Patate Lib  0.5
 All Classes Namespaces Functions Variables Typedefs Enumerations Enumerator Pages
Grenaille::SmoothWeightKernel< _Scalar > Class Template Reference

Inherits Grenaille::Concept::WeightKernelConcept< _Scalar >.

Detailed Description

template<typename _Scalar>
class Grenaille::SmoothWeightKernel< _Scalar >

Smooth WeightKernel defined in \(\left[0 : 1\right]\).

Public Types

typedef _Scalar Scalar
 Scalar type defined outside the class.
 
- Public Types inherited from Grenaille::Concept::WeightKernelConcept< _Scalar >
typedef _Scalar Scalar
 

Public Member Functions

Scalar f (const Scalar &_x) const
 Defines the smooth weighting function \( w(x) = (x^2-1)^2 \).
 
Scalar df (const Scalar &_x) const
 Defines the smooth first order weighting function \( \nabla w(x) = 4x(x^2-1) \).
 
Scalar ddf (const Scalar &_x) const
 Defines the smooth second order weighting function \( \nabla^2 w(x) = 12x^2-4 \).
 
- Public Member Functions inherited from Grenaille::Concept::WeightKernelConcept< _Scalar >
Scalar f (const Scalar &x) const
 Apply the weighting kernel to the scalar value \(f(x)\).
 
Scalar df (const Scalar &x) const
 Apply the first derivative of the weighting kernel to the scalar value \(f'(x)\).
 
Scalar ddf (const Scalar &x) const
 Apply the second derivative of the weighting kernel to the scalar value \(f''(x)\).