DUNE PDELab (git)

Function implementations

Concrete function implementations. More...

Classes

struct  Dune::Functions::MonomialSet< RangeFieldType, dimension, maxDegree >
 Function, which evaluates all monomials up to degree maxDegree in a given coordinate. More...
 
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
fA function object supporting evaluation with global coordinates of the passed gridView.
gridViewThe 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
fA function object supporting evaluation with global coordinates of the passed gridView.
gridViewThe 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
outerFunctionThe outer-function to be composed with the grid-functions.
innerFunctionsThe 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
outerFunctionThe outer-function to be composed with the grid-functions.
innerFunctionsThe 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
signatureTagA dummy parameter to pass the signature and derivative traits
fCallable 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
RThe 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
basisThe global basis or subspace basis associated with this grid-function
vectorThe 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
RThe 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
basisThe global basis or subspace basis associated with this grid-function
vectorThe 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.

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