Radial scalar functions. More...

Inheritance diagram for IG.Num.ScalarFunctionRadial:

Collaboration diagram for IG.Num.ScalarFunctionRadial:

Public Member Functions
	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...

Properties
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...

Private Member Functions
	ScalarFunctionRadial ()

Private Attributes
IRealFunction	_function

double	_epsilon

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

Radial scalar functions.

$A Igor xx Nov10;

Constructor & Destructor Documentation

IG.Num.ScalarFunctionRadial.ScalarFunctionRadial ( )

inlineprivate

IG.Num.ScalarFunctionRadial.ScalarFunctionRadial	(	IRealFunction	function,
		IAffineTransformation	transf
	)

inline

Constructor. Creates a new radial 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.ScalarFunctionRadial.ScalarFunctionRadial ( IRealFunction function )

inline

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

Parameters

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

Member Function Documentation

virtual void IG.Num.ScalarFunctionRadial.SetFunction ( IRealFunction function1d )

inlinevirtual

Changes the 1D function that defines the current radial function.

Warning: the function should be set only exceptionally. Do not do this when immutability is required.

Parameters

function1d Function to be set.

override double IG.Num.ScalarFunctionRadial.ReferenceValue ( IVector x )

inlinevirtual

Returns the value of this function at the specified parameter.

Implements IG.Num.ScalarFunctionBase.

override void IG.Num.ScalarFunctionRadial.ReferenceGradientPlain	(	IVector	x,
		IVector	gradient
	)

inlinevirtual

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

Parameters

x	Vector of parameters where derivatives are evaluated.
gradient	Vector where first derivatives (gradient) are stored.

Implements IG.Num.ScalarFunctionBase.

References IG.Num.VectorBase.CopyPlain(), IG.Num.IVector.GetNew(), and IG.Num.VectorBase.MultiplyPlain().

override void IG.Num.ScalarFunctionRadial.ReferenceHessianPlain	(	IVector	x,
		IMatrix	hessian
	)

inlinevirtual

Returns the second derivative (Hessian) of this function at the specified arameter.

Parameters

x	Vector of parameters where derivatives are evaluated.
hessian	Matrix where second derivatives (Hessian) are stored.

Implements IG.Num.ScalarFunctionBase.

Member Data Documentation

IRealFunction IG.Num.ScalarFunctionRadial._function

private

double IG.Num.ScalarFunctionRadial._epsilon

private

Property Documentation

virtual IRealFunction IG.Num.ScalarFunctionRadial.Function

getprotected set

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

double IG.Num.ScalarFunctionRadial.Epsilon

getset

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.

override string IG.Num.ScalarFunctionRadial.Name

get

Returns a short name of the function.

override string IG.Num.ScalarFunctionRadial.Description

get

Returns a short description of the function.

override bool IG.Num.ScalarFunctionRadial.ValueDefined

getprotected set

Tells whether value of the function is defined by implementation.

override bool IG.Num.ScalarFunctionRadial.GradientDefined

getprotected set

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

override bool IG.Num.ScalarFunctionRadial.HessianDefined

getprotected set

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

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

igbase/numeric/FunctionScalarRadial.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