IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent Class Reference

Generalzed multivariate RosenBrock function for Dim >= 2. f(x,y) = Sum[i=0...N-2]{(1-x_{i})^2 + 100 * (x_{i+1}-x_{i}^2)^2} More...

Inheritance diagram for IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent:

Collaboration diagram for IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent:

List of all members.

Public Member Functions
	RosenbrockGeneralizedAdjacent ()
	Creates a new untransformed Rosenbrock's function.
	RosenbrockGeneralizedAdjacent (IAffineTransformation transf)
	Creates a new transformed Rosenbrock's function.
override double	ReferenceValue (IVector parameters)
	Returns the value of this function at the specified parameter in the reference coordinate system.
override void	ReferenceGradientPlain (IVector parameters, IVector gradient)
	Calculates the first derivative (gradient) of this function at the specified parameter in the reference coordinate system.
override void	ReferenceHessianPlain (IVector parameters, IMatrix hessian)
	Calculates the second derivative (Hessian) of this function at the specified parameters in the reference coordinate system.
Properties
override string	Name [get]
	Returns a short name of the function.
override string	Description [get]
	Returns a short description of the function.
override bool	ValueDefined [get, set]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically)
override bool	GradientDefined [get, set]
	Tells whether the first derivative is defined for this function (by implementation, not mathematically)
override bool	HessianDefined [get, set]
	Tells whether the second derivative is defined for this function (by implementation, not mathematically)

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Detailed Description

Generalzed multivariate RosenBrock function for Dim >= 2.

f(x,y) = Sum[i=0...N-2]{(1-x_{i})^2 + 100 * (x_{i+1}-x_{i}^2)^2}

This is one of the generalizations of the 2D Rosenbrock function.

Moved from stand-alone class, now nested in the ScalarFunctionExamples class.

See also:

I. Grešovnik: Test functions for Unconstrained Minimization, Igor's internal report.

Definition at AlgLib page: http://www.alglib.net/optimization/lbfgsandcg.php#header4

Definition at Wikipedia: http://en.wikipedia.org/wiki/Rosenbrock_function#Multidimensional_generalisations

$A Igor Nov08 Dec10;

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Constructor & Destructor Documentation

IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::RosenbrockGeneralizedAdjacent

(

)

[inline]

Creates a new untransformed Rosenbrock's function.

IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::RosenbrockGeneralizedAdjacent

(

IAffineTransformation

transf

)

[inline]

Creates a new transformed Rosenbrock's function.

Parameters:

transf

Affine transformation that is applied on parameters. If null then the fuction is identical to the untransformed Rosenbrock function.

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Member Function Documentation

override double IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::ReferenceValue

(

IVector

parameters

)

[inline, virtual]

Returns the value of this function at the specified parameter in the reference coordinate system.

Parameters:

parameters

Vector of parameters (in the REFERENCE system) where function is evaluated.

Implements IG::Num::ScalarFunctionBase.

override void IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::ReferenceGradientPlain	(	IVector	parameters,
		IVector	gradient
	)		[inline, virtual]

Calculates the first derivative (gradient) of this function at the specified parameter in the reference coordinate system.

Parameters:

parameters	Vector of parameters (in the REFERENCE system) where derivatives are evaluated.
gradient	Vector where first derivatives (gradient) are stored.

Implements IG::Num::ScalarFunctionBase.

override void IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::ReferenceHessianPlain	(	IVector	parameters,
		IMatrix	hessian
	)		[inline, virtual]

Calculates the second derivative (Hessian) of this function at the specified parameters in the reference coordinate system.

Parameters:

parameters	Vector of parameters (in the REFERENCE system) where Hessian is evaluated.
hessian	Matrix where second derivatives (Hessian) are stored.

Implements IG::Num::ScalarFunctionBase.

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Property Documentation

override string IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::Name [get]

Returns a short name of the function.

Implements IG::Num::IScalarFunctionUntransformed.

override string IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::Description [get]

Returns a short description of the function.

Implements IG::Num::IScalarFunctionUntransformed.

override bool IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::ValueDefined [get, set]

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

Implements IG::Num::IScalarFunctionUntransformed.

override bool IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::GradientDefined [get, set]

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

Implements IG::Num::IScalarFunctionUntransformed.

override bool IG::Num::ScalarFunctionExamples::RosenbrockGeneralizedAdjacent::HessianDefined [get, set]

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

Implements IG::Num::IScalarFunctionUntransformed.

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

• FunctionScalarExamples.cs