mm::Polyharmonic< scal_t, k > Class Template Reference

#include <Polyharmonic_fwd.hpp>

Detailed Description

template<typename scal_t, int k = -1>
class mm::Polyharmonic< scal_t, k >

Polyharmonic Radial Basis Function of odd order.

Specifically, this class represents a function \( f(r^2) = r^k, k = 1, 3, \ldots\) as a function of squared distance with exponent \(k\). This class satisfies the Radial Basis Function concept.

Template Parameters

k	Order of the RBF. Must be odd.

Usage example:

    Polyharmonic<double, 3> ph;  // order given compile time
    double val = ph(4.0);     // value at 4.0 (this is the squared radius)
    double der = ph(0.0, 2);  // second derivative at 0.0
    std::cout << ph << std::endl;

Definition at line 32 of file Polyharmonic_fwd.hpp.

Public Member Functions
	Polyharmonic ()
	Default constructor. Only applicable when order given as template argument. More...
	Polyharmonic (int order)
	If template argument was -1, the order is accepted as runtime parameter. More...
int	order () const
	Get order of the RBF. More...
scalar_t	operator() (scalar_t r2, int derivative) const
	Evaluate derivative of this RBF wrt. More...
template<int dimension>
scalar_t	operator() (scalar_t r2, Lap< dimension > lap) const
	Evaluate Laplacian of this RBF wrt. More...
scalar_t	operator() (scalar_t r2) const
	Evaluate this RBF given squared radial distance. More...

Public Types
typedef scal_t	scalar_t
	Scalar type used for computations. More...

Friends
template<typename S , int K>
std::ostream &	operator<< (std::ostream &os, const Polyharmonic< S, K > &m)
	Output basic information about given Gaussian RBF. More...

Private Attributes
const int	order_
	Exponent of the RBF. More...

Constructor & Destructor Documentation

Polyharmonic() [1/2]

template<typename scal_t , int k>

mm::Polyharmonic< scal_t, k >::Polyharmonic

Default constructor. Only applicable when order given as template argument.

Definition at line 15 of file Polyharmonic.hpp.

Polyharmonic() [2/2]

template<typename scal_t , int k>

mm::Polyharmonic< scal_t, k >::Polyharmonic

(

int

order

)

If template argument was -1, the order is accepted as runtime parameter.

Definition at line 20 of file Polyharmonic.hpp.

Member Function Documentation

operator()() [1/3]

template<typename scal_t , int k = -1>

scalar_t mm::Polyharmonic< scal_t, k >::operator() ( scalar_t  r2 ) const

inline

Evaluate this RBF given squared radial distance.

Definition at line 67 of file Polyharmonic_fwd.hpp.

operator()() [2/3]

template<typename scal_t , int k>

scal_t mm::Polyharmonic< scal_t, k >::operator() ( scalar_t  r2, int  derivative  ) const

inline

Evaluate derivative of this RBF wrt.

r2 at given point.

Parameters

r2	Squared radial distance.
derivative	Order of derivative to evaluate.

Exceptions

Assertion

fails if derivative order is negative.

Definition at line 25 of file Polyharmonic.hpp.

operator()() [3/3]

template<typename scal_t , int k = -1>

template<int dimension>

scalar_t mm::Polyharmonic< scal_t, k >::operator() ( scalar_t  r2, Lap< dimension >  lap  ) const

inline

Evaluate Laplacian of this RBF wrt.

r at given point.

Parameters

r2	Squared radial distance.
lap	Laplacian operator object.

order()

template<typename scal_t , int k = -1>

int mm::Polyharmonic< scal_t, k >::order ( ) const

inline

Get order of the RBF.

Definition at line 47 of file Polyharmonic_fwd.hpp.

Friends And Related Function Documentation

operator<<

template<typename scal_t , int k = -1>

template<typename S , int K>

std::ostream& operator<< ( std::ostream &  os, const Polyharmonic< S, K > &  m  )

friend

Output basic information about given Gaussian RBF.

Definition at line 47 of file Polyharmonic.hpp.

Member Data Documentation

order_

template<typename scal_t , int k = -1>

const int mm::Polyharmonic< scal_t, k >::order_

private

Exponent of the RBF.

Definition at line 38 of file Polyharmonic_fwd.hpp.

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

• include/medusa/bits/approximations/Polyharmonic_fwd.hpp
• include/medusa/bits/approximations/Polyharmonic.hpp