Base class for scalar functions of 2 variables (base for implementation of IFunc2d interface). More...

Inheritance diagram for IG.Num.Func2dBase:

Collaboration diagram for IG.Num.Func2dBase:

Public Member Functions
	Func2dBase ()

abstract double	Value (double x, double y)
	Calculates and returns value of the current 2D scalar function. More...

virtual double	Value (vec2 parameters)
	Calculates and returns value of the current 2D scalar function. More...

abstract void	Gradient (double x, double y, out double gradx, out double grady)
	Calculates gradient of the current 2D scalar function and returns its components through the specified output variables. More...

virtual vec2	Gradient (vec2 parameters)
	Calculates and returns gradient of the current 2D scalar function. More...

abstract void	Hessian (double x, double y, out double dxx, out double dyy, out double dxy)
	Calculates Hessian of the current 2D scalar function and returns its component through the specified output variables. More...

virtual mat2	Hessian (vec2 parameters)
	Calculates and returns Hessian of the current 2D scalar function and returns it (in the form of a mat2 struct). More...

override double	Value (IVector parameters)
	Returns the value of the current function at the specified parameters. More...

override void	GradientPlain (IVector parameters, IVector gradient)
	Calculates first order derivatives (gradient) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments. More...

override void	HessianPlain (IVector parameters, IMatrix hessian)
	Calculates the second derivative (Hessian matrix) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments. 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 Public Member Functions
static void	Example ()
	Example of use of a 2D function. More...

Static Protected Member Functions
static void	TestFunction (IFunc2d f)
	Demonstrates use of a 2D function by printing to the console 5 values and gradients of the function on the line connecting the two points (0, 0, 0) and (1, 1, 1). More...

static void	TestFunction (IFunc2d f, double xmin, double xmax, double ymin, double ymax, int numPoints)
	Demonstrates use of a 2D function by printing to the console some values and gradients of the function on the line connecting the two specified points. More...

Properties
override bool	ValueDefined `[get, protected set]`
	Whether calculation of function value is defined. Defaulet is true. More...

override bool	GradientDefined `[get, protected set]`
	Whether calculation of functio ngradient is defined. Default is false. More...

override bool	HessianDefined `[get, protected set]`
	Whether calculation of function Hessian is defined. Default is false. More...

int	NumParam `[get]`
	Gets number of 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.IFunc2d
bool	ValueDefined `[get]`
	Whether calculation of function value is defined. More...

bool	GradientDefined `[get]`
	Whether calculation of function ngradient is defined. More...

bool	HessianDefined `[get]`
	Whether calculation of function Hessian is defined. More...

Private Attributes
bool	_valueDefined = true

bool	_gradientDefined = false

bool	_hessianDefined = false

Additional Inherited Members
Protected Attributes inherited from IG.Num.ScalarFunctionUntransformedBase
string	_name

string	_description

Detailed Description

Base class for scalar functions of 2 variables (base for implementation of IFunc2d interface).

Beside the IFunc2d

interface, this class also implements the IScalarFunction

interface. This does not affect efficiency but adds the functionality for using objects as general (untransformed) scalar functions.

$A Igor Apr09;

Constructor & Destructor Documentation

IG.Num.Func2dBase.Func2dBase ( )

inline

Member Function Documentation

abstract double IG.Num.Func2dBase.Value	(	double	x,
		double	y
	)

pure virtual

Calculates and returns value of the current 2D scalar function.

Parameters

x	First parameter.
y	Second parameter.

Implements IG.Num.IFunc2d.

Implemented in IG.Gr3d.VtkPlotBase.ExampleFuncDiff, IG.Gr3d.VtkPlotBase.ExampleFunc2dShifted, IG.Gr3d.VtkPlotBase.ExampleFunc2dSquare, IG.Gr3d.VtkPlotBase.ExampleFunc2dLinear, IG.Gr3d.VtkPlotBase.ExampleFunc2dXY, IG.Gr3d.VtkPlotBase.Func2dZero, IG.Gr3d.VtkPlotBase.Func2dY, IG.Gr3d.VtkPlotBase.Func2dX, IG.Num.Func2dExamples.Func2dXY, IG.Num.Func3d2dBase.ComponentFunction3, IG.Num.Func3d2dBase.ComponentFunction2, IG.Num.Func3d2dBase.ComponentFunction1, IG.Num.Func2dVectorFormBase, IG.Num.Func2dFromScalarFunction, and IG.Neural.Func2dFromApproximator.

Referenced by IG.Gr3d.VtkPlotBase.ExampleSurfacePlotManualScaled(), and IG.Gr3d.VtkPlotBase.ExampleSurfacePlotScaled().

virtual double IG.Num.Func2dBase.Value ( vec2 parameters )

inlinevirtual

Calculates and returns value of the current 2D scalar function.

Parameters

parameters Vector of function parameters (in form of the Value) struct.

Returns: Function value.

Implements IG.Num.IFunc2d.

Reimplemented in IG.Num.Func2dQuadratic, IG.Num.Func2dLinear, and IG.Num.Func2dVectorFormBase.

References IG.Num.vec2.x, and IG.Num.vec2.y.

abstract void IG.Num.Func2dBase.Gradient	(	double	x,
		double	y,
		out double	gradx,
		out double	grady
	)

pure virtual

Calculates gradient of the current 2D scalar function and returns its components through the specified output variables.

Parameters

x	First parameter.
y	Second parameter.
gradx	First component of the returned gradient.
grady	Second component of the returned gradient.

Implements IG.Num.IFunc2d.

Implemented in IG.Gr3d.VtkPlotBase.ExampleFuncDiff, IG.Gr3d.VtkPlotBase.ExampleFunc2dSquare, IG.Gr3d.VtkPlotBase.ExampleFunc2dLinear, IG.Gr3d.VtkPlotBase.ExampleFunc2dXY, IG.Gr3d.VtkPlotBase.Func2dZero, IG.Gr3d.VtkPlotBase.Func2dY, IG.Gr3d.VtkPlotBase.Func2dX, IG.Num.Func2dExamples.Func2dXY, IG.Num.Func3d2dBase.ComponentFunction3, IG.Num.Func3d2dBase.ComponentFunction2, IG.Num.Func3d2dBase.ComponentFunction1, IG.Num.Func2dVectorFormBase, IG.Num.Func2dBaseNoGradient, IG.Num.Func2dFromScalarFunction, and IG.Neural.Func2dFromApproximator.

virtual vec2 IG.Num.Func2dBase.Gradient ( vec2 parameters )

inlinevirtual

Calculates and returns gradient of the current 2D scalar function.

Parameters

parameters Vector of parameters (in form of the vec2 struct)

<returnreturns>Gradient of the current 2D scalar function (in form of the vec2 struct)</returnreturns>

Implements IG.Num.IFunc2d.

Reimplemented in IG.Num.Func2dQuadratic, IG.Num.Func2dLinear, and IG.Num.Func2dVectorFormBase.

References IG.Num.vec2.x, and IG.Num.vec2.y.

abstract void IG.Num.Func2dBase.Hessian	(	double	x,
		double	y,
		out double	dxx,
		out double	dyy,
		out double	dxy
	)

pure virtual

Calculates Hessian of the current 2D scalar function and returns its component through the specified output variables.

Parameters

x	First parameter.
y	Second parameter.
dxx	Component 1-1 of the calculated Hessian.
dyy	Component 2-2 of the calculated Hessian.
dxy	Component 1-2 of the calculated Hessian.

Implements IG.Num.IFunc2d.

Implemented in IG.Num.Func3d2dBase.ComponentFunction3, IG.Num.Func3d2dBase.ComponentFunction2, IG.Num.Func3d2dBase.ComponentFunction1, IG.Num.Func2dVectorFormBase, IG.Num.Func2dBaseNoGradient, IG.Num.Func2dBaseNoHessian, IG.Num.Func2dFromScalarFunction, and IG.Neural.Func2dFromApproximator.

virtual mat2 IG.Num.Func2dBase.Hessian ( vec2 parameters )

inlinevirtual

Calculates and returns Hessian of the current 2D scalar function and returns it (in the form of a mat2 struct).

Implements IG.Num.IFunc2d.

Reimplemented in IG.Num.Func2dQuadratic, IG.Num.Func2dLinear, and IG.Num.Func2dVectorFormBase.

References IG.Num.vec2.x, and IG.Num.vec2.y.

override double IG.Num.Func2dBase.Value ( IVector parameters )

inline

Returns the value of the current function at the specified parameters.

Parameters

parameters Vector of parameters for which value is evaluated. Its dimension must be equal to 2.

Implements IG.Num.IScalarFunctionUntransformed.

override void IG.Num.Func2dBase.GradientPlain	(	IVector	parameters,
		IVector	gradient
	)

inline

Calculates first order derivatives (gradient) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments.

Parameters

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

Implements IG.Num.IScalarFunctionUntransformed.

override void IG.Num.Func2dBase.HessianPlain	(	IVector	parameters,
		IMatrix	hessian
	)

inline

Calculates the second derivative (Hessian matrix) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments.

Parameters

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

Implements IG.Num.IScalarFunctionUntransformed.

static void IG.Num.Func2dBase.TestFunction ( IFunc2d f )

inlinestaticprotected

Demonstrates use of a 2D function by printing to the console 5 values and gradients of the function on the line connecting the two points (0, 0, 0) and (1, 1, 1).

Parameters

f	Function whose values and gradients are evaluated and printed.

static void IG.Num.Func2dBase.TestFunction	(	IFunc2d	f,
		double	xmin,
		double	xmax,
		double	ymin,
		double	ymax,
		int	numPoints
	)

inlinestaticprotected

Demonstrates use of a 2D function by printing to the console some values and gradients of the function on the line connecting the two specified points.

Parameters

f	Function whose values and gradients are evaluated and printed.
xmin	Min. x.
xmax	Max. x.
ymin	Min. y.
ymax	Max. y.
numPoints	Number of points in which function values and gradients are printed.

References IG.Num.IFunc2d.Gradient(), IG.Num.IFunc2d.GradientDefined, IG.Num.IFunc2d.Value(), and IG.Num.IFunc2d.ValueDefined.

static void IG.Num.Func2dBase.Example ( )

inlinestatic

Example of use of a 2D function.

Member Data Documentation

bool IG.Num.Func2dBase._valueDefined = true

private

bool IG.Num.Func2dBase._gradientDefined = false

private

bool IG.Num.Func2dBase._hessianDefined = false

private

Property Documentation

override bool IG.Num.Func2dBase.ValueDefined

getprotected set

Whether calculation of function value is defined. Defaulet is true.

override bool IG.Num.Func2dBase.GradientDefined

getprotected set

Whether calculation of functio ngradient is defined. Default is false.

override bool IG.Num.Func2dBase.HessianDefined

getprotected set

Whether calculation of function Hessian is defined. Default is false.

int IG.Num.Func2dBase.NumParam

get

Gets number of parameters.

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

igbase/numeric/geometry/Function2d.cs

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Properties

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation