Function implementations

Concrete function implementations. More...

Classes
class	Dune::Functions::Polynomial< K, C >
	A univariate polynomial implementation. More...
class	Dune::Functions::TrigonometricFunction< K, sinFactor, cosFactor >
	A linear combination of trigonomic functions. More...
class	Dune::Functions::DifferentiableFunctionFromCallables< Range(Domain), DerivativeTraits, F >
	Wrap a list of callable objects as derivative sequence modelling Concept::DifferentiableFunction<Range(Domain), DerivativeTraits> More...
class	Dune::Functions::DifferentiableFunctionFromCallables< Range(Domain), DerivativeTraits, F, DF, Derivatives... >
	Wrap a list of callable objects as derivative sequence modelling Concept::DifferentiableFunction<Range(Domain), DerivativeTraits> More...
class	Dune::Functions::AnalyticGridViewFunction< Range(Domain), GV, F, DerivativeTraits >
	Class wrapping any differentiable function as grid function. More...
class	Dune::Functions::ComposedGridFunction< OF, IF >
	Composition of grid functions with another function. More...
class	Dune::Functions::DiscreteGlobalBasisFunction< B, V, NTRE, R >
	A grid function induced by a global basis and a coefficient vector. More...
class	Dune::Functions::DiscreteGlobalBasisFunctionDerivative< DGBF >
	Derivative of a DiscreteGlobalBasisFunction More...
class	Dune::Functions::FaceNormalGridFunction< GV >
	Grid function implementing the piecewise element face normal. More...

Functions
template<class K , int sinFactor, int cosFactor>
TrigonometricFunction< K, -cosFactor, sinFactor >	Dune::Functions::derivative (const TrigonometricFunction< K, sinFactor, cosFactor > &f)
	Obtain derivative of TrigonometricFunction function.
template<class Signature , template< class > class DerivativeTraits, class... F>
DifferentiableFunctionFromCallables< Signature, DerivativeTraits, F... >	Dune::Functions::makeDifferentiableFunctionFromCallables (const SignatureTag< Signature, DerivativeTraits > &signatureTag, F &&... f)
	Create a DifferentiableFunction from callables. More...
template<class F , class GridView >
auto	Dune::Functions::makeAnalyticGridViewFunction (F &&f, const GridView &gridView)
	Create an AnalyticGridViewFunction from a function and a grid view. More...
template<class OF , class... IF>
auto	Dune::Functions::makeComposedGridFunction (OF &&outerFunction, IF &&... innerFunction)
	Create a ComposedGridFunction that composes grid-functions with another function. More...
template<typename R , typename B , typename V >
auto	Dune::Functions::makeDiscreteGlobalBasisFunction (B &&basis, V &&vector)
	Generate a DiscreteGlobalBasisFunction. More...
template<class F , class GridView >
auto	makeAnalyticGridViewFunction (F &&f, const GridView &gridView)
	Create an AnalyticGridViewFunction from a function and a grid view. More...
template<class OF , class... IF>
auto	makeComposedGridFunction (OF &&outerFunction, IF &&... innerFunction)
	Create a ComposedGridFunction that composes grid-functions with another function. More...
template<typename R , typename B , typename V >
auto	makeDiscreteGlobalBasisFunction (B &&basis, V &&vector)
	Generate a DiscreteGlobalBasisFunction. More...

Friends
auto	Dune::Functions::Polynomial< K, C >::derivative (const Polynomial &p)
	Obtain derivative of Polynomial function. More...
Derivative	Dune::Functions::DifferentiableFunctionFromCallables< Range(Domain), DerivativeTraits, F >::derivative (const DifferentiableFunctionFromCallables &t)
	Get derivative of DifferentiableFunctionFromCallables.
Derivative	Dune::Functions::DifferentiableFunctionFromCallables< Range(Domain), DerivativeTraits, F, DF, Derivatives... >::derivative (const DifferentiableFunctionFromCallables &t)
	Get derivative of DifferentiableFunctionFromCallables.

Detailed Description

Concrete function implementations.

Function Documentation

makeAnalyticGridViewFunction() [1/2]

template<class F , class GridView >

auto makeAnalyticGridViewFunction	(	F &&	f,
		const GridView &	gridView
	)

Create an AnalyticGridViewFunction from a function and a grid view.

The returned function supports localFunction() and stores a copy of the original function.

Parameters

f	A function object supporting evaluation with global coordinates of the passed gridView.
gridView	The GridView the function should act on.

Returns

A function that models the GridFunction interface.

makeAnalyticGridViewFunction() [2/2]

template<class F , class GridView >

auto makeAnalyticGridViewFunction ( F &&  f, const GridView &  gridView  )

related

Create an AnalyticGridViewFunction from a function and a grid view.

The returned function supports localFunction() and stores a copy of the original function.

Parameters

f	A function object supporting evaluation with global coordinates of the passed gridView.
gridView	The GridView the function should act on.

Returns

A function that models the GridFunction interface.

makeComposedGridFunction() [1/2]

template<class OF , class... IF>

auto makeComposedGridFunction	(	OF &&	outerFunction,
		IF &&...	innerFunction
	)

Create a ComposedGridFunction that composes grid-functions with another function.

For given inner grid-functions g0, ..., gn and an outer-function f this creates a grid-function representing f(g0(x), ..., gn(x)). The only assumption made, is that the range types of the inner-functions can be passed to the outer ones, and that all grid-functions are defined on the same EntitySet.

Notice that all functions are captured by value. To store references you can pass std::ref().

Parameters

outerFunction	The outer-function to be composed with the grid-functions.
innerFunctions	The inner grid-functions

Returns

A grid-function defined on the same EntitySet as the input-functions.

makeComposedGridFunction() [2/2]

template<class OF , class... IF>

auto makeComposedGridFunction ( OF &&  outerFunction, IF &&...  innerFunction  )

related

Create a ComposedGridFunction that composes grid-functions with another function.

For given inner grid-functions g0, ..., gn and an outer-function f this creates a grid-function representing f(g0(x), ..., gn(x)). The only assumption made, is that the range types of the inner-functions can be passed to the outer ones, and that all grid-functions are defined on the same EntitySet.

Notice that all functions are captured by value. To store references you can pass std::ref().

Parameters

outerFunction	The outer-function to be composed with the grid-functions.
innerFunctions	The inner grid-functions

Returns

A grid-function defined on the same EntitySet as the input-functions.

makeDifferentiableFunctionFromCallables()

template<class Signature , template< class > class DerivativeTraits, class... F>

DifferentiableFunctionFromCallables< Signature, DerivativeTraits, F... > Dune::Functions::makeDifferentiableFunctionFromCallables	(	const SignatureTag< Signature, DerivativeTraits > &	signatureTag,
		F &&...	f
	)

Create a DifferentiableFunction from callables.

This will return a wrapper modelling the DifferentiableFunction interface where the evaluation of the function and its derivatives are implemented by the given callable objects.

Parameters

signatureTag	A dummy parameter to pass the signature and derivative traits
f	Callable objects implementing the evaluation of the function and its derivatives

Returns

Object modelling DifferentiableFunction interface

makeDiscreteGlobalBasisFunction() [1/2]

template<typename R , typename B , typename V >

auto makeDiscreteGlobalBasisFunction	(	B &&	basis,
		V &&	vector
	)

Generate a DiscreteGlobalBasisFunction.

Create a new DiscreteGlobalBasisFunction by wrapping the vector in a VectorBackend that allows the hierarchic resize and multi-index access in the DiscreteGlobalBasisFunction, if the vector does not yet fulfill the ConstVectorBackend concept.

Template Parameters

R

The range type this grid-function should represent when seen as a mapping R(Domain) with Domain the global coordinates of the associated GridView. This must be compatible with the basis and coefficients. See the documentation of DiscreteGlobalBasisFunction for more details. The type R must be default constructible and by this default construction provides a well resized container to be filled in the evaluation method of the grid function.

Parameters

basis	The global basis or subspace basis associated with this grid-function
vector	The coefficient vector to use in combination with the basis.

makeDiscreteGlobalBasisFunction() [2/2]

template<typename R , typename B , typename V >

auto makeDiscreteGlobalBasisFunction ( B &&  basis, V &&  vector  )

related

Generate a DiscreteGlobalBasisFunction.

Create a new DiscreteGlobalBasisFunction by wrapping the vector in a VectorBackend that allows the hierarchic resize and multi-index access in the DiscreteGlobalBasisFunction, if the vector does not yet fulfill the ConstVectorBackend concept.

Template Parameters

R

The range type this grid-function should represent when seen as a mapping R(Domain) with Domain the global coordinates of the associated GridView. This must be compatible with the basis and coefficients. See the documentation of DiscreteGlobalBasisFunction for more details. The type R must be default constructible and by this default construction provides a well resized container to be filled in the evaluation method of the grid function.

Parameters

basis	The global basis or subspace basis associated with this grid-function
vector	The coefficient vector to use in combination with the basis.

References Dune::Functions::istlVectorBackend().

Friends

derivative

template<class K , class C = std::vector<K>>

auto derivative ( const Polynomial< K, C > &  p )

friend

Obtain derivative of Polynomial function.

The derivative contains its own coefficient list and is not updated if the original function is changed.