Base class for one parametric families of 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.ScalarFunctionOneParametric:

Collaboration diagram for IG.Num.ScalarFunctionOneParametric:

Public Member Functions
	ScalarFunctionOneParametric (double parameter)
	Constructor. Does not define affine transformation of the function. More...

	ScalarFunctionOneParametric (double parameter, IAffineTransformation transformation)
	Constructor. Creates a new parametric scalar function with the specified parameter and transformation of coordinates. More...

	ScalarFunctionOneParametric (IVector parameters)
	Constructor. Does not define affine transformation of the function. More...

	ScalarFunctionOneParametric (IVector parameters, IAffineTransformation transformation)
	Cobnstructor. Creates a new parametric scalar function with the specified parameters and transformation of coordinates. 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.ScalarFunctionParametricBase
	ScalarFunctionParametricBase (IVector parameters)
	Constructor. Does not define affine transformation of the function. More...

	ScalarFunctionParametricBase (IVector parameters, IAffineTransformation transformation)
	Cobnstructor. Creates a new parametric scalar function with the specified parameters and transformation of coordinates. 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...

abstract double	ReferenceValue (IVector parameters)
	Returns the value of this function at the specified parameter in the reference coordinate system. More...

abstract void	ReferenceGradientPlain (IVector parameters, IVector gradient)
	Calculates the first derivative (gradient) of this function at the specified parameter in the reference coordinate system. More...

abstract void	ReferenceHessianPlain (IVector parameters, IMatrix hessian)
	Calculates the second derivative (Hessian) of this function at the specified parameters in the reference coordinate system. 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
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.ScalarFunctionParametricBase
abstract IVector	Parameters `[get, set]`
	Gets or sets parameters that define the specific function out of parametric familiy of scalar functions. Usually a reference is set or returned. 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.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...

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

Private Attributes
double	_parameter

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 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.

$A Igor Dec10;

Constructor & Destructor Documentation

IG.Num.ScalarFunctionOneParametric.ScalarFunctionOneParametric ( )

inlineprivate

Default constructor is inaccessible because it has no meaning.

IG.Num.ScalarFunctionOneParametric.ScalarFunctionOneParametric ( double parameter )

inline

Constructor. Does not define affine transformation of the function.

Parameters

parameter Parameter that define a specific function out of a parametric family of functions.

IG.Num.ScalarFunctionOneParametric.ScalarFunctionOneParametric	(	double	parameter,
		IAffineTransformation	transformation
	)

inline

Constructor. Creates a new parametric scalar function with the specified parameter and transformation of coordinates.

Parameters

parameter	Parameter that defines a specific function out of a parametric family of functions.
transformation	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.ScalarFunctionOneParametric.ScalarFunctionOneParametric ( IVector parameters )

inline

Constructor. Does not define affine transformation of the function.

Parameters

parameters Vector of parameters that define a specific function out of a parametric family of functions.

IG.Num.ScalarFunctionOneParametric.ScalarFunctionOneParametric	(	IVector	parameters,
		IAffineTransformation	transformation
	)

inline

Cobnstructor. Creates a new parametric scalar function with the specified parameters and transformation of coordinates.

Parameters

parameters	Vector of parameters that define a specific function out of a parametric family of functions.
transformation	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.

Member Function Documentation

override double [] IG.Num.ScalarFunctionOneParametric.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.ScalarFunctionOneParametric.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.ScalarFunctionOneParametric.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.ScalarFunctionOneParametric.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.ScalarFunctionOneParametric._parAux = new Vector(1)

staticprotected

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

double IG.Num.ScalarFunctionOneParametric._parameter

private

Property Documentation

override IVector IG.Num.ScalarFunctionOneParametric.Parameters

getset

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

virtual double IG.Num.ScalarFunctionOneParametric.Parameter

getset

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

override int IG.Num.ScalarFunctionOneParametric.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.

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

igbase/numeric/FunctionScalarParametric.cs

Public Member Functions

Static Protected Attributes

Properties

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation