Reference documentation for deal.II version Git 98872c4d47 2020-10-01 08:48:12 +0200
Functions::ParsedFunction< dim > Class Template Reference

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

Inheritance diagram for Functions::ParsedFunction< dim >:
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## Public Types

enum  DifferenceFormula { Euler, UpwindEuler, FourthOrder }

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

## Public Member Functions

ParsedFunction (const unsigned int n_components=1, const double h=1e-8)

void parse_parameters (ParameterHandler &prm)

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

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

virtual void set_time (const double newtime) override

void set_formula (const DifferenceFormula formula=Euler)

void set_h (const double h)

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

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

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 >> &gradients, const unsigned int component=0) const override

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_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim >>> &gradients) const override

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

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

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_gradients (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 void declare_parameters (ParameterHandler &prm, const unsigned int n_components=1)

static DifferenceFormula get_formula_of_order (const unsigned int ord)

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

FunctionParser< dim > function_object

## Detailed Description

### template<int dim> class Functions::ParsedFunction< dim >

Friendly interface to the FunctionParser class. This class is meant as a wrapper for the FunctionParser class. It is used in the step-34 tutorial program.

It provides two methods to declare and parse a ParameterHandler object and creates the Function object declared in the parameter file. This class is derived from the AutoDerivativeFunction class, so you don't need to specify derivatives. An example of usage of this class is as follows:

// A parameter handler
// Declare a section for the function we need
prm.enter_subsection("My vector function");
// Create a ParsedFunction
ParsedFunction<dim> my_vector_function(dim);
// Parse an input file.
prm.parse_input(some_input_file);
// Initialize the ParsedFunction object with the given file
prm.enter_subsection("My vector function");
my_vector_function.parse_parameters(prm);

And here is an example of how the input parameter could look like (see the documentation of the FunctionParser class for a detailed description of the syntax of the function definition):

# A test two dimensional vector function, depending on time
subsection My vector function
set Function constants = kappa=.1, lambda=2.
set Function expression = if(y>.5, kappa*x*(1-x),0); t^2*cos(lambda*pi*x)
set Variable names = x,y,t

Definition at line 80 of file parsed_function.h.

## ◆ time_type

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

The scalar-valued real type used for representing time.

Definition at line 170 of file function.h.

## ◆ DifferenceFormula

template<int dim>
 inherited

Names of difference formulas.

Enumerator
Euler

The symmetric Euler formula of second order:

$u'(t) \approx \frac{u(t+h) - u(t-h)}{2h}.$

UpwindEuler

The upwind Euler formula of first order:

$u'(t) \approx \frac{u(t) - u(t-h)}{h}.$

FourthOrder

The fourth order scheme

$u'(t) \approx \frac{u(t-2h) - 8u(t-h) + 8u(t+h) - u(t+2h)}{12h}.$

Definition at line 88 of file auto_derivative_function.h.

## ◆ ParsedFunction()

template<int dim>
 Functions::ParsedFunction< dim >::ParsedFunction ( const unsigned int n_components = 1, const double h = 1e-8 )

Construct a vector function. The vector function which is generated has n_components components (defaults to 1). The parameter h is used to initialize the AutoDerivativeFunction class from which this class is derived.

Definition at line 26 of file parsed_function.cc.

## ◆ declare_parameters()

template<int dim>
 void Functions::ParsedFunction< dim >::declare_parameters ( ParameterHandler & prm, const unsigned int n_components = 1 )
static

Declare parameters needed by this class. The additional parameter n_components is used to generate the right code according to the number of components of the function that will parse this ParameterHandler. If the number of components which is parsed does not match the number of components of this object, an assertion is thrown and the program is aborted. The default behavior for this class is to declare the following entries:

set Function constants =
set Function expression = 0
set Variable names = x,y,t

Definition at line 36 of file parsed_function.cc.

## ◆ parse_parameters()

template<int dim>
 void Functions::ParsedFunction< dim >::parse_parameters ( ParameterHandler & prm )

Parse parameters needed by this class. If the number of components which is parsed does not match the number of components of this object, an assertion is thrown and the program is aborted. In order for the class to function properly, we follow the same conventions declared in the FunctionParser class (look there for a detailed description of the syntax for function declarations).

The three variables that can be parsed from a parameter file are the following:

set Function constants =
set Function expression =
set Variable names =

Function constants is a collection of pairs in the form name=value, separated by commas, for example:

set Function constants = lambda=1., alpha=2., gamma=3.

These constants can be used in the declaration of the function expression, which follows the convention of the FunctionParser class. In order to specify vector functions, semicolons have to be used to separate the different components, e.g.:

set Function expression = cos(pi*x); cos(pi*y)

The variable names entry can be used to customize the name of the variables used in the Function. It defaults to

set Variable names = x,t

for one dimensional problems,

set Variable names = x,y,t

for two dimensional problems and

set Variable names = x,y,z,t

for three dimensional problems.

The time variable can be set according to specifications in the FunctionTime base class.

Definition at line 115 of file parsed_function.cc.

## ◆ vector_value()

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

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

Reimplemented from Function< dim >.

Definition at line 167 of file parsed_function.cc.

## ◆ value()

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

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.

Reimplemented from Function< dim >.

Definition at line 177 of file parsed_function.cc.

## ◆ set_time() [1/2]

template<int dim>
 void Functions::ParsedFunction< dim >::set_time ( const double newtime )
overridevirtual

Set the time to a specific value for time-dependent functions.

We need to overwrite this to set the time also in the accessor FunctionParser<dim>.

Definition at line 186 of file parsed_function.cc.

## ◆ set_formula()

template<int dim>
 void AutoDerivativeFunction< dim >::set_formula ( const DifferenceFormula formula = Euler )
inherited

Choose the difference formula. See the enum DifferenceFormula for available choices.

Definition at line 43 of file auto_derivative_function.cc.

## ◆ set_h()

template<int dim>
 void AutoDerivativeFunction< dim >::set_h ( const double h )
inherited

Takes the difference step size h. It's within the user's responsibility to choose an appropriate value here. h should be chosen taking into account the absolute value of as well as the amount of local variation of the function. Setting h=1e-6 might be a good choice for functions with an absolute value of about 1, that furthermore does not vary to much.

Definition at line 65 of file auto_derivative_function.cc.

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

Return the gradient of the specified component of the function at the given point.

Compute numerical difference quotients using the preset DifferenceFormula.

Reimplemented from Function< dim >.

Definition at line 75 of file auto_derivative_function.cc.

template<int dim>
 void AutoDerivativeFunction< dim >::vector_gradient ( const Point< dim > & p, std::vector< Tensor< 1, dim >> & gradients ) const
overridevirtualinherited

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

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 127 of file auto_derivative_function.cc.

 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.

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

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.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 204 of file auto_derivative_function.cc.

 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.

template<int dim>
 void AutoDerivativeFunction< dim >::vector_gradient_list ( const std::vector< Point< dim >> & points, std::vector< std::vector< Tensor< 1, dim >>> & gradients ) const
overridevirtualinherited

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.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 268 of file auto_derivative_function.cc.

 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.

## ◆ get_formula_of_order()

template<int dim>
 AutoDerivativeFunction< dim >::DifferenceFormula AutoDerivativeFunction< dim >::get_formula_of_order ( const unsigned int ord )
staticinherited

Return a DifferenceFormula of the order ord at minimum.

Definition at line 336 of file auto_derivative_function.cc.

## ◆ value_list()

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

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.

## ◆ 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.

## ◆ 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.

 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.

## ◆ laplacian()

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

Compute the Laplacian of a given component at point p.

## ◆ 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

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

## ◆ 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() [2/2]

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.

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.

## ◆ function_object

template<int dim>
 FunctionParser Functions::ParsedFunction< dim >::function_object
private

The object with which we do computations.

Definition at line 213 of file parsed_function.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: