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

Inheritance diagram for FunctionParser< dim >:

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

using	ConstMapIterator = ConstMap::iterator

Public Types inherited from AutoDerivativeFunction< dim >
enum	DifferenceFormula { Euler, UpwindEuler, FourthOrder }

Public Types inherited from Function< dim >
using	time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type

Public Types inherited from FunctionTime< Number >
using	time_type = Number

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 () override

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

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

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

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

Public Member Functions inherited from AutoDerivativeFunction< dim >
	AutoDerivativeFunction (const double h, const unsigned int n_components=1, const double initial_time=0.0)

virtual	~AutoDerivativeFunction () override=default

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

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

Public Member Functions inherited from Function< dim >
	Function (const unsigned int n_components=1, const time_type initial_time=0.0)

virtual	~Function () override=0

Function &	operator= (const Function &f)

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_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double >> &gradients) const

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

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

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

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

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

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

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

virtual SymmetricTensor< 2, dim, double >	hessian (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

Public Member Functions inherited from FunctionTime< Number >
	FunctionTime (const Number initial_time=Number(0.0))

virtual	~FunctionTime ()=default

Number	get_time () const

virtual void	set_time (const Number new_time)

virtual void	advance_time (const Number delta_t)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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 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 Public Member Functions inherited from AutoDerivativeFunction< dim >
static DifferenceFormula	get_formula_of_order (const unsigned int ord)

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

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

Private Member Functions
void	init_muparser () const

Private Attributes
Threads::ThreadLocalStorage< std::vector< double > >	vars

Threads::ThreadLocalStorage< std::vector< std::unique_ptr< mu::Parser > > >	fp

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

std::vector< std::string >	var_names

std::vector< std::string >	expressions

bool	initialized

unsigned int	n_vars

Additional Inherited Members
Public Attributes inherited from Function< dim >
const unsigned int	n_components

Static Public Attributes inherited from Function< dim >
static const unsigned int	dimension

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 http://muparser.beltoforion.de/). 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 http://muparser.beltoforion.de/ .

For a wrapper of the FunctionParser class that supports ParameterHandler, see 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,
                    true);        // This tells the parser that
                                  // it is a time-dependent function
                                  // and there is another variable
                                  // to be taken into account (t).

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);

Author: Luca Heltai, Timo Heister 2005, 2014

Definition at line 220 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 257 of file function_parser.h.

◆ ConstMapIterator

template<int dim>

using FunctionParser< dim >::ConstMapIterator = ConstMap::iterator

Iterator for the constants map. Used by the initialize() method.

Definition at line 262 of file function_parser.h.

Constructor & Destructor Documentation

◆ FunctionParser() [1/2]

template<int dim>

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

Constructor for parsed functions. 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 55 of file function_parser.cc.

◆ FunctionParser() [2/2]

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 difference.

Definition at line 65 of file function_parser.cc.

◆ ~FunctionParser()

template<int dim>

FunctionParser< dim >::~FunctionParser ( )

overridedefault

Destructor. Explicitly delete the FunctionParser objects (there is one for each component of the function).

Member Function Documentation

◆ 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`
	)

Initialize the function. This methods accepts the following parameters:

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).

expressions: a list of strings containing the expressions that will be byte compiled by the internal parser (FunctionParser). 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.

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.

time_dependent. If this is a time dependent function, then the last variable declared in vars is assumed to be the time variable, and this->get_time() is used to initialize it when evaluating the function. Naturally the number of variables parsed by the initialize() method in this case is dim+1. The value of this parameter defaults to false, i.e. do not consider time.

Definition at line 102 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 419 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 432 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 >.

Definition at line 434 of file function_parser.cc.

◆ vector_value()

template<int dim>

void FunctionParser< 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.

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

Reimplemented from Function< dim >.

Definition at line 470 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 47 of file function_parser.cc.

◆ init_muparser()

template<int dim>

void FunctionParser< dim >::init_muparser ( ) const

private

Initialize fp and vars on the current thread. This function may only be called once per thread. A thread can test whether the function has already been called by testing whether 'fp.get().size()==0' (not initialized) or >0 (already initialized).

Definition at line 278 of file function_parser.cc.

Member Data Documentation

◆ vars

template<int dim>

Threads::ThreadLocalStorage<std::vector<double> > FunctionParser< dim >::vars

mutableprivate

Place for the variables for each thread

Definition at line 375 of file function_parser.h.

◆ fp

template<int dim>

Threads::ThreadLocalStorage<std::vector<std::unique_ptr<mu::Parser> > > FunctionParser< dim >::fp

mutableprivate

The muParser objects for each thread (and one for each component). We are storing a unique_ptr so that we don't need to include the definition of mu::Parser in this header.

Definition at line 383 of file function_parser.h.

◆ constants

template<int dim>

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

private

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

Definition at line 389 of file function_parser.h.

◆ var_names

template<int dim>

std::vector<std::string> FunctionParser< dim >::var_names

private

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

Definition at line 395 of file function_parser.h.

◆ expressions

template<int dim>

std::vector<std::string> FunctionParser< dim >::expressions

private

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

Definition at line 411 of file function_parser.h.

◆ initialized

template<int dim>

bool FunctionParser< dim >::initialized

private

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 417 of file function_parser.h.

◆ n_vars

template<int dim>

unsigned int FunctionParser< dim >::n_vars

private

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 426 of file function_parser.h.

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

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

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim> class FunctionParser< dim >

Member Typedef Documentation

◆ ConstMap

◆ ConstMapIterator

Constructor & Destructor Documentation

◆ FunctionParser() [1/2]

◆ FunctionParser() [2/2]

◆ ~FunctionParser()

Member Function Documentation

◆ initialize() [1/2]

◆ initialize() [2/2]

◆ default_variable_names()

◆ value()

◆ vector_value()

◆ get_expressions()

◆ init_muparser()

Member Data Documentation

◆ vars

◆ fp

◆ constants

◆ var_names

◆ expressions

◆ initialized

◆ n_vars

template<int dim>
class FunctionParser< dim >