IG.Num.Func3dLinear Class Reference

Linear (Affine) function of 3 variables. More...

Inheritance diagram for IG.Num.Func3dLinear:

Collaboration diagram for IG.Num.Func3dLinear:

Public Member Functions
	Func3dLinear (vec3 gradient0, double scalarTerm)
	Creation of a linear 3D scalar function. More...
override double	Value (vec3 parameters)
	Calculates and returns value of the current 3D linear function. More...
override vec3	Gradient (vec3 parameters)
	Calculates and returns gradient of the current 3D linear function. More...
override mat3	Hessian (vec3 parameters)
	Calculates and returns Hessian of the current 3D linear function (identical to zero matrix) and returns it (in the form of a mat3 struct). More...
Public Member Functions inherited from IG.Num.Func3dVectorFormBase
override double	Value (vec3 parameters)
	Calculates and returns value of the current 3D scalar function. More...
override vec3	Gradient (vec3 parameters)
	Calculates and returns gradient of the current 3D scalar function. More...
override mat3	Hessian (vec3 parameters)
	Calculates and returns Hessian of the current 3D scalar function and returns it (in the form of a mat3 struct). More...
sealed override double	Value (double x, double y, double z)
	Calculates and returns value of the current 3D scalar function. More...
sealed override void	Gradient (double x, double y, double z, out double gradx, out double grady, out double gradz)
	Calculates gradient of the current 3D scalar function and returns its components through the specified output variables. More...
sealed override void	Hessian (double x, double y, double z, out double dxx, out double dyy, out double dzz, out double dxy, out double dxz, out double dyz)
	Calculates Hessian of the current 3D scalar function and returns its component through the specified output variables. More...
Public Member Functions inherited from IG.Num.Func3dBase
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 int	GetNumConstants ()
	Returns the number of scalar constants that specify the current function. More...
Static Public Member Functions inherited from IG.Num.Func3dBase
static void	Example ()
	Example of use of a 3D function. More...

Properties
vec3	Gradient0 [get, protected set]
	Vector of linear coefficients (equal to gradient of the function). More...
double	ScalarTerm [get, protected set]
	Scalar additive constant. More...
Properties inherited from IG.Num.Func3dBase
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.IFunc3d
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 Member Functions
	Func3dLinear ()

Private Attributes
vec3	_b
double	_c

Additional Inherited Members
Protected Member Functions inherited from IG.Num.Func3dVectorFormBase
	Func3dVectorFormBase ()
	Constructor. More...
Protected Member Functions inherited from IG.Num.Func3dBase
	Func3dBase ()
Static Protected Member Functions inherited from IG.Num.Func3dBase
static void	TestFunction (IFunc3d f)
	Demonstrates use of a 3D 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 (IFunc3d f, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax, int numPoints)
	Demonstrates use of a 3D 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

Linear (Affine) function of 3 variables.

Function is evaluated according to fl(x) = b^T*x + c where x is vector of parameters, b is the vector of linear coefficients (gradient at x=0) and c is the scalar term (function value at x=0).

$A Igor Aug09;

Constructor & Destructor Documentation

IG.Num.Func3dLinear.Func3dLinear ( )

inlineprivate

IG.Num.Func3dLinear.Func3dLinear ( vec3  gradient0, double  scalarTerm  )

inline

Creation of a linear 3D scalar function.

Parameters

gradient0	Vector of linear coefficients - gradient of the linear function.
scalarTerm	Constant term.

Member Function Documentation

static int IG.Num.Func3dLinear.GetNumConstants ( )

inlinestatic

Returns the number of scalar constants that specify the current function.

override double IG.Num.Func3dLinear.Value ( vec3  parameters )

inline

Calculates and returns value of the current 3D linear function.

Parameters

parameters

Vector of function parameters (in form of the vec3) struct.

Returns

Function value.

Implements IG.Num.IFunc3d.

override vec3 IG.Num.Func3dLinear.Gradient ( vec3  parameters )

inline

Calculates and returns gradient of the current 3D linear function.

Parameters

parameters

Vector of parameters (in form of the vec3 struct).

<returnreturns>Gradient of the current 3D scalar function (in form of the vec3 struct)</returnreturns>

Implements IG.Num.IFunc3d.

override mat3 IG.Num.Func3dLinear.Hessian ( vec3  parameters )

inline

Calculates and returns Hessian of the current 3D linear function (identical to zero matrix) and returns it (in the form of a mat3 struct).

Implements IG.Num.IFunc3d.

Member Data Documentation

vec3 IG.Num.Func3dLinear._b

private

double IG.Num.Func3dLinear._c

private

Property Documentation

vec3 IG.Num.Func3dLinear.Gradient0

getprotected set

Vector of linear coefficients (equal to gradient of the function).

double IG.Num.Func3dLinear.ScalarTerm

getprotected set

Scalar additive constant.

---

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

• igbase/numeric/geometry/Function3d.cs