionOneParametric

getprotected set

Gets or sets the parametrivc real-valued function of one variable that defines the current radial function.

override IRealFunctionParametric IG.Num.ScalarFunctionRadialOneParametric.FunctionParametric

getprotected set

Gets or sets the oneparametric real-valued function of one variable that defines the current radial function. When setting, the argument must be of appropriate type (IRealFunctionOneParametric).

override IRealFunction IG.Num.ScalarFunctionRadialOneParametric.Function

getprotected set

Gets or sets a real-valued function of one variable that defines the current radial function. When setting, the argument must be of appropriate type (IRealFunctionOneParametric).

override IVector IG.Num.ScalarFunctionRadialOneParametric.Parameters

getset

Gets or sets parameters that define the specific function out of parametric familiy of scalar functions.

virtual double IG.Num.ScalarFunctionRadialOneParametric.Parameter

getset

Gets or sets the (only) parameter that defines the current function out of parametric family of functions.

override int IG.Num.ScalarFunctionRadialOneParametric.NumParameters

get

Gets number of parameters that define the current function out of parametric family of scalar functions. Always evaluates to 1 because this is a one parametric family of functions.

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

• igbase/numeric/FunctionScalarRadial.cs