Reference documentation for deal.II version GIT 9465d3a511 2022-11-30 23:00:02+00:00
FunctionParser< dim > Class Template Reference

#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 = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::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

FunctionParseroperator= (const FunctionParser &)=delete

FunctionParseroperator= (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 ::ExceptionBaseExcParseError (int arg1, std::string arg2)

static ::ExceptionBaseExcInvalidExpressionSize (int arg1, int arg2)

static DifferenceFormula get_formula_of_order (const unsigned int ord)

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Public Attributes

const unsigned int n_components

## Static Public Attributes

static 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

std::map< std::string, doubleconstants

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

atan2, log2, log10, log, ln, exp, sqrt, sign, rint, abs, min, max, sum, avg
Expression atanh(const Expression &x)
Expression atan2(const Expression &y, const Expression &x)
Expression asin(const Expression &x)
Expression asinh(const Expression &x)
Expression cosh(const Expression &x)
Expression sinh(const Expression &x)
Expression atan(const Expression &x)
Expression tanh(const Expression &x)
Expression sign(const Expression &x)
Expression acos(const Expression &x)
Expression acosh(const Expression &x)
Expression log10(const Expression &x)
T sum(const T &t, const MPI_Comm &mpi_communicator)
::VectorizedArray< Number, width > cos(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > sin(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > exp(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > log(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > tan(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > sqrt(const ::VectorizedArray< Number, width > &)

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:
fp.initialize(variables,
expression,
// 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;
LogStream deallog
Definition: logstream.cc:37
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
Definition: utilities.cc:189

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;
// 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,
// 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;
static constexpr double PI
Definition: numbers.h:248

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/.

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
// And populate it with the newly created objects.
function.initialize(variables,
expression,
// Treat the last variable ("t") as time.
true);
virtual void initialize(const std::string &vars, const std::vector< std::string > &expressions, const ConstMap &constants, const bool time_dependent=false) override

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,
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 217 of file function_parser.h.

## ◆ ConstMap

template<int dim>
 using FunctionParser< dim >::ConstMap = std::map

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

Definition at line 275 of file function_parser.h.

## ◆ time_type

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

The scalar-valued real type used for representing time.

Definition at line 169 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 230 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 235 of file subscriptor.h.

## ◆ DifferenceFormula

template<int dim>
 inherited

Names of difference formulas.

Enumerator
Euler

The symmetric Euler formula of second order:

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

UpwindEuler

The upwind Euler formula of first order:

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

FourthOrder

The fourth order scheme

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

Definition at line 88 of file auto_derivative_function.h.

## ◆ 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 39 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 47 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.

## ◆ 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 74 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 89 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 377 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 104 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 31 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 43 of file auto_derivative_function.cc.

## ◆ set_h()

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

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

Definition at line 65 of file auto_derivative_function.cc.

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

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

Compute numerical difference quotients using the preset DifferenceFormula.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 75 of file auto_derivative_function.cc.

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

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

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 127 of file auto_derivative_function.cc.

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.

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

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 204 of file auto_derivative_function.cc.

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.

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

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 268 of file auto_derivative_function.cc.

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.

## ◆ get_formula_of_order()

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

Return a DifferenceFormula of the order ord at minimum.

Definition at line 336 of file auto_derivative_function.cc.

## ◆ 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.

## ◆ 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.

## ◆ 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.

## ◆ 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.

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

## ◆ 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 >.

## ◆ 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.

## ◆ 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.

## ◆ 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 Number new_time )
virtualinherited

Set the time to new_time, overwriting the old value.

 virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::advance_time ( const Number delta_t )
virtualinherited

Advance the time by the given time step delta_t.

## ◆ subscribe()

 void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

## ◆ unsubscribe()

 void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

## ◆ n_subscriptions()

 unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

## ◆ list_subscribers() [1/2]

template<typename StreamType >
 void Subscriptor::list_subscribers ( StreamType & stream ) const
inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

## ◆ list_subscribers() [2/2]

 void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

## ◆ serialize()

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

Read or write the data of this object to or from a stream for the purpose of serialization 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 53 of file subscriptor.cc.

## ◆ init_muparser()

 void internal::FunctionParser::ParserImplementation< dim, double >::init_muparser
inherited

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

Definition at line 181 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 187 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 195 of file mu_parser_internal.cc.

## ◆ h

template<int dim>
 double AutoDerivativeFunction< dim >::h
privateinherited

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

Definition at line 223 of file auto_derivative_function.h.

## ◆ ht

template<int dim>
 std::vector > AutoDerivativeFunction< dim >::ht
privateinherited

Includes the unit vectors scaled by h.

Definition at line 228 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 233 of file auto_derivative_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

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

Store the present time.

Definition at line 113 of file function_time.h.

## ◆ counter

 std::atomic 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 219 of file subscriptor.h.

## ◆ counter_map

 std::map Subscriptor::counter_map
mutableprivateinherited

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

Definition at line 225 of file subscriptor.h.

## ◆ validity_pointers

 std::vector *> 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 241 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 249 of file subscriptor.h.

## ◆ mutex

 std::mutex Subscriptor::mutex
staticprivateinherited

A mutex used to ensure data consistency when printing out the list of subscribers.

Definition at line 271 of file subscriptor.h.

## ◆ expressions

 std::vector 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 203 of file mu_parser_internal.h.

## ◆ parser_data

 mutableprivateinherited

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

Definition at line 211 of file mu_parser_internal.h.

## ◆ constants

 std::map 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 217 of file mu_parser_internal.h.

## ◆ var_names

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

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

Definition at line 223 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 229 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 238 of file mu_parser_internal.h.

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