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

Inheritance diagram for FunctionParser< dim >:

[legend]

Public Types
using	ConstMap = std::map<std::string, double>

enum	DifferenceFormula { Euler , UpwindEuler , FourthOrder }

using	time_type

Public Member Functions
	FunctionParser (const unsigned int n_components=1, const double initial_time=0.0, const double h=1e-8)

	FunctionParser (const std::string &expression, const std::string &constants="", const std::string &variable_names=default_variable_names()+",t", const double h=1e-8)

	FunctionParser (const FunctionParser &)=delete

	FunctionParser (FunctionParser &&)=delete

FunctionParser &	operator= (const FunctionParser &)=delete

FunctionParser &	operator= (FunctionParser &&)=delete

virtual void	initialize (const std::string &vars, const std::vector< std::string > &expressions, const ConstMap &constants, const bool time_dependent=false) override

void	initialize (const std::string &vars, const std::string &expression, const ConstMap &constants, const bool time_dependent=false)

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

const std::vector< std::string > &	get_expressions () const

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, RangeNumberType > > &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, RangeNumberType > > &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, RangeNumberType > > > &gradients) 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 void	vector_gradients (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

virtual std::size_t	memory_consumption () const

numbers::NumberTraits< double >::real_type	get_time () const

virtual void	set_time (const numbers::NumberTraits< double >::real_type new_time)

virtual void	advance_time (const numbers::NumberTraits< double >::real_type 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 std::string	default_variable_names ()

static ::ExceptionBase &	ExcParseError (int arg1, std::string arg2)

static ::ExceptionBase &	ExcInvalidExpressionSize (int arg1, int arg2)

static DifferenceFormula	get_formula_of_order (const unsigned int ord)

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Public Attributes
const unsigned int	n_components

Static Public Attributes
static constexpr unsigned int	dimension = dim

Protected Member Functions
void	init_muparser () const

double	do_value (const Point< dim > &p, const double time, unsigned int component) const

void	do_all_values (const Point< dim > &p, const double time, ArrayView< double > &values) const

Protected Attributes
std::vector< std::string >	expressions

Private Types
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

Private Attributes
double	h

std::vector< Tensor< 1, dim > >	ht

DifferenceFormula	formula

numbers::NumberTraits< double >::real_type	time

std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

Threads::ThreadLocalStorage< internal::FunctionParser::ParserData >	parser_data

std::map< std::string, double >	constants

std::vector< std::string >	var_names

bool	initialized

unsigned int	n_vars

Static Private Attributes
static std::mutex	mutex

Detailed Description

template<int dim>
class FunctionParser< dim >

This class implements a function object that gets its value by parsing a string describing this function. It is a wrapper class for the muparser library (see https://beltoforion.de/en/muparser/). This class lets you evaluate strings such as "sqrt(1-x^2+y^2)" for given values of 'x' and 'y'. Please refer to the muparser documentation for more information. This class is used in the step-33 and step-36 tutorial programs (the latter being much simpler to understand).

In addition to the built-in functions of muparser, namely

sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh,

atan2, log2, log10, log, ln, exp, sqrt, sign, rint, abs, min, max, sum, avg

this class also supports the following operations:

if(condition, then-value, else-value)
| and & (logic or and and)
int(x), ceil(x), floor(x) (rounding)
cot(x), csc(x), sec(x)
pow(x,n), log(x)
erfc(x)
rand(), rand_seed(seed)

Note: This class implements the list of functions just mentioned as user-defined functions by extending muparser. This means, in particular, that the if(condition, then-value, else-value) syntax evaluates all three arguments before determining whether the condition is true, and then discarding either the "then" or the "else" expressions. In almost all situations, this is not a problem except if the evaluation of one of the expressions throws a floating point exception in cases where it will later be discarded. (Assuming floating point exceptions are switched on, as is the default for deal.II in debug mode on most systems.) An example would be the expression if(x>0, sqrt(x), 0) which is mathematically well defined, but on systems where this is enabled will abort the program with a floating point exception when evaluated with a negative x. This is because the square root of x is computed before the if statement's condition is considered to determine whether the result should be the second or third argument. If this kind of behavior is a problem, you can resort to the muparser built-in syntax (condition ? then-value : else-value), using the ternary syntax familiar to C++ programmers. If this syntax is used, muparser uses lazy evaluation in which only one of the branches is evaluated, depending on whether the condition is true or false.

The following examples shows how to use this class:

// set up problem:
std::string variables = "x,y";
std::string expression = "cos(x) + sqrt(y)";
std::map<std::string, double> constants;
 
// FunctionParser with 2 variables and 1 component:
FunctionParser<2> fp(1);
fp.initialize(variables,
              expression,
              constants);
 
// Point at which we want to evaluate the function
Point<2> point(0.0, 4.0);
 
// evaluate the expression at 'point':
double result = fp.value(point);
 
deallog << "Function '" << expression << "'"
        << " @ " << point
        << " is " << result << std::endl;

The second example is a bit more complex:

// Define some constants that will be used by the function parser
std::map<std::string, double> constants;
constants["pi"] = numbers::PI;
 
// Define the variables that will be used inside the expressions
std::string variables = "x,y,z";
 
// Define the expressions of the individual components of a
// vector valued function with two components:
std::vector<std::string> expressions(2);
expressions[0] = "sin(2*pi*x)+sinh(pi*z)";
expressions[1] = "sin(2*pi*y)*exp(x^2)";
 
// function parser with 3 variables and 2 components
FunctionParser<3> vector_function(2);
 
// And populate it with the newly created objects.
vector_function.initialize(variables,
                           expressions,
                           constants);
 
// Point at which we want to evaluate the function
Point<3> point(0.0, 1.0, 1.0);
 
// This Vector will store the result
Vector<double> result(2);
 
// Fill 'result' by evaluating the function
vector_function.vector_value(point, result);
 
// We can also only evaluate the 2nd component:
const double c = vector_function.value(point, 1);
 
// Output the evaluated function
deallog << "Function '" << expressions[0] << ',' << expressions[1] << "'"
        << " at " << point
        << " is " << result << std::endl;

This class overloads the virtual methods value() and vector_value() of the Function base class with the byte compiled versions of the expressions given to the initialize() methods. Note that the class will not work unless you first call the initialize() method that accepts the text description of the function as an argument (among other things).

The syntax to describe a function follows usual programming practice, and is explained in detail at the homepage of the underlying muparser library at https://beltoforion.de/en/muparser/.

If you would like to check that muparser is parsing your functions correctly, and to evaluate the functions at given parameter values, you may consider running your expressions through pymuparser (https://github.com/bobmyhill/pymuparser), which can be installed using pip (python -m pip install pymuparser). This module also allows users to define functions not included in MuParser, such as the extended library provided by deal.II.

For a wrapper of the FunctionParser class that supports ParameterHandler, see Functions::ParsedFunction.

Vector-valued functions can either be declared using strings where the function components are separated by semicolons, or using a vector of strings each defining one vector component.

An example of time dependent scalar function is the following:

   // Empty constants object
   std::map<std::string,double> constants;
 
   // Variables that will be used inside the expressions
   std::string variables = "x,y,t";
 
   // Define the expression of the scalar time dependent function.
   std::string expression = "exp(y*x)*exp(-t)";
 
   // Generate an empty scalar function
   FunctionParser<2> function;
 
   // And populate it with the newly created objects.
   function.initialize(variables,
                       expression,
                       constants,
// Treat the last variable ("t") as time.
                       true);

The following is another example of how to instantiate a vector valued function by using a single string:

// Empty constants object
std::map<std::string,double> constants;
 
// Variables that will be used inside the expressions
std::string variables = "x,y";
 
// Define the expression of the vector valued  function.
std::string expression = "cos(2*pi*x)*y^2; sin(2*pi*x)*exp(y)";
 
// Generate an empty vector valued function
FunctionParser<2> function(2);
 
// And populate it with the newly created objects.
function.initialize(variables,
                    expression,
                    constants);

Note: The difference between this class and the SymbolicFunction class is that the SymbolicFunction class allows to compute first and second order derivatives (in a symbolic way), while this class computes first order derivatives only, using finite differences. For complicated expressions, this class is generally faster than SymbolicFunction.

Definition at line 224 of file function_parser.h.

Member Typedef Documentation

◆ ConstMap

template<int dim>

using FunctionParser< dim >::ConstMap = std::map<std::string, double>

Type for the constant map. Used by the initialize() method.

Definition at line 282 of file function_parser.h.

◆ time_type

template<int dim, typename RangeNumberType = double>

using Function< dim, RangeNumberType >::time_type

inherited

Initial value:

typename FunctionTime<

typename numbers::NumberTraits<RangeNumberType>::real_type>::time_type

FunctionTime

Definition function_time.h:72

Function::time_type

typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type time_type

Definition function.h:168

numbers::NumberTraits::real_type

number real_type

Definition numbers.h:441

The scalar-valued real type used for representing time.

Definition at line 168 of file function.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Member Enumeration Documentation

◆ DifferenceFormula

template<int dim>

enum AutoDerivativeFunction::DifferenceFormula

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 87 of file auto_derivative_function.h.

Constructor & Destructor Documentation

◆ FunctionParser() [1/4]

template<int dim>

FunctionParser< dim >::FunctionParser	(	const unsigned int	n_components = 1,
		const double	initial_time = 0.0,
		const double	h = 1e-8 )

Constructor. Its arguments are the same of the base class Function, with the additional parameter h, used for the computation of gradients using finite differences. This object needs to be initialized with the initialize() method before you can use it. If an attempt to use this function is made before the initialize() method has been called, then an exception is thrown.

Definition at line 38 of file function_parser.cc.

◆ FunctionParser() [2/4]

template<int dim>

FunctionParser< dim >::FunctionParser	(	const std::string &	expression,
		const std::string &	constants = "",
		const std::string &	variable_names = default_variable_names() + ",t",
		const double	h = 1e-8 )

Constructor for parsed functions. Takes directly a semi-colon separated list of expressions (one for each component of the function), an optional comma-separated list of constants, variable names and step size for the computation of first order derivatives by finite differences.

Definition at line 46 of file function_parser.cc.

◆ FunctionParser() [3/4]

template<int dim>

FunctionParser< dim >::FunctionParser ( const FunctionParser< dim > & )

delete

Copy constructor. Objects of this type can not be copied, and consequently this constructor is deleted.

◆ FunctionParser() [4/4]

template<int dim>

FunctionParser< dim >::FunctionParser ( FunctionParser< dim > && )

delete

Move constructor. Objects of this type can not be moved, and consequently this constructor is deleted.

Member Function Documentation

◆ operator=() [1/2]

template<int dim>

FunctionParser & FunctionParser< dim >::operator= ( const FunctionParser< dim > & )

delete

Copy operator. Objects of this type can not be copied, and consequently this operator is deleted.

◆ operator=() [2/2]

template<int dim>

FunctionParser & FunctionParser< dim >::operator= ( FunctionParser< dim > && )

delete

Move operator. Objects of this type can not be moved, and consequently this operator is deleted.

◆ initialize() [1/2]

template<int dim>

void FunctionParser< dim >::initialize	(	const std::string &	vars,
		const std::vector< std::string > &	expressions,
		const ConstMap &	constants,
		const bool	time_dependent = false )

overridevirtual

Initialize the object by setting the actual parsed functions.

Parameters

[in]	vars	a string with the variables that will be used by the expressions to be evaluated. Note that the variables can have any name (of course different from the function names defined above!), but the order IS important. The first variable will correspond to the first component of the point in which the function is evaluated, the second variable to the second component and so forth. If this function is also time dependent, then it is necessary to specify it by setting the `time_dependent` parameter to true. An exception is thrown if the number of variables specified here is different from dim (if this function is not time-dependent) or from dim+1 (if it is time-dependent).
[in]	expressions	a list of strings containing the expressions that will be byte compiled by the internal parser (muParser). Note that the size of this vector must match exactly the number of components of the FunctionParser, as declared in the constructor. If this is not the case, an exception is thrown.
[in]	constants	a map of constants used to pass any necessary constant that we want to specify in our expressions (in the example above the number pi). An expression is valid if and only if it contains only defined variables and defined constants (other than the functions specified above). If a constant is given whose name is not valid (eg: `constants["sin"] = 1.5;`) an exception is thrown.
[in]	time_dependent	If this is a time dependent function, then the last variable declared in `vars` is assumed to be the time variable, and FunctionTime::get_time() is used to initialize it when evaluating the function. Naturally the number of variables parsed by initialize() in this case is dim+1. The value of this parameter defaults to false, i.e., do not consider time.

Reimplemented from internal::FunctionParser::ParserImplementation< dim, double >.

Definition at line 73 of file function_parser.cc.

◆ initialize() [2/2]

template<int dim>

void FunctionParser< dim >::initialize	(	const std::string &	vars,
		const std::string &	expression,
		const ConstMap &	constants,
		const bool	time_dependent = false )

Initialize the function. Same as above, but accepts a string rather than a vector of strings. If this is a vector valued function, its components are expected to be separated by a semicolon. An exception is thrown if this method is called and the number of components successfully parsed does not match the number of components of the base function.

Definition at line 88 of file function_parser.cc.

◆ default_variable_names()

template<int dim>

std::string FunctionParser< dim >::default_variable_names ( )

static

A function that returns default names for variables, to be used in the first argument of the initialize() functions: it returns "x" in 1d, "x,y" in 2d, and "x,y,z" in 3d.

Definition at line 384 of file function_parser.h.

◆ value()

template<int dim>

double FunctionParser< 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, RangeNumberType >.

Definition at line 103 of file function_parser.cc.

◆ get_expressions()

template<int dim>

const std::vector< std::string > & FunctionParser< dim >::get_expressions ( ) const

Return an array of function expressions (one per component), used to initialize this function.

Definition at line 30 of file function_parser.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 42 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 64 of file auto_derivative_function.cc.

◆ gradient()

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, RangeNumberType >.

Definition at line 74 of file auto_derivative_function.cc.

◆ vector_gradient() [1/2]

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 126 of file auto_derivative_function.cc.

◆ vector_gradient() [2/2]

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

virtualinherited

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

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ gradient_list() [1/2]

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 203 of file auto_derivative_function.cc.

◆ gradient_list() [2/2]

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

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.

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ vector_gradient_list() [1/2]

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 267 of file auto_derivative_function.cc.

◆ vector_gradient_list() [2/2]

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

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.

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ 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 335 of file auto_derivative_function.cc.

◆ vector_value()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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.

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ value_list()

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

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.

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ vector_value_list()

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

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::ConstantFunction< dim, double >.

◆ vector_values()

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

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.

◆ vector_gradients()

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

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()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

Compute the Laplacian of a given component at point p.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CosineFunction< dim >, Functions::CosineGradFunction< dim >, Functions::CSpline< dim >, Functions::ExpFunction< dim >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::FourierCosineFunction< dim >, Functions::FourierCosineSum< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::JumpFunction< dim >, Functions::PillowFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::SquareFunction< dim >, and Functions::SymbolicFunction< dim, RangeNumberType >.

◆ vector_laplacian()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

◆ laplacian_list()

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

virtualinherited

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

◆ vector_laplacian_list()

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

virtualinherited

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

◆ hessian()

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

virtualinherited

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

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CoordinateRestriction< dim >, Functions::CosineFunction< dim >, Functions::CSpline< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::SignedDistance::Plane< dim >, Functions::SignedDistance::Sphere< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, and NonMatching::internal::DiscreteQuadratureGeneratorImplementation::RefSpaceFEFieldFunction< dim, VectorType >.

◆ vector_hessian()

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

virtualinherited

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

◆ hessian_list()

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

virtualinherited

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

◆ vector_hessian_list()

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

virtualinherited

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

◆ memory_consumption()

template<int dim, typename RangeNumberType = double>

virtual std::size_t Function< dim, RangeNumberType >::memory_consumption ( ) const

virtualinherited

Return an estimate for the memory consumption, in bytes, of this object.

This function is virtual and can be overloaded by derived classes.

Reimplemented in ComponentSelectFunction< dim, RangeNumberType >, FunctionDerivative< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CSpline< dim >, Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::JumpFunction< dim >, Functions::Polynomial< dim >, and Functions::Spherical< dim >.

◆ get_time()

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::get_time ( ) const

inherited

Return the value of the time variable.

◆ set_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::set_time ( const numbers::NumberTraits< double >::real_type new_time )

virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::advance_time ( const numbers::NumberTraits< double >::real_type 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 135 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 155 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 203 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 using the BOOST serialization library.

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.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

◆ init_muparser()

void internal::FunctionParser::ParserImplementation< dim, double >::init_muparser ( ) const

inherited

Set up the internal muParser objects to parse and evaluate mathematical expressions.

Definition at line 180 of file mu_parser_internal.cc.

◆ do_value()

double internal::FunctionParser::ParserImplementation< dim, double >::do_value	(	const Point< dim > &	p,
		const double	time,
		unsigned int	component ) const

inherited

Compute the value of a single component.

Definition at line 186 of file mu_parser_internal.cc.

◆ do_all_values()

void internal::FunctionParser::ParserImplementation< dim, double >::do_all_values	(	const Point< dim > &	p,
		const double	time,
		ArrayView< double > &	values ) const

inherited

Compute the values of all components.

Definition at line 194 of file mu_parser_internal.cc.

Member Data Documentation

◆ h

template<int dim>

double AutoDerivativeFunction< dim >::h

privateinherited

Step size of the difference formula. Set by the set_h() function.

Definition at line 222 of file auto_derivative_function.h.

◆ ht

template<int dim>

std::vector<Tensor<1, dim> > AutoDerivativeFunction< dim >::ht

privateinherited

Includes the unit vectors scaled by h.

Definition at line 227 of file auto_derivative_function.h.

◆ formula

template<int dim>

DifferenceFormula AutoDerivativeFunction< dim >::formula

privateinherited

Difference formula. Set by the set_formula() function.

Definition at line 232 of file auto_derivative_function.h.

◆ dimension

template<int dim, typename RangeNumberType = double>

unsigned int Function< dim, RangeNumberType >::dimension = dim

staticconstexprinherited

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

Definition at line 158 of file function.h.

◆ n_components

template<int dim, typename RangeNumberType = double>

const unsigned int Function< dim, RangeNumberType >::n_components

inherited

Number of vector components.

Definition at line 163 of file function.h.

◆ time

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::time

privateinherited

Store the present time.

Definition at line 112 of file function_time.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

◆ counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

◆ expressions

std::vector<std::string> internal::FunctionParser::ParserImplementation< dim, double >::expressions

inherited

An array of function expressions (one per component), required to initialize tfp in each thread.

Definition at line 202 of file mu_parser_internal.h.

◆ parser_data

Threads::ThreadLocalStorage<internal::FunctionParser::ParserData> internal::FunctionParser::ParserImplementation< dim, double >::parser_data

mutableprivateinherited

The muParser objects (hidden with the PIMPL idiom) for each thread (and one for each component).

Definition at line 210 of file mu_parser_internal.h.

◆ constants

std::map<std::string, double> internal::FunctionParser::ParserImplementation< dim, double >::constants

privateinherited

An array to keep track of all the constants, required to initialize fp in each thread.

Definition at line 216 of file mu_parser_internal.h.

◆ var_names

std::vector<std::string> internal::FunctionParser::ParserImplementation< dim, double >::var_names

privateinherited

An array for the variable names, required to initialize fp in each thread.

Definition at line 222 of file mu_parser_internal.h.

◆ initialized

bool internal::FunctionParser::ParserImplementation< dim, double >::initialized

privateinherited

State of usability. This variable is checked every time the function is called for evaluation. It's set to true in the initialize() methods.

Definition at line 228 of file mu_parser_internal.h.

◆ n_vars

unsigned int internal::FunctionParser::ParserImplementation< dim, double >::n_vars

privateinherited

Number of variables. If this is also a function of time, then the number of variables is dim+1, otherwise it is dim. In the case that this is a time dependent function, the time is supposed to be the last variable. If n_vars is not identical to the number of the variables parsed by the initialize() method, then an exception is thrown.

Definition at line 237 of file mu_parser_internal.h.

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

include/deal.II/base/function_parser.h
source/base/function_parser.cc

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ ConstMap

◆ time_type

◆ map_value_type

◆ map_iterator

Member Enumeration Documentation

◆ DifferenceFormula

Constructor & Destructor Documentation

◆ FunctionParser() [1/4]

◆ FunctionParser() [2/4]

◆ FunctionParser() [3/4]

◆ FunctionParser() [4/4]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ initialize() [1/2]

◆ initialize() [2/2]

◆ default_variable_names()

◆ value()

◆ get_expressions()

◆ set_formula()

◆ set_h()

◆ gradient()

◆ vector_gradient() [1/2]

◆ vector_gradient() [2/2]

◆ gradient_list() [1/2]

◆ gradient_list() [2/2]

◆ vector_gradient_list() [1/2]

◆ vector_gradient_list() [2/2]

◆ get_formula_of_order()

◆ vector_value()

◆ value_list()

◆ vector_value_list()

◆ vector_values()

◆ vector_gradients()

◆ laplacian()

◆ vector_laplacian()

◆ laplacian_list()

◆ vector_laplacian_list()

◆ hessian()

◆ vector_hessian()

◆ hessian_list()

◆ vector_hessian_list()

◆ memory_consumption()

◆ get_time()

◆ set_time()

◆ advance_time()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ check_no_subscribers()

◆ init_muparser()

◆ do_value()

◆ do_all_values()

Member Data Documentation

◆ h

◆ ht

◆ formula

◆ dimension

◆ n_components

◆ time

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info