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

Inheritance diagram for Functions::SymbolicFunction< dim, RangeNumberType >:

Public Types
using	time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type

Public Member Functions
	SymbolicFunction (const std::vector< Differentiation::SD::Expression > &function, const Tensor< 1, dim, Differentiation::SD::Expression > &coordinate_symbols=get_default_coordinate_symbols(), const Differentiation::SD::Expression &time_symbol=Differentiation::SD::make_symbol("t"), const Differentiation::SD::types::substitution_map &user_substitution_map={})

	SymbolicFunction (const std::string &expressions)

void	update_user_substitution_map (const Differentiation::SD::types::substitution_map &substitutions)

void	set_additional_function_arguments (const Differentiation::SD::types::substitution_map &arguments)

const Tensor< 1, dim, Differentiation::SD::Expression > &	get_coordinate_symbols () const

const Differentiation::SD::Expression &	get_time_symbol () const

const std::vector< Differentiation::SD::Expression > &	get_symbolic_function_expressions () const

const Differentiation::SD::types::substitution_map &	get_user_substitution_map () const

SymbolicFunction< dim, RangeNumberType >	time_derivative () const

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

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

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

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

template<typename StreamType >
StreamType &	print (StreamType &out) 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_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 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 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

Number	get_time () const

virtual void	set_time (const Number new_time)

virtual void	advance_time (const Number delta_t)

Static Public Member Functions
static Tensor< 1, dim, Differentiation::SD::Expression >	get_default_coordinate_symbols ()

Public Attributes
const unsigned int	n_components

Static Public Attributes
static constexpr unsigned int	dimension = dim

Private Member Functions
Differentiation::SD::types::substitution_map	create_evaluation_substitution_map (const Point< dim > &point) const

void	update_values () const

void	update_first_derivatives () const

void	update_second_derivatives () const

Private Attributes
const std::vector< Differentiation::SD::Expression >	user_function

Differentiation::SD::types::substitution_map	user_substitution_map

Differentiation::SD::types::substitution_map	additional_function_arguments

std::vector< Differentiation::SD::Expression >	function

std::vector< Tensor< 1, dim, Differentiation::SD::Expression > >	function_gradient

std::vector< Tensor< 2, dim, Differentiation::SD::Expression > >	function_hessian

std::vector< Differentiation::SD::Expression >	function_laplacian

Tensor< 1, dim, Differentiation::SD::Expression >	coordinate_symbols

Differentiation::SD::Expression	time_symbol

Number	time

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

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

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

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

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

void	check_no_subscribers () const noexcept

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

Detailed Description

template<int dim, typename RangeNumberType = double>
class Functions::SymbolicFunction< dim, RangeNumberType >

A Function class that leverages symbolic differentiation to compute gradients, Laplacians, Hessians, and time derivatives.

This class can be used to define functions using methods provided by the Differentiation::SD namespace. In particular, one can define a symbolic evaluation point (the argument of the function), as well as a symbolic expression.

The symbolic gradients and the symbolic Hessians are computed at construction time, and when a substitution in the symbolic functions is requested by the user using the method update_user_substitution_map().

Whenever one of the evaluation methods is called, a substitution is attempted with the coordinate symbols argument replaced by the evaluation point and the symbolic time replaced by the current time, as returned by the get_time() method. The user has to make sure that at evaluation time argument substitution provides a fully evaluated expression (i.e., no other symbols are contained in the function expression, except numerical values), or an exception will be thrown. Additional symbols can be partially evaluated or substituted by storing them in a user supplied substitution maps, that can be updated by calling update_user_substitution_map() or the set_additional_function_arguments() methods.

The simplest use case of this class is given in the following example:

SymbolicFunction<2> fun("x^2+y; t*x*y");
fun.set_time(3.0);
Point<2> p(1.0, 2.0);
 
auto a = fun.value(p, / * component * / 0); // a = 3.0
auto b = fun.value(p, / * component * / 1); // b = 6.0
 
auto df_dt = fun.time_derivative();
 
auto c = df_dt.value(p, / * component * / 0); // c = 0.0
auto d = df_dt.value(p, / * component * / 1); // d = 2.0

where a Function with two components is defined using a string containing their expressions separated by semicolons.

A more involved example, that explicitly uses Differentiation::SD::Expression objects, is given by

using namespace Differentiation::SD;
// Create a position Tensor<1,2,Differentiation::SD::Expression>
// with symbols "x" and "y", and the symbol "t"
const auto x = SymbolicFunction<2>::get_default_coordinate_symbols();
const auto t = make_symbol("t");
 
// Use directly x[0] (the symbol "x"), x[1] (the symbol "y"), and t
// (the symbol "t").
Expression f = std::sin(x[0])*std::cos(x[1])*std::sin(t);
// Alternatively, you can achieve the same result parsing a string:
// Expression f("sin(x)*cos(y)*sin(t)", true);
SymbolicFunction<2> function({f}, x);
 
// Evaluate the function, its gradient, and its Laplacian
Point<2> p(1.0, 2.0);
auto fp = function.value(p);
auto gradfp = function.gradient(p);
auto lapfp = function.laplacian(p);
 
// Evaluate the time derivative of the function, its gradient, and its
// Laplacian
auto time_derivative = function.time_derivative();
auto dt_fp = time_derivative.value(p);
auto dt_gradfp = time_derivative.gradient(p);
auto dt_lapfp = time_derivative.laplacian(p);

Partial substitution is possible (i.e., you can define the function using additional symbols). However, as soon as you evaluate the function, you have to make sure that all extraneous symbols (i.e., those not referring to the spacial coordinate_symbols or to the time_symbol variable) have been substituted with numerical values, or expressions of the spatial or temporal argument, by calling the update_user_substitution_map() or the set_additional_function_arguments() methods.

If your function requires additional arguments to be evaluated, you can specify them by calling the set_additional_function_arguments() method.

If you call update_user_substitution_map() and set_additional_function_arguments() with the same argument, the effect on the function evaluation will be the same, however, the internal behavior and function derivatives will be different. The method update_user_substitution_map() performs the substitution once (the first time it is required), and then stores internally a copy of the resulting expression, together with its derivatives (if required). These are then used in all subsequent evaluations. Calling set_additional_function_arguments() will evaluate the passed substitution map on the fly during evaluation time, after all derivatives have been computed.

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

Definition at line 153 of file symbolic_function.h.

Member Typedef Documentation

◆ time_type

template<int dim, typename RangeNumberType = double>

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

inherited

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

Constructor & Destructor Documentation

◆ SymbolicFunction() [1/2]

template<int dim, typename RangeNumberType = double>

Functions::SymbolicFunction< dim, RangeNumberType >::SymbolicFunction	(	const std::vector< Differentiation::SD::Expression > &	function,
		const Tensor< 1, dim, Differentiation::SD::Expression > &	coordinate_symbols = `get_default_coordinate_symbols()`,
		const Differentiation::SD::Expression &	time_symbol = `Differentiation::SD::make_symbol("t")`,
		const Differentiation::SD::types::substitution_map &	user_substitution_map = `{}`
	)

Constructor.

The resulting Function object will have as many components as there are entries in the vector of symbolic expressions function.

The vector function should contain a list of symbolic expression involving the coordinate symbols argument coordinate_symbols and possibly the symbolic time argument time_symbol. It is possible to define it in terms of other symbols, as long as the optional parameter user_substitution_map replaces all symbols except coordinate_symbols and time_symbol. This is useful if, for example, you want to express formulas in terms of material parameters that you want to name symbolically, rather than through their numeric values when defining the formula, or when you want to express your formula in terms of polar coordinates rather than cartesian ones, and you want the symbolic engine to compute the derivatives for you. You may later update the symbol map contained in user_substitution_map by calling update_user_substitution_map().

Parameters

function	A vector of symbolic expressions of type Differentiation::SD::Expression, representing the components of this Function.
coordinate_symbols	A tensor of symbols representing coordinates, used as input argument in the symbolic expressions contained in the `function` vector. The default `coordinate_symbols` is a Tensor<1,dim,Differentiation::SD::Expression> containing the symbols "x" for `dim` equal to one, "x", "y" for `dim` equal to two, and "x", "y", "z" for `dim` equal to three.
time_symbol	A symbolic variable representing time. It defaults to a symbolic variable named "t".
user_substitution_map	Any other symbol that may be contained in the symbolic function needs to be specified in this map. The map may be empty, and the functions may still contain unevaluated symbols, provided that you call update_user_substitution_map() and provide a replacement of all symbols except `coordinate_symbols` and `time_symbol` before any evaluation occurs.

◆ SymbolicFunction() [2/2]

template<int dim, typename RangeNumberType = double>

Functions::SymbolicFunction< dim, RangeNumberType >::SymbolicFunction ( const std::string & expressions )

Constructor that takes a single string that describes the function expression as a semicolon separated list of expressions.

The symbolic expression can use the default argument and the default symbolic time variable, plus any additional symbols that you may need, provided that you update the user substitution map that substitutes all of them before you try to evaluate the function or its derivatives, by calling update_user_substitution_map(), and that you provide all the additional function arguments of your function using the method set_additional_function_arguments().

Member Function Documentation

◆ update_user_substitution_map()

template<int dim, typename RangeNumberType = double>

void Functions::SymbolicFunction< dim, RangeNumberType >::update_user_substitution_map ( const Differentiation::SD::types::substitution_map & substitutions )

Store and apply the substitution map substitutions to each symbolic component of this Function object.

Notice that this method will trigger a recomputation of the gradients, Hessians, and Laplacians of each component.

◆ set_additional_function_arguments()

template<int dim, typename RangeNumberType = double>

void Functions::SymbolicFunction< dim, RangeNumberType >::set_additional_function_arguments ( const Differentiation::SD::types::substitution_map & arguments )

Set the additional arguments to be substituted in next evaluation step.

Notice that the arguments are substituted after evaluating the permanent_user_substitution_map, and after all derivatives are computed. If the additional arguments you pass still depend on the coordinate or time symbols, then evaluation of derivatives will result in a partial derivative evaluation.

This method provides a way to evaluate functions that depend on more arguments than simply the coordinates and time. If you want to compute the total derivative w.r.t. to complicated symbolic expressions, you should call update_user_substitution_map() instead.

◆ get_default_coordinate_symbols()

template<int dim, typename RangeNumberType = double>

static Tensor< 1, dim, Differentiation::SD::Expression > Functions::SymbolicFunction< dim, RangeNumberType >::get_default_coordinate_symbols ( )

static

Return a tensor of coordinate symbols that can be used to define the expressions of this symbolic function object.

The default argument is a Tensor<1,dim,Differentiation::SD::Expression> containing the symbols "x" for dim equal to one, "x", "y" for dim equal to two, and "x", "y", "z" for dim equal to three.

◆ get_coordinate_symbols()

template<int dim, typename RangeNumberType = double>

const Tensor< 1, dim, Differentiation::SD::Expression > & Functions::SymbolicFunction< dim, RangeNumberType >::get_coordinate_symbols ( ) const

Get the actual arguments used for the coordinates in the symbolic function. This object does not include any user-defined arguments.

◆ get_time_symbol()

template<int dim, typename RangeNumberType = double>

const Differentiation::SD::Expression & Functions::SymbolicFunction< dim, RangeNumberType >::get_time_symbol ( ) const

Get the actual symbolic time in use in this symbolic function.

◆ get_symbolic_function_expressions()

template<int dim, typename RangeNumberType = double>

const std::vector< Differentiation::SD::Expression > & Functions::SymbolicFunction< dim, RangeNumberType >::get_symbolic_function_expressions ( ) const

Get the actual symbolic expressions used in this symbolic function.

◆ get_user_substitution_map()

template<int dim, typename RangeNumberType = double>

const Differentiation::SD::types::substitution_map & Functions::SymbolicFunction< dim, RangeNumberType >::get_user_substitution_map ( ) const

Get the currently stored user_substitution_map.

◆ time_derivative()

template<int dim, typename RangeNumberType = double>

SymbolicFunction< dim, RangeNumberType > Functions::SymbolicFunction< dim, RangeNumberType >::time_derivative ( ) const

Return a SymbolicFunction object that represents the time derivative of this function. The spatial argument, the symbolic time, and the currently stored user substitution map are forwarded to the new function.

◆ value()

template<int dim, typename RangeNumberType = double>

virtual RangeNumberType Functions::SymbolicFunction< dim, RangeNumberType >::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 >.

◆ gradient()

template<int dim, typename RangeNumberType = double>

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

overridevirtual

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

Reimplemented from Function< dim, RangeNumberType >.

◆ laplacian()

template<int dim, typename RangeNumberType = double>

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

overridevirtual

Compute the Laplacian of a given component at point p.

Reimplemented from Function< dim, RangeNumberType >.

◆ hessian()

template<int dim, typename RangeNumberType = double>

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

overridevirtual

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

Reimplemented from Function< dim, RangeNumberType >.

◆ print()

template<int dim, typename RangeNumberType >

template<typename StreamType >

StreamType & Functions::SymbolicFunction< dim, RangeNumberType >::print ( StreamType & out ) const

Print the stored arguments and function expression, as it would be evaluated when calling the method value().

Definition at line 441 of file symbolic_function.h.

◆ create_evaluation_substitution_map()

template<int dim, typename RangeNumberType = double>

Differentiation::SD::types::substitution_map Functions::SymbolicFunction< dim, RangeNumberType >::create_evaluation_substitution_map ( const Point< dim > & point ) const

private

Return a substitution map that replaces the argument with the values of point, the symbolic time with the value of this->get_time(), and any additional arguments with the substitution map given by additional_function_arguments.

◆ update_values()

template<int dim, typename RangeNumberType = double>

void Functions::SymbolicFunction< dim, RangeNumberType >::update_values ( ) const

private

Recompute the symbolic value of the function, applying the user substitution map. This may be an expensive computation, and it is called only if necessary.

◆ update_first_derivatives()

template<int dim, typename RangeNumberType = double>

void Functions::SymbolicFunction< dim, RangeNumberType >::update_first_derivatives ( ) const

private

Recompute the symbolic gradient of the function, applying the user substitution map. This may be an expensive computation, and it is called only if necessary.

◆ update_second_derivatives()

template<int dim, typename RangeNumberType = double>

void Functions::SymbolicFunction< dim, RangeNumberType >::update_second_derivatives ( ) const

private

Recompute the symbolic Hessian and the symbolic Lapalacian of the function. This may be an expensive computation, and it is called only if necessary.

◆ 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, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, VectorFunctionFromScalarFunctionObject< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, Functions::IncrementalFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ 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, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ 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, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ 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_gradient()

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, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ gradient_list()

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::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.

◆ 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.

◆ vector_gradient_list()

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::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< 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.

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

◆ 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.

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

◆ 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.

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

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

◆ 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.

Member Data Documentation

◆ user_function

template<int dim, typename RangeNumberType = double>

const std::vector<Differentiation::SD::Expression> Functions::SymbolicFunction< dim, RangeNumberType >::user_function

private

The components of this symbolic function, before any subustitution took place. This is immutable, and generated at construction time.

Before any evaluation takes place, the user_substitution_map is applied to this object, and the result is stored in the internal variable function.

During evaluation, the symbolic_coordinate, the symbolic_time, and any remaining symbols are substituted with the input evaluation point, the current time, and the content of additional_function_arguments.

Definition at line 368 of file symbolic_function.h.

◆ user_substitution_map

template<int dim, typename RangeNumberType = double>

Differentiation::SD::types::substitution_map Functions::SymbolicFunction< dim, RangeNumberType >::user_substitution_map

private

Store the user substitution map used for expression substitutions. This may be updated with a call to update_user_substitution_map(). Notice that the function may still have unresolved symbols, provided that they are resolved by a call to set_additional_function_arguments().

Definition at line 376 of file symbolic_function.h.

◆ additional_function_arguments

template<int dim, typename RangeNumberType = double>

Differentiation::SD::types::substitution_map Functions::SymbolicFunction< dim, RangeNumberType >::additional_function_arguments

private

Store a user substitution map used for additional argument substitutions. This will be updated by a call to set_additional_function_arguments().

Definition at line 383 of file symbolic_function.h.

◆ function

template<int dim, typename RangeNumberType = double>

std::vector<Differentiation::SD::Expression> Functions::SymbolicFunction< dim, RangeNumberType >::function

mutableprivate

The actual components of this symbolic function. This is obtained from the user_function, after applying the user_substitution_map.

Definition at line 389 of file symbolic_function.h.

◆ function_gradient

template<int dim, typename RangeNumberType = double>

std::vector<Tensor<1, dim, Differentiation::SD::Expression> > Functions::SymbolicFunction< dim, RangeNumberType >::function_gradient

mutableprivate

The gradients of each component of this symbolic function. This is obtained by computing the symbolic gradient of the object function, that is, after applying the user_substitution_map to user_function.

Definition at line 397 of file symbolic_function.h.

◆ function_hessian

template<int dim, typename RangeNumberType = double>

std::vector<Tensor<2, dim, Differentiation::SD::Expression> > Functions::SymbolicFunction< dim, RangeNumberType >::function_hessian

mutableprivate

The Hessians of each component of this symbolic function. This is obtained by computing the symbolic Hessian of the object function, that is, after applying the user_substitution_map to user_function.

Definition at line 405 of file symbolic_function.h.

◆ function_laplacian

template<int dim, typename RangeNumberType = double>

std::vector<Differentiation::SD::Expression> Functions::SymbolicFunction< dim, RangeNumberType >::function_laplacian

mutableprivate

The Laplacians of each component of this symbolic function. This is obtained by computing the symbolic Laplacian of the object function, that is, after applying the user_substitution_map to user_function.

Definition at line 412 of file symbolic_function.h.

◆ coordinate_symbols

template<int dim, typename RangeNumberType = double>

Tensor<1, dim, Differentiation::SD::Expression> Functions::SymbolicFunction< dim, RangeNumberType >::coordinate_symbols

private

The coordinate symbols argument of the function.

Definition at line 417 of file symbolic_function.h.

◆ time_symbol

template<int dim, typename RangeNumberType = double>

Differentiation::SD::Expression Functions::SymbolicFunction< dim, RangeNumberType >::time_symbol

mutableprivate

The symbolic time argument of the function.

Definition at line 422 of file symbolic_function.h.

◆ dimension

template<int dim, typename RangeNumberType = double>

constexpr 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 159 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 164 of file function.h.

◆ time

template<typename Number = double>

Number FunctionTime< Number >::time

privateinherited

Store the present time.

Definition at line 113 of file function_time.h.

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

include/deal.II/base/symbolic_function.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Private Member Functions

Private Attributes

Subscriptor functionality

Detailed Description

Member Typedef Documentation

◆ time_type

Constructor & Destructor Documentation

◆ SymbolicFunction() [1/2]

◆ SymbolicFunction() [2/2]

Member Function Documentation

◆ update_user_substitution_map()

◆ set_additional_function_arguments()

◆ get_default_coordinate_symbols()

◆ get_coordinate_symbols()

◆ get_time_symbol()

◆ get_symbolic_function_expressions()

◆ get_user_substitution_map()

◆ time_derivative()

◆ value()

◆ gradient()

◆ laplacian()

◆ hessian()

◆ print()

◆ create_evaluation_substitution_map()

◆ update_values()

◆ update_first_derivatives()

◆ update_second_derivatives()

◆ vector_value()

◆ value_list()

◆ vector_value_list()

◆ vector_values()

◆ vector_gradient()

◆ gradient_list()

◆ vector_gradients()

◆ vector_gradient_list()

◆ vector_laplacian()

◆ laplacian_list()

◆ vector_laplacian_list()

◆ vector_hessian()

◆ hessian_list()

◆ vector_hessian_list()

◆ memory_consumption()

◆ get_time()

◆ set_time()

◆ advance_time()

Member Data Documentation

◆ user_function

◆ user_substitution_map

◆ additional_function_arguments

◆ function

◆ function_gradient

◆ function_hessian

◆ function_laplacian

◆ coordinate_symbols

◆ time_symbol

◆ dimension

◆ n_components

◆ time