mm::Multiquadric< scal_t > Class Template Reference

#include <Multiquadric_fwd.hpp>

Detailed Description

template<class scal_t>
class mm::Multiquadric< scal_t >

Multiquadric Radial Basis Function.

Specifically, this class represents a function \( f(r^2) = \sqrt{1+r^2/\sigma^2} \) as a function of squared distance with shape parameter \(\sigma \). This class satisfies the Radial Basis Function concept.

Usage example:

    Multiquadric<double> m(1.324);
    double val = m(4.0);     // value at 4.0 (this is the squared radius)
    double der = m(0.0, 2);  // second derivative at 0.0
    std::cout << m << std::endl;

Definition at line 29 of file Multiquadric_fwd.hpp.

Public Member Functions
	Multiquadric (scalar_t shape=1.0)
	Creates a MultiQuadratic with shape parameter shape. More...
scalar_t	shape () const
	Returns shape parameter. More...
void	setShape (scalar_t shape)
	Sets shape parameter to a new value. 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 at a given squared radial distance. More...

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

Friends
template<typename V >
std::ostream &	operator<< (std::ostream &os, const Multiquadric< V > &m)
	Output basic information about given basis function. More...

Private Attributes
scalar_t	shape_
	Shape parameter. More...

Constructor & Destructor Documentation

Multiquadric()

template<typename scal_t >

mm::Multiquadric< scal_t >::Multiquadric

(

scalar_t

shape = 1.0

)

Creates a MultiQuadratic with shape parameter shape.

Definition at line 17 of file Multiquadric.hpp.

Member Function Documentation

operator()() [1/3]

template<class scal_t >

scal_t mm::Multiquadric< scal_t >::operator() ( scalar_t  r2 ) const

inline

Evaluate at a given squared radial distance.

Definition at line 42 of file Multiquadric.hpp.

operator()() [2/3]

template<class scal_t >

scal_t mm::Multiquadric< scal_t >::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 22 of file Multiquadric.hpp.

operator()() [3/3]

template<class scal_t >

template<int dimension>

scalar_t mm::Multiquadric< scal_t >::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.

setShape()

template<class scal_t >

void mm::Multiquadric< scal_t >::setShape ( scalar_t  shape )

inline

Sets shape parameter to a new value.

Definition at line 44 of file Multiquadric_fwd.hpp.

shape()

template<class scal_t >

scalar_t mm::Multiquadric< scal_t >::shape ( ) const

inline

Returns shape parameter.

Definition at line 41 of file Multiquadric_fwd.hpp.

Friends And Related Function Documentation

operator<<

template<class scal_t >

template<typename V >

std::ostream& operator<< ( std::ostream &  os, const Multiquadric< V > &  m  )

friend

Output basic information about given basis function.

Member Data Documentation

shape_

template<class scal_t >

scalar_t mm::Multiquadric< scal_t >::shape_

private

Shape parameter.

Definition at line 34 of file Multiquadric_fwd.hpp.

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

• include/medusa/bits/approximations/Multiquadric_fwd.hpp
• include/medusa/bits/approximations/Multiquadric.hpp