Reference documentation for deal.II version Git 5d9b33e 2018-08-16 23:18:17 -0400
Function< dim, RangeNumberType > Class Template Referenceabstract

#include <deal.II/base/function.h>

Inheritance diagram for Function< dim, RangeNumberType >:
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## Public Member Functions

Function (const unsigned int n_components=1, const RangeNumberType initial_time=0.0)

virtual ~Function () override=0

Functionoperator= (const Function &f)

virtual RangeNumberType value (const Point< dim > &p, const unsigned int component=0) const

virtual void vector_value (const Point< dim > &p, Vector< RangeNumberType > &values) const

virtual void value_list (const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const

virtual void vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const

virtual void vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< RangeNumberType >> &values) const

virtual Tensor< 1, dim, RangeNumberType > gradient (const Point< dim > &p, const unsigned int component=0) const

virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients) const

virtual void gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients, const unsigned int component=0) const

virtual void vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const

virtual void vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const

virtual RangeNumberType laplacian (const Point< dim > &p, const unsigned int component=0) const

virtual void vector_laplacian (const Point< dim > &p, Vector< RangeNumberType > &values) const

virtual void laplacian_list (const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const

virtual void vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const

virtual SymmetricTensor< 2, dim, RangeNumberType > hessian (const Point< dim > &p, const unsigned int component=0) const

virtual void vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &values) const

virtual void hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &values, const unsigned int component=0) const

virtual void vector_hessian_list (const std::vector< Point< dim >> &points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType >>> &values) const

std::size_t memory_consumption () const

Public Member Functions inherited from FunctionTime< RangeNumberType >
FunctionTime (const RangeNumberTypeinitial_time=RangeNumberType(0.0))

virtual ~FunctionTime ()=default

RangeNumberType get_time () const

virtual void set_time (const RangeNumberTypenew_time)

Public Member Functions inherited from Subscriptor
Subscriptor ()

Subscriptor (const Subscriptor &)

Subscriptor (Subscriptor &&) noexcept

virtual ~Subscriptor ()

Subscriptoroperator= (const Subscriptor &)

Subscriptoroperator= (Subscriptor &&) noexcept

void subscribe (const char *identifier=nullptr) const

void unsubscribe (const char *identifier=nullptr) const

unsigned int n_subscriptions () const

template<typename StreamType >
void list_subscribers (StreamType &stream) const

void list_subscribers () const

template<class Archive >
void serialize (Archive &ar, const unsigned int version)

## Public Attributes

const unsigned int n_components

## Static Public Attributes

static const unsigned int dimension = dim

Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, std::string arg2, std::string arg3)

static::ExceptionBase & ExcNoSubscriber (std::string arg1, std::string arg2)

## Detailed Description

### template<int dim, typename RangeNumberType = double> class Function< dim, RangeNumberType >

This class is a model for a general function that, given a point at which to evaluate the function, returns a vector of values with one or more components.

The class serves the purpose of representing both scalar and vector valued functions. To this end, we consider scalar functions as a special case of vector valued functions, in the former case only having a single component return vector. Since handling vectors is comparatively expensive, the interface of this class has functions which only ask for a single component of the vector-valued results (this is what you will usually need in case you know that your function is scalar-valued) as well as functions you can ask for an entire vector of results with as many components as the function object represents. Access to function objects therefore is through the following methods:

double
value(const Point<dim> & p,
const unsigned int component = 0) const;
// return all components at one point
void

For more efficiency, there are other functions returning one or all components at a list of points at once:

void
value_list(const std::vector<Point<dim>> &point_list,
std::vector<double> & value_list,
const unsigned int component = 0) const;
// return all components at several points
void
vector_value_list(const std::vector<Point<dim>> &point_list,
std::vector<Vector<double>> & value_list) const;

Furthermore, there are functions returning the gradient of the function or even higher derivatives at one or several points.

You will usually only overload those functions you need; the functions returning several values at a time (value_list(), vector_value_list(), and gradient analogs) will call those returning only one value (value(), vector_value(), and gradient analogs), while those ones will throw an exception when called but not overloaded.

Conversely, the functions returning all components of the function at one or several points (i.e. vector_value(), vector_value_list()), will not call the function returning one component at one point repeatedly, once for each point and component. The reason is efficiency: this would amount to too many virtual function calls. If you have vector- valued functions, you should therefore also provide overloads of the virtual functions for all components at a time.

Also note, that unless only called a very small number of times, you should overload all sets of functions (returning only one value, as well as those returning a whole array), since the cost of evaluation of a point value is often less than the virtual function call itself.

Support for time dependent functions can be found in the base class FunctionTime.

### Functions that return tensors

If the functions you are dealing with have a number of components that are a priori known (for example, dim elements), you might consider using the TensorFunction class instead. This is, in particular, true if the objects you return have the properties of a tensor, i.e., they are for example dim-dimensional vectors or dim-by-dim matrices. On the other hand, functions like VectorTools::interpolate or VectorTools::interpolate_boundary_values definitely only want objects of the current type. You can use the VectorFunctionFromTensorFunction class to convert the former to the latter.

### Functions that return vectors of other data types

Most of the time, your functions will have the form $$f : \Omega \rightarrow {\mathbb R}^{n_\text{components}}$$. However, there are occasions where you want the function to return vectors (or scalars) over a different number field, for example functions that return complex numbers or vectors of complex numbers: $$f : \Omega \rightarrow {\mathbb C}^{n_\text{components}}$$. In such cases, you can choose a value different than the default double for the second template argument of this class: it describes the scalar type to be used for each component of your return values. It defaults to double, but in the example above, it could be set to std::complex<double>.

Template Parameters
 dim The space dimension of the range space within which the domain $$\Omega$$ of the function lies. Consequently, the function will be evaluated at objects of type Point. RangeNumberType The scalar type of the vector space that is the range (or image) of this function. As discussed above, objects of the current type represent functions from $${\mathbb R}^\text{dim}$$ to $$S^{n_\text{components}}$$ where $$S$$ is the underlying scalar type of the vector space. The type of $$S$$ is given by the RangeNumberType template argument.

Definition at line 148 of file function.h.

## Constructor & Destructor Documentation

template<int dim, typename RangeNumberType = double>
 Function< dim, RangeNumberType >::Function ( const unsigned int n_components = 1, const RangeNumberType initial_time = 0.0 )

Constructor. May take an initial value for the number of components (which defaults to one, i.e. a scalar function), and the time variable, which defaults to zero.

template<int dim, typename RangeNumberType = double>
 virtual Function< dim, RangeNumberType >::~Function ( )
overridepure virtual

Virtual destructor; absolutely necessary in this case.

This destructor is declared pure virtual, such that objects of this class cannot be created. Since all the other virtual functions have a pseudo- implementation to avoid overhead in derived classes, they can not be abstract. As a consequence, we could generate an object of this class because none of this class's functions are abstract.

We circumvent this problem by making the destructor of this class abstract virtual. This ensures that at least one member function is abstract, and consequently, no objects of type Function can be created. However, there is no need for derived classes to explicitly implement a destructor: every class has a destructor, either explicitly implemented or implicitly generated by the compiler, and this resolves the abstractness of any derived class even if they do not have an explicitly declared destructor.

Nonetheless, since derived classes want to call the destructor of a base class, this destructor is implemented (despite it being pure virtual).

## Member Function Documentation

template<int dim, typename RangeNumberType = double>
 Function& Function< dim, RangeNumberType >::operator= ( const Function< dim, RangeNumberType > & f )

Assignment operator. This is here only so that you can have objects of derived classes in containers, or assign them otherwise. It will raise an exception if the object from which you assign has a different number of components than the one being assigned to.

template<int dim, typename RangeNumberType = double>
 virtual RangeNumberType Function< dim, RangeNumberType >::value ( const Point< dim > & p, const unsigned int component = 0 ) const
virtual

Return the value of the function at the given point. Unless there is only one component (i.e. the function is scalar), you should state the component you want to have evaluated; it defaults to zero, i.e. the first component.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_value ( const Point< dim > & p, Vector< RangeNumberType > & values ) const
virtual

Return all components of a vector-valued function at a given point.

values shall have the right size beforehand, i.e. n_components.

The default implementation will call value() for each component.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::value_list ( const std::vector< Point< dim >> & points, std::vector< RangeNumberType > & values, const unsigned int component = 0 ) const
virtual

Set values to the point values of the specified component of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array.

By default, this function repeatedly calls value() for each point separately, to fill the output array.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_value_list ( const std::vector< Point< dim >> & points, std::vector< Vector< RangeNumberType >> & values ) const
virtual

Set values to the point values of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array, and that all elements be vectors with the same number of components as this function has.

By default, this function repeatedly calls vector_value() for each point separately, to fill the output array.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_values ( const std::vector< Point< dim >> & points, std::vector< std::vector< RangeNumberType >> & values ) const
virtual

For each component of the function, fill a vector of values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

template<int dim, typename RangeNumberType = double>
 virtual Tensor<1, dim, RangeNumberType> Function< dim, RangeNumberType >::gradient ( const Point< dim > & p, const unsigned int component = 0 ) const
virtual
template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_gradient ( const Point< dim > & p, std::vector< Tensor< 1, dim, RangeNumberType >> & gradients ) const
virtual

Return the gradient of all components of the function at the given point.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::gradient_list ( const std::vector< Point< dim >> & points, std::vector< Tensor< 1, dim, RangeNumberType >> & gradients, const unsigned int component = 0 ) const
virtual

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_gradients ( const std::vector< Point< dim >> & points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> & gradients ) const
virtual

For each component of the function, fill a vector of gradient values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_gradient_list ( const std::vector< Point< dim >> & points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> & gradients ) const
virtual

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

template<int dim, typename RangeNumberType = double>
 virtual RangeNumberType Function< dim, RangeNumberType >::laplacian ( const Point< dim > & p, const unsigned int component = 0 ) const
virtual
template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_laplacian ( const Point< dim > & p, Vector< RangeNumberType > & values ) const
virtual

Compute the Laplacian of all components at point p and store them in values.

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::laplacian_list ( const std::vector< Point< dim >> & points, std::vector< RangeNumberType > & values, const unsigned int component = 0 ) const
virtual

Compute the Laplacian of one component at a set of points.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_laplacian_list ( const std::vector< Point< dim >> & points, std::vector< Vector< RangeNumberType >> & values ) const
virtual

Compute the Laplacians of all components at a set of points.

template<int dim, typename RangeNumberType = double>
 virtual SymmetricTensor<2, dim, RangeNumberType> Function< dim, RangeNumberType >::hessian ( const Point< dim > & p, const unsigned int component = 0 ) const
virtual

Compute the Hessian of a given component at point p, that is the gradient of the gradient of the function.

Reimplemented in Functions::CosineFunction< dim >, Functions::CSpline< dim >, and Functions::Spherical< dim >.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_hessian ( const Point< dim > & p, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> & values ) const
virtual

Compute the Hessian of all components at point p and store them in values.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::hessian_list ( const std::vector< Point< dim >> & points, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> & values, const unsigned int component = 0 ) const
virtual

Compute the Hessian of one component at a set of points.

template<int dim, typename RangeNumberType = double>
 virtual void Function< dim, RangeNumberType >::vector_hessian_list ( const std::vector< Point< dim >> & points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType >>> & values ) const
virtual

Compute the Hessians of all components at a set of points.

template<int dim, typename RangeNumberType = double>
 std::size_t Function< dim, RangeNumberType >::memory_consumption ( ) const

Return an estimate for the memory consumption, in bytes, of this object. This is not exact (but will usually be close) because calculating the memory usage of trees (e.g., std::map) is difficult.

## Member Data Documentation

template<int dim, typename RangeNumberType = double>
 const unsigned int Function< dim, RangeNumberType >::dimension = dim
static

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 155 of file function.h.

template<int dim, typename RangeNumberType = double>
 const unsigned int Function< dim, RangeNumberType >::n_components

Number of vector components.

Definition at line 160 of file function.h.

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