Quadratic scalar function of vector variable. Function is evaluated according to q(x) = (1/2)*x^T*G*x + b^T*x + c where x is vector of parameters, G is constant Hessian matrix, b is vector of linear coefficients (gradient at x=0) and c is the scalar term (function value at x=0). More...

Inheritance diagram for IG.Num.ScalarFunctionQuadratic:

Collaboration diagram for IG.Num.ScalarFunctionQuadratic:

Public Member Functions
	ScalarFunctionQuadratic (IMatrix hessian, IVector gradient0, double scalarTerm)
	Creation of a quadratic scalar function. WARNING: Matrix argument is interpreted as Hessian, i.e. twice the matrix of quadratic coefficients. More...

override double	Value (IVector parameters)
	Returns the value of this function at the specified parameter. 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 ScalarFunctionQuadratic	ExampleFunction2d ()
	Creates and returns quadratic scalar function in 2D. More...

static ScalarFunctionQuadratic	ExampleFunctionDiagonal2d ()
	Creates and returns quadratic scalar function with diagonal Hessian. More...

static ScalarFunctionQuadratic	ExampleFunctionPureQuadratic2d ()
	Creates and returns quadratic scalar function with only quadratic terms. More...

static ScalarFunctionQuadratic	ExampleFunctionDiagonalPureQuadratic2d ()
	Creates and returns quadratic function with diagonal Hessian. More...

static int	GetNumConstants (int dim)
	Returns the number of constants that specify the quadratic function of the specified dimension. More...

Properties
int	NumActualConstants `[get]`
	Gets the number of constants that define the current function. If e.g. the matrix coefficient or the vector coefficient is not defined then the corresponding constants are not counted. More...

IMatrix	HessianMatrix `[get, protected set]`
	Twice the matrix of quadratic coefficients (Hessian matrix). More...

IVector	Gradient0 `[get, protected set]`
	Vector of linear coefficients (equal to gradient of the function at x=0). More...

double	ScalarTerm `[get, protected set]`
	Scalar additive constant. More...

override bool	ValueDefined `[get, protected set]`
	Tells whether value of the function is defined by implementation. Always true for this case. 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.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...

Private Member Functions
	ScalarFunctionQuadratic ()

Private Attributes
IMatrix	_G

IVector	_b

double	_c

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

string	_description

Detailed Description

Quadratic scalar function of vector variable. Function is evaluated according to q(x) = (1/2)*x^T*G*x + b^T*x + c where x is vector of parameters, G is constant Hessian matrix, b is vector of linear coefficients (gradient at x=0) and c is the scalar term (function value at x=0).

When quadratic function is created or its parameters set, the Matrix parameter of the function is interpreted as Hessian, i.e. twice the matrix of quadratic coefficients.

$A Igor xx Dec10;

Constructor & Destructor Documentation

IG.Num.ScalarFunctionQuadratic.ScalarFunctionQuadratic ( )

inlineprivate

IG.Num.ScalarFunctionQuadratic.ScalarFunctionQuadratic	(	IMatrix	hessian,
		IVector	gradient0,
		double	scalarTerm
	)

inline

Creation of a quadratic scalar function. WARNING: Matrix argument is interpreted as Hessian, i.e. twice the matrix of quadratic coefficients.

Parameters

hessian	Matrix of second derivatives (Hessian). Can be null (in this case function degrades to linear function).
gradient0	Vector of linear coefficients - gradient of quadratic function at x = 0. Can be null.
scalarTerm	Constant term.

Member Function Documentation

static ScalarFunctionQuadratic IG.Num.ScalarFunctionQuadratic.ExampleFunction2d ( )

inlinestatic

Creates and returns quadratic scalar function in 2D.

static ScalarFunctionQuadratic IG.Num.ScalarFunctionQuadratic.ExampleFunctionDiagonal2d ( )

inlinestatic

Creates and returns quadratic scalar function with diagonal Hessian.

Returns

static ScalarFunctionQuadratic IG.Num.ScalarFunctionQuadratic.ExampleFunctionPureQuadratic2d ( )

inlinestatic

Creates and returns quadratic scalar function with only quadratic terms.

Returns

static ScalarFunctionQuadratic IG.Num.ScalarFunctionQuadratic.ExampleFunctionDiagonalPureQuadratic2d ( )

inlinestatic

Creates and returns quadratic function with diagonal Hessian.

Returns

static int IG.Num.ScalarFunctionQuadratic.GetNumConstants ( int dim )

inlinestatic

Returns the number of constants that specify the quadratic function of the specified dimension.

Parameters

dim	Dimension of the space in which quadratic function is defined.

Referenced by IG.Num.SampledDataSet.CreateExampleQuadratic().

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

inline

Returns the value of this function at the specified parameter.

Implements IG.Num.IScalarFunctionUntransformed.

References IG.Num.MatrixBase.Multiply(), and IG.Num.VectorBase.ScalarProduct().

override void IG.Num.ScalarFunctionQuadratic.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.

References IG.Num.VectorBase.Add(), IG.Num.MatrixBase.MultiplyPlain(), and IG.Num.IVector.SetZero().

override void IG.Num.ScalarFunctionQuadratic.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.

Member Data Documentation

IMatrix IG.Num.ScalarFunctionQuadratic._G

private

IVector IG.Num.ScalarFunctionQuadratic._b

private

double IG.Num.ScalarFunctionQuadratic._c

private

Property Documentation

int IG.Num.ScalarFunctionQuadratic.NumActualConstants

get

Gets the number of constants that define the current function. If e.g. the matrix coefficient or the vector coefficient is not defined then the corresponding constants are not counted.

IMatrix IG.Num.ScalarFunctionQuadratic.HessianMatrix

getprotected set

Twice the matrix of quadratic coefficients (Hessian matrix).

IVector IG.Num.ScalarFunctionQuadratic.Gradient0

getprotected set

Vector of linear coefficients (equal to gradient of the function at x=0).

double IG.Num.ScalarFunctionQuadratic.ScalarTerm

getprotected set

Scalar additive constant.

override bool IG.Num.ScalarFunctionQuadratic.ValueDefined

getprotected set

Tells whether value of the function is defined by implementation. Always true for this case.

override bool IG.Num.ScalarFunctionQuadratic.GradientDefined

getprotected set

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

override bool IG.Num.ScalarFunctionQuadratic.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/FunctionScalarExamples.cs

Public Member Functions

Static 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