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# IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D Class Reference

Symmetric paraboloid centered at coordinate origin. f(x,y) = x^2 + y^2 - R2. If R2 is positive then 0-level is a circle, if it is negative then the paraboloid does not intersect with zero-plane. Default is R2 = 1 (default constructor). More...

Inheritance diagram for IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D:
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Collaboration diagram for IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D:
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List of all members.

## Public Member Functions
| ParaboloidSymmetric2D ()
| Creates a new untransformed Rosenbrock's function.
| ParaboloidSymmetric2D (double r0Square)
| 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.
## Protected Attributes
double | R0Square
| Parameter that specifies square of the radius of the circle f(x,y) = 0 when positive, otherwise it denotes a negative height of the paraboloid above the zero plane.
## 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)

## Detailed Description

Symmetric paraboloid centered at coordinate origin. f(x,y) = x^2 + y^2 - R2. If R2 is positive then 0-level is a circle, if it is negative then the paraboloid does not intersect with zero-plane. Default is R2 = 1 (default constructor).

$A Igor Dec10;

## Constructor & Destructor Documentation

IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::ParaboloidSymmetric2D | ( |  | ) | `[inline]`

Creates a new untransformed Rosenbrock's function.

IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::ParaboloidSymmetric2D | ( | double | r0Square | ) | `[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.

## Member Function Documentation

override double IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::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::ParaboloidSymmetric2D::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::ParaboloidSymmetric2D::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.

## Member Data Documentation

double IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::R0Square`[protected]`

Parameter that specifies square of the radius of the circle f(x,y) = 0 when positive, otherwise it denotes a negative height of the paraboloid above the zero plane.

## Property Documentation

override string IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::Name`[get]`

Returns a short name of the function.

Implements IG::Num::IScalarFunctionUntransformed.

override string IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::Description`[get]`

Returns a short description of the function.

Implements IG::Num::IScalarFunctionUntransformed.

override bool IG::Num::ScalarFunctionExamples::ParaboloidSymmetric2D::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::ParaboloidSymmetric2D::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::ParaboloidSymmetric2D::HessianDefined`[get, set]`

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

Implements IG::Num::IScalarFunctionUntransformed.

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

- FunctionScalarExamples.cs

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