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//
// Copyright (C) 2005 - 2015 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__function_parser_h
#define dealii__function_parser_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/function.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/point.h>
#include <deal.II/base/thread_local_storage.h>
#include <vector>
#include <map>
namespace mu
{
class Parser;
}
DEAL_II_NAMESPACE_OPEN
template <typename> class Vector;
/**
* 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).
*
* The following examples shows how to use this class:
* @code
* // 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;
* @endcode
* The second example is a bit more complex:
* @code
* // 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;
* @endcode
*
* 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:
* @code
* // Empty constants object
* std::map<std::string> 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).
* @endcode
*
* The following is another example of how to instantiate a vector valued
* function by using a single string:
* @code
* // Empty constants object
* std::map<std::string> 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);
* @endcode
*
*
* @ingroup functions
* @author Luca Heltai, Timo Heister 2005, 2014
*/
template <int dim>
class FunctionParser : public Function<dim>
{
public:
/**
* Constructor for Parsed functions. Its arguments are the same of the base
* class Function. The only difference is that this object needs to be
* initialized with 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.
*/
FunctionParser (const unsigned int n_components = 1,
const double initial_time = 0.0);
/**
* Destructor. Explicitly delete the FunctionParser objects (there is one
* for each component of the function).
*/
~FunctionParser();
/**
* Type for the constant map. Used by the initialize() method.
*/
typedef std::map<std::string, double> ConstMap;
/**
* Iterator for the constants map. Used by the initialize() method.
*/
typedef ConstMap::iterator ConstMapIterator;
/**
* Initialize the function. This methods accepts the following parameters:
*
* <b>vars</b>: 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
* <tt>time_dependent</tt> 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).
*
* <b>expressions</b>: 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.
*
* <b>constants</b>: 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:
* <tt>constants["sin"] = 1.5;</tt>) an exception is thrown.
*
* <b>time_dependent</b>. If this is a time dependent function, then the
* last variable declared in <b>vars</b> 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.
*/
void initialize (const std::string &vars,
const std::vector<std::string> &expressions,
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.
*/
void initialize (const std::string &vars,
const std::string &expression,
const ConstMap &constants,
const bool time_dependent = false);
/**
* 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.
*/
static
std::string
default_variable_names ();
/**
* 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.
*/
virtual double value (const Point<dim> &p,
const unsigned int component = 0) const;
/**
* Return all components of a vector-valued function at the given point @p
* p.
*
* <tt>values</tt> shall have the right size beforehand, i.e. #n_components.
*/
virtual void vector_value (const Point<dim> &p,
Vector<double> &values) const;
/**
* @addtogroup Exceptions
* @{
*/
DeclException2 (ExcParseError,
int, char *,
<< "Parsing Error at Column " << arg1
<< ". The parser said: " << arg2);
DeclException2 (ExcInvalidExpressionSize,
int, int,
<< "The number of components (" << arg1
<< ") is not equal to the number of expressions ("
<< arg2 << ").");
//@}
private:
#ifdef DEAL_II_WITH_MUPARSER
/**
* Place for the variables for each thread
*/
mutable Threads::ThreadLocalStorage<std::vector<double> > vars;
/**
* The muParser objects for each thread (and one for each component)
*/
mutable Threads::ThreadLocalStorage<std::vector<mu::Parser> > fp;
/**
* An array to keep track of all the constants, required to initialize fp in
* each thread.
*/
std::map<std::string, double> constants;
/**
* An array for the variable names, required to initialize fp in each
* thread.
*/
std::vector<std::string> var_names;
/**
* An array of function expressions (one per component), required to
* initialize fp in each thread.
*/
std::vector<std::string> expressions;
/**
* 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).
*/
void init_muparser() const;
#endif
/**
* State of usability. This variable is checked every time the function is
* called for evaluation. It's set to true in the initialize() methods.
*/
bool initialized;
/**
* 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.
*/
unsigned int n_vars;
};
template <int dim>
std::string
FunctionParser<dim>::default_variable_names ()
{
switch (dim)
{
case 1:
return "x";
case 2:
return "x,y";
case 3:
return "x,y,z";
default:
Assert (false, ExcNotImplemented());
}
return "";
}
DEAL_II_NAMESPACE_CLOSE
#endif
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