FunctionParser< dim > Class Template Reference

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

Inheritance diagram for FunctionParser< dim >:

Public Types
using	ConstMap = std::map< std::string, double >
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< numbers::NumberTraits< double >::real_type >
using	time_type = numbers::NumberTraits< double >::real_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
virtual	~FunctionParser () override
FunctionParser &	operator= (const FunctionParser &)=delete
FunctionParser &	operator= (FunctionParser &&)=delete
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)
	Function (const Function &f)=default
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< numbers::NumberTraits< double >::real_type >
	FunctionTime (const numbers::NumberTraits< double >::real_type initial_time=numbers::NumberTraits< double >::real_type(0.0))
virtual	~FunctionTime ()=default
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)
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 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.

Author

Luca Heltai, Timo Heister 2005, 2014

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 285 of file function_parser.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 45 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 55 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.

~FunctionParser()

template<int dim>

FunctionParser< dim >::~FunctionParser ( )

overridevirtualdefault

Destructor.

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
	)

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.

Definition at line 94 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 261 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 455 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 276 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 311 of file function_parser.cc.

get_expressions()

template<int dim>

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

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

Definition at line 37 of file function_parser.cc.

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

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