Reference documentation for deal.II version Git d51799cb54 2020-09-28 09:22:08 +0200
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
Public Types | Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | Private Attributes | List of all members
Functions::Monomial< dim > Class Template Reference

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

Inheritance diagram for Functions::Monomial< dim >:
[legend]

Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type
 

Public Member Functions

 Monomial (const Tensor< 1, dim > &exponents, const unsigned int n_components=1)
 
virtual double value (const Point< dim > &p, const unsigned int component=0) const override
 
virtual void vector_value (const Point< dim > &p, Vector< double > &values) const override
 
virtual void value_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const override
 
virtual Tensor< 1, dim > gradient (const Point< dim > &p, const unsigned int component=0) const override
 
virtual void vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const
 
virtual void vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const
 
virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double >> &gradients) const
 
virtual void gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, double >> &gradients, const unsigned int component=0) const
 
virtual void vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const
 
virtual void vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const
 
virtual double laplacian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_laplacian (const Point< dim > &p, Vector< double > &values) const
 
virtual void laplacian_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const
 
virtual void vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const
 
virtual SymmetricTensor< 2, dim, doublehessian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, double >> &values) const
 
virtual void hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, double >> &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, double >>> &values) const
 
std::size_t memory_consumption () const
 
Number get_time () const
 
virtual void set_time (const Number new_time)
 
virtual void advance_time (const Number delta_t)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 

Static Public Member Functions

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Public Attributes

const unsigned int n_components
 

Static Public Attributes

static const unsigned int dimension
 

Private Attributes

const Tensor< 1, dim > exponents
 

Detailed Description

template<int dim>
class Functions::Monomial< dim >

A class that represents a function object for a monomial. Monomials are polynomials with only a single term, i.e. in 1-d they have the form \(x^\alpha\), in 2-d the form \(x_1^{\alpha_1}x_2^{\alpha_2}\), and in 3-d \(x_1^{\alpha_1}x_2^{\alpha_2}x_3^{\alpha_3}\). Monomials are therefore described by a \(dim\)-tuple of exponents. Consequently, the class's constructor takes a Tensor<1,dim> to describe the set of exponents. Most of the time these exponents will of course be integers, but real exponents are of course equally valid. Exponents can't be real when the bases are negative numbers.

Definition at line 1302 of file function_lib.h.

Member Typedef Documentation

◆ time_type

using Function< dim, double >::time_type = typename FunctionTime< typename numbers::NumberTraits<double >::real_type>::time_type
inherited

The scalar-valued real type used for representing time.

Definition at line 170 of file function.h.

Constructor & Destructor Documentation

◆ Monomial()

template<int dim>
Functions::Monomial< dim >::Monomial ( const Tensor< 1, dim > &  exponents,
const unsigned int  n_components = 1 
)

Constructor. The first argument is explained in the general description of the class. The second argument denotes the number of vector components this object shall represent. All vector components will have the same value.

Definition at line 2170 of file function_lib.cc.

Member Function Documentation

◆ value()

template<int dim>
double Functions::Monomial< dim >::value ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
overridevirtual

Function value at one point.

Reimplemented from Function< dim >.

Definition at line 2180 of file function_lib.cc.

◆ vector_value()

template<int dim>
void Functions::Monomial< dim >::vector_value ( const Point< dim > &  p,
Vector< double > &  values 
) const
overridevirtual

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

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

Reimplemented from Function< dim >.

Definition at line 2201 of file function_lib.cc.

◆ value_list()

template<int dim>
void Functions::Monomial< dim >::value_list ( const std::vector< Point< dim >> &  points,
std::vector< double > &  values,
const unsigned int  component = 0 
) const
overridevirtual

Function values at multiple points.

Reimplemented from Function< dim >.

Definition at line 2253 of file function_lib.cc.

◆ gradient()

template<int dim>
Tensor< 1, dim > Functions::Monomial< dim >::gradient ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
overridevirtual

Function gradient at one point.

Reimplemented from Function< dim >.

Definition at line 2214 of file function_lib.cc.

◆ vector_value_list()

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

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.

Reimplemented in Functions::CutOffFunctionCinfty< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionW1< dim >, Functions::CutOffFunctionLinfty< dim >, Functions::SlitSingularityFunction< dim >, Functions::CosineGradFunction< dim >, Functions::CosineFunction< dim >, Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, and Functions::Q1WedgeFunction< dim >.

◆ vector_values()

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

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.

Reimplemented in Functions::StokesCosine< dim >, Functions::PoisseuilleFlow< dim >, Functions::FlowFunction< dim >, and Functions::FlowFunction< 2 >.

◆ vector_gradient()

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

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

◆ gradient_list()

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

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.

◆ vector_gradients()

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

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.

◆ vector_gradient_list()

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

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.

◆ laplacian()

virtual double Function< dim, double >::laplacian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_laplacian()

virtual void Function< dim, double >::vector_laplacian ( const Point< dim > &  p,
Vector< double > &  values 
) const
virtualinherited

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

◆ laplacian_list()

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

◆ vector_laplacian_list()

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

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

Reimplemented in Functions::FlowFunction< dim >, and Functions::FlowFunction< 2 >.

◆ hessian()

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

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 >.

◆ vector_hessian()

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

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

◆ hessian_list()

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

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

◆ vector_hessian_list()

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

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

◆ memory_consumption()

std::size_t Function< dim, double >::memory_consumption ( ) const
inherited

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.

◆ get_time()

template<typename Number = double>
Number FunctionTime< Number >::get_time ( ) const
inherited

Return the value of the time variable.

◆ set_time()

template<typename Number = double>
virtual void FunctionTime< Number >::set_time ( const Number  new_time)
virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

template<typename Number = double>
virtual void FunctionTime< Number >::advance_time ( const Number  delta_t)
virtualinherited

Advance the time by the given time step delta_t.

◆ subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

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

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

◆ serialize()

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

Read or write the data of this object to or from a stream for the purpose of serialization.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

Member Data Documentation

◆ exponents

template<int dim>
const Tensor<1, dim> Functions::Monomial< dim >::exponents
private

The set of exponents.

Definition at line 1348 of file function_lib.h.

◆ dimension

const unsigned int Function< dim, double >::dimension
staticinherited

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

Definition at line 159 of file function.h.

◆ n_components

const unsigned int Function< dim, double >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.


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