A class for storing a heterogeneous collection of FunctionSpaceElement s. More...

#include <variables.hh>

Detailed Description

template<class VSDescriptions>
class Kaskade::VariableSet< VSDescriptions >

A class for storing a heterogeneous collection of FunctionSpaceElement s.

Template Parameters

Descriptions a VariableSetDescription class

Basic vector operations and I/O are supported.

The type of a VariableSet is defined via a VariableSetDescription, which contains information about the variables in form of a boost::fusion::vector of FEFunctionSpace s and VariableDescription s. The type of a VariableSet can be determined by VariableSetDescription::VariableSet.

VariableSet s contains a collection of FunctionSpaceElement s (vars) and a reference to its VariableSetDescription (descriptions). Simultaneous evaluation of all functions is supported by evaluateVariables.

Usually, solutions are stored in VariableSets. Access to data is via the public member variable data, which is a boost::fusion::vector of FunctionSpaceElement s

Definition at line 339 of file variables.hh.

Inheritance diagram for Kaskade::VariableSet< VSDescriptions >:

Public Types
typedef VSDescriptions	Descriptions
	Type of the VariableSetDescription. More...

typedef VSDescriptions::RepresentationData	Functions
	boost::fusion::vector of data elements (of type FunctionSpaceElement) More...

typedef LinearProductSpace< Scalar, Functions >	LinearSpace

typedef Scalar	field_type

typedef VSDescriptions::RepresentationData	Sequence
	boost::fusion::vector of element vectors. More...

using	Component = std::remove_reference_t< typename boost::fusion::result_of::at_c< Sequence const, m >::type >
	The type of the m-th component. More...

Public Member Functions
	VariableSet (Self const &vs)
	Copy constructor. More...

	VariableSet (Descriptions const &d)
	Constructor. More...

Self &	operator= (Self const &v)
	Assignment. More...

template<class S >
Self &	operator= (S const &s)
	Assignment from other (compatible) types. More...

size_t	dim () const
	Number of scalar degrees of freedom. This computes the total number of degrees of freedom, i.e. the sum of the dimensions of the components. More...

Self &	operator+= (LinearProductSpace< Scalar, SequenceY > const &y)
	In place addition. More...

Self &	operator-= (Self const &y)
	In place subtraction. More...

Self &	axpy (Scalar a, Self const &y)
	this <- this + a*y More...

void	read (InIterator i)
	DEPRECATED use vectorFromSequence instead. More...

void	read (int rbegin, int rend, InIterator i)
	Reads the coefficients of the subrange [rbegin,rend[ sequentially from an input iterator. The InIterator's value type must be convertible to field_type. More...

void	write (OutIterator i) const
	DEPRECATED use vectorToSequence instead. More...

void	write (int rbegin, int rend, DataOutIter i) const
	Writes the coefficients of the subrange [rbegin,rend[ sequentially to an output iterator. The InIterator's value type must be convertible to field_type. More...

Evaluation of variables
template<int i, class Evaluators >
auto	value (Evaluators const &evals) const
	Value of an individual variable in the set. More...

template<int i>
auto	value (Cell< GridView > const &cell, LocalPosition< GridView > const &xi) const
	Value of an individual variable in the set. More...

template<int i>
auto	value (GlobalPosition< GridView > const &x) const
	Value of an individual variable in the set. More...

template<int i, class Evaluators >
auto	derivative (Evaluators const &evals) const
	Derivative of an individual variable in the set. More...

template<int i>
auto	derivative (Cell< GridView > const &cell, LocalPosition< GridView > const &xi) const
	Derivative of an individual variable in the set. More...

template<int i>
auto	derivative (GlobalPosition< GridView > const &x) const
	derivative of an individual variable in the set. \WARNING This method is comparatively DEAD SLOW. More...

template<int i, class Evaluators >
auto	hessian (Evaluators const &evals) const
	Hessian of an individual variable in the set. More...

template<int i>
auto	hessian (Cell< GridView > const &cell, LocalPosition< GridView > const &xi) const
	Hessian of an individual variable in the set. More...

template<int i>
auto	hessian (GlobalPosition< GridView > const &x) const
	Hessian of an individual variable in the set. \WARNING This method is comparatively DEAD SLOW. More...

Assignment
Self &	operator*= (Scalar a)
	Scaling. More...

Scalar products and norms
field_type	operator* (Self const &y) const
	Scalar product. More...

field_type	dot (Self const &y) const
	Scalar product. More...

double	two_norm2 () const
	squared euclidean norm More...

double	two_norm () const
	euclidean norm More...

Public Attributes
Descriptions const &	descriptions
	Descriptions of variable set, of type VariableSetDescription (lots of useful infos) More...

Sequence	data
	Data. More...

Related Functions
(Note that these are not member functions.)
auto const &	component (LinearProductSpace< Scalar, Sequence > const &x)
	Provides access to the m-th component of a product space. More...

auto	cartesianProduct (X0 const &x0, Xs const &... xs)
	Creates a cartesian product of the given vectors, i.e. a LinearProductSpace object. More...

OutIter	vectorToSequence (LinearProductSpace< Scalar, VSDescriptions::RepresentationData > const &v, OutIter i)
	writes the coefficients of a vector to a flat scalar sequence <Scalar,Seq> More...

InIter	vectorFromSequence (LinearProductSpace< Scalar, VSDescriptions::RepresentationData > &v, InIter i)
	reads the coefficients of a vector from a flat scalar sequence <Scalar,Seq> More...

Member Typedef Documentation

◆ Component

using Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::Component = std::remove_reference_t<typename boost::fusion::result_of::at_c<Sequence const,m>::type>

inherited

The type of the m-th component.

Definition at line 104 of file linearspace.hh.

◆ Descriptions

template<class VSDescriptions >

typedef VSDescriptions Kaskade::VariableSet< VSDescriptions >::Descriptions

Type of the VariableSetDescription.

Definition at line 344 of file variables.hh.

◆ field_type

typedef Scalar Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::field_type

inherited

Definition at line 94 of file linearspace.hh.

◆ Functions

template<class VSDescriptions >

typedef VSDescriptions::RepresentationData Kaskade::VariableSet< VSDescriptions >::Functions

boost::fusion::vector of data elements (of type FunctionSpaceElement)

Definition at line 347 of file variables.hh.

◆ LinearSpace

template<class VSDescriptions >

typedef LinearProductSpace<Scalar,Functions> Kaskade::VariableSet< VSDescriptions >::LinearSpace

Definition at line 359 of file variables.hh.

◆ Sequence

typedef VSDescriptions::RepresentationData Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::Sequence

inherited

boost::fusion::vector of element vectors.

Definition at line 97 of file linearspace.hh.

Constructor & Destructor Documentation

◆ VariableSet() [1/2]

template<class VSDescriptions >

Kaskade::VariableSet< VSDescriptions >::VariableSet ( Self const & vs )

inline

Copy constructor.

Definition at line 362 of file variables.hh.

Referenced by Kaskade::BWErrorIndicator(), Kaskade::Giant< Grid, Equation, VariableSet, Spaces >::giantGbit(), and Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::nleqErr().

◆ VariableSet() [2/2]

template<class VSDescriptions >

Kaskade::VariableSet< VSDescriptions >::VariableSet ( Descriptions const & d )

inlineexplicit

Constructor.

This creates a zero-initialized set of variables.

Parameters

d	the VariableSetDescription object (has to exist during the lifetime of this VariableSet).

Definition at line 372 of file variables.hh.

Member Function Documentation

◆ axpy()

Self & Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::axpy	(	Scalar	a,
		Self const &	y
	)

inlineinherited

this <- this + a*y

Definition at line 233 of file linearspace.hh.

◆ derivative() [1/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::derivative	(	Cell< GridView > const &	cell,
		LocalPosition< GridView > const &	xi
	)		const

inline

Derivative of an individual variable in the set.

Definition at line 463 of file variables.hh.

◆ derivative() [2/3]

template<class VSDescriptions >

template<int i, class Evaluators >

auto Kaskade::VariableSet< VSDescriptions >::derivative ( Evaluators const & evals ) const

inline

Derivative of an individual variable in the set.

Definition at line 453 of file variables.hh.

◆ derivative() [3/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::derivative ( GlobalPosition< GridView > const & x ) const

inline

derivative of an individual variable in the set. \WARNING This method is comparatively DEAD SLOW.

Definition at line 473 of file variables.hh.

◆ dim()

size_t Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::dim ( ) const

inlineinherited

Number of scalar degrees of freedom. This computes the total number of degrees of freedom, i.e. the sum of the dimensions of the components.

Definition at line 154 of file linearspace.hh.

◆ dot()

field_type Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::dot ( Self const & y ) const

inlineinherited

Scalar product.

Definition at line 302 of file linearspace.hh.

◆ hessian() [1/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::hessian	(	Cell< GridView > const &	cell,
		LocalPosition< GridView > const &	xi
	)		const

inline

Hessian of an individual variable in the set.

Definition at line 492 of file variables.hh.

◆ hessian() [2/3]

template<class VSDescriptions >

template<int i, class Evaluators >

auto Kaskade::VariableSet< VSDescriptions >::hessian ( Evaluators const & evals ) const

inline

Hessian of an individual variable in the set.

Definition at line 482 of file variables.hh.

◆ hessian() [3/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::hessian ( GlobalPosition< GridView > const & x ) const

inline

Hessian of an individual variable in the set. \WARNING This method is comparatively DEAD SLOW.

Definition at line 502 of file variables.hh.

◆ operator*()

field_type Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::operator* ( Self const & y ) const

inlineinherited

Scalar product.

For two vectors \( (x_i)_{i=0,\dots,n-1} \) and \( (y_i)_{i=0,\dots,n-1}\) this computes and returns the euclidean scalar product

\[ \sum_{i=0}^{n-1} \langle x_i , y_i \rangle. \]

For the entries' scalar products, the operator*() is called.

Definition at line 292 of file linearspace.hh.

◆ operator*=()

Self & Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::operator*= ( Scalar a )

inlineinherited

Scaling.

Definition at line 213 of file linearspace.hh.

◆ operator+=()

Self & Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::operator+= ( LinearProductSpace< Scalar, SequenceY > const & y )

inlineinherited

In place addition.

Definition at line 221 of file linearspace.hh.

◆ operator-=()

Self & Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::operator-= ( Self const & y )

inlineinherited

In place subtraction.

Definition at line 227 of file linearspace.hh.

◆ operator=() [1/2]

template<class VSDescriptions >

template<class S >

Self & Kaskade::VariableSet< VSDescriptions >::operator= ( S const & s )

inline

Assignment from other (compatible) types.

Compatible types are those for which the base class LinearProductSpace<...> has a matching assignment operator. This includes, in particular, the coefficient vector representation Descriptions::CoefficientVectorRepresentation::type, i.e. a LinearProductSpace<Scalar,DuneBlockVector<...>> with matching entries and lengths.

Definition at line 399 of file variables.hh.

◆ operator=() [2/2]

template<class VSDescriptions >

Self & Kaskade::VariableSet< VSDescriptions >::operator= ( Self const & v )

inline

Assignment.

Definition at line 383 of file variables.hh.

◆ read() [1/2]

void Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::read ( InIterator i )

inlineinherited

DEPRECATED use vectorFromSequence instead.

Reads the coefficients sequentially from an input iterator. The InIterator's value type must be convertible to field_type.

Definition at line 245 of file linearspace.hh.

◆ read() [2/2]

void Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::read	(	int	rbegin,
		int	rend,
		InIterator	i
	)

inlineinherited

Reads the coefficients of the subrange [rbegin,rend[ sequentially from an input iterator. The InIterator's value type must be convertible to field_type.

Definition at line 255 of file linearspace.hh.

◆ two_norm()

double Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::two_norm ( ) const

inlineinherited

euclidean norm

Definition at line 318 of file linearspace.hh.

◆ two_norm2()

double Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::two_norm2 ( ) const

inlineinherited

squared euclidean norm

Definition at line 310 of file linearspace.hh.

◆ value() [1/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::value	(	Cell< GridView > const &	cell,
		LocalPosition< GridView > const &	xi
	)		const

inline

Value of an individual variable in the set.

Template Parameters

i	the index of the variable to evaluate

Parameters

cell	the cell in which to evaluate the variable
xi	the local coordinate within the cell at which to evaluate

Definition at line 432 of file variables.hh.

◆ value() [2/3]

template<class VSDescriptions >

template<int i, class Evaluators >

auto Kaskade::VariableSet< VSDescriptions >::value ( Evaluators const & evals ) const

inline

Value of an individual variable in the set.

Template Parameters

i	the index of the variable to evaluate
Evaluators	a boost::fusion sequence of evaluators, corresponding to the list of spaces of this variable set

Definition at line 417 of file variables.hh.

◆ value() [3/3]

template<class VSDescriptions >

template<int i>

auto Kaskade::VariableSet< VSDescriptions >::value ( GlobalPosition< GridView > const & x ) const

inline

Value of an individual variable in the set.

Template Parameters

i	the index of the variable to evaluate

Parameters

x	the global coordinate within the geometry at which to evaluate \WARNING This method is comparatively DEAD SLOW.

Definition at line 444 of file variables.hh.

◆ write() [1/2]

void Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::write	(	int	rbegin,
		int	rend,
		DataOutIter	i
	)		const

inlineinherited

Writes the coefficients of the subrange [rbegin,rend[ sequentially to an output iterator. The InIterator's value type must be convertible to field_type.

Definition at line 274 of file linearspace.hh.

◆ write() [2/2]

void Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::write ( OutIterator i ) const

inlineinherited

DEPRECATED use vectorToSequence instead.

Writes the coefficients sequentially to an output iterator (flattening). The field_type must be convertible to the OutIterator's value type.

Definition at line 264 of file linearspace.hh.

Friends And Related Function Documentation

◆ cartesianProduct()

auto cartesianProduct	(	X0 const &	x0,
		Xs const &...	xs
	)

Definition at line 478 of file linearspace.hh.

◆ component()

auto const & component ( LinearProductSpace< Scalar, Sequence > const & x )

This simplifies the access to individual components of a product space, e.g., a variable set of finite element functions. Instead of

boost::fusion::at_c<m>(x.data)

one can write

component<m>(x)

Template Parameters

m	the index of the component (nonnegative)
Scalar	a scalar type
Sequence	a boost::fusion sequence type

Returns: a reference to the m-th component

Definition at line 457 of file linearspace.hh.

◆ vectorFromSequence()

InIter vectorFromSequence	(	LinearProductSpace< Scalar, VSDescriptions::RepresentationData > &	v,
		InIter	i
	)

Definition at line 505 of file linearspace.hh.

◆ vectorToSequence()

OutIter vectorToSequence	(	LinearProductSpace< Scalar, VSDescriptions::RepresentationData > const &	v,
		OutIter	i
	)

Definition at line 493 of file linearspace.hh.

Member Data Documentation

◆ data

Sequence Kaskade::LinearProductSpace< VSDescriptions::Scalar , VSDescriptions::RepresentationData >::data

inherited

Data.

Definition at line 328 of file linearspace.hh.

◆ descriptions

template<class VSDescriptions >

Descriptions const& Kaskade::VariableSet< VSDescriptions >::descriptions

Descriptions of variable set, of type VariableSetDescription (lots of useful infos)

Definition at line 510 of file variables.hh.

Referenced by Kaskade::BWErrorFunction< Description, Grid, Functional, FunctionalSimpl >::getErrorFunction(), Kaskade::BWErrorFunction< Description, Grid, Functional, FunctionalSimpl >::getFullErrorFunction(), Kaskade::Bridge::VectorTraits< VariableSet< Descr > >::getRole(), Kaskade::gridIterate(), Kaskade::projectHierarchically(), Kaskade::Bridge::VectorTraits< VariableSet< Descr > >::read(), Kaskade::uniformEmbeddedErrorEstimation(), Kaskade::Bridge::VectorTraits< VariableSet< Descr > >::write(), Kaskade::writeAMIRAFile(), Kaskade::writePartialFile(), Kaskade::Bridge::VectorTraits< VariableSet< Descr > >::writeToFile(), and Kaskade::writeVTK().

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

Detailed Description

Public Types

Public Member Functions

Public Attributes

Related Functions

Member Typedef Documentation

◆ Component

◆ Descriptions

◆ field_type

◆ Functions

◆ LinearSpace

◆ Sequence

Constructor & Destructor Documentation

◆ VariableSet() [1/2]

◆ VariableSet() [2/2]

Member Function Documentation

◆ axpy()

◆ derivative() [1/3]

◆ derivative() [2/3]

◆ derivative() [3/3]

◆ dim()

◆ dot()

◆ hessian() [1/3]

◆ hessian() [2/3]

◆ hessian() [3/3]

◆ operator*()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ read() [1/2]

◆ read() [2/2]

◆ two_norm()

◆ two_norm2()

◆ value() [1/3]

◆ value() [2/3]

◆ value() [3/3]

◆ write() [1/2]

◆ write() [2/2]

Friends And Related Function Documentation

◆ cartesianProduct()

◆ component()

◆ vectorFromSequence()

◆ vectorToSequence()

Member Data Documentation

◆ data

◆ descriptions