IG.Num.Func2dFromScalarFunction Class Reference

Scalar function of 2 variables that is based on a general scalar function of vector argument. More...

Inheritance diagram for IG.Num.Func2dFromScalarFunction:

Collaboration diagram for IG.Num.Func2dFromScalarFunction:

Public Member Functions
	Func2dFromScalarFunction (IScalarFunction originalFunction)
	Constructs a scalar function of 2 variables from the specified scalar function of a vector argument. More...
override double	Value (double x, double y)
	Calculates and returns value of the current 2D scalar function. More...
override 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...
override 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...
Public Member Functions inherited from IG.Num.Func2dBase
	Func2dBase ()
virtual double	Value (vec2 parameters)
	Calculates and returns value of the current 2D scalar function. More...
virtual vec2	Gradient (vec2 parameters)
	Calculates and returns gradient of the current 2D scalar function. 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...

Protected Member Functions
	Func2dFromScalarFunction ()

Properties
IScalarFunction	OriginalFunction [get, protected set]
	Scalar function of vector argument that is used for evaluation of the current function value, gradient, and Hessian. More...
Properties inherited from IG.Num.Func2dBase
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
IScalarFunction	_originalFunction

Additional Inherited Members
Static Public Member Functions inherited from IG.Num.Func2dBase
static void	Example ()
	Example of use of a 2D function. More...
Static Protected Member Functions inherited from IG.Num.Func2dBase
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...
Protected Attributes inherited from IG.Num.ScalarFunctionUntransformedBase
string	_name
string	_description

Detailed Description

Scalar function of 2 variables that is based on a general scalar function of vector argument.

$A Igor Oct11;

Constructor & Destructor Documentation

IG.Num.Func2dFromScalarFunction.Func2dFromScalarFunction ( )

inlineprotected

IG.Num.Func2dFromScalarFunction.Func2dFromScalarFunction ( IScalarFunction  originalFunction )

inline

Constructs a scalar function of 2 variables from the specified scalar function of a vector argument.

Parameters

scalarFunction

Original scalar function of vector argument used for evaluation.

Member Function Documentation

override double IG.Num.Func2dFromScalarFunction.Value ( double  x, double  y  )

inline

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

Parameters

x	First parameter.
y	Second parameter.

Implements IG.Num.IFunc2d.

References IG.Num.IScalarFunctionUntransformed.Value().

override void IG.Num.Func2dFromScalarFunction.Gradient ( double  x, double  y, out double  gradx, out double  grady  )

inline

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.

override void IG.Num.Func2dFromScalarFunction.Hessian ( double  x, double  y, out double  dxx, out double  dyy, out double  dxy  )

inline

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.

Member Data Documentation

IScalarFunction IG.Num.Func2dFromScalarFunction._originalFunction

private

Property Documentation

IScalarFunction IG.Num.Func2dFromScalarFunction.OriginalFunction

getprotected set

Scalar function of vector argument that is used for evaluation of the current function value, gradient, and Hessian.

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

• extensions/igplot3d/plot3d/vtkbased/functions/Func2dFromScalar.cs