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// $Id: function.h 20602 2010-02-13 17:44:17Z bangerth $
// Version: $Name$
//
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__function_h
#define __deal2__function_h
#include <base/config.h>
#include <base/exceptions.h>
#include <base/function_time.h>
#include <base/subscriptor.h>
#include <vector>
DEAL_II_NAMESPACE_OPEN
template <int dim> class Point;
template <int rank_, int dim> class Tensor;
template <int dim> class Tensor<1,dim>;
template <typename number> class Vector;
/**
* This class is a model for a general function. It serves the purpose
* of representing scalar and vector valued functions. To this end, we
* consider scalar functions as a special case of vector valued
* functions, in the former case only having a single component return
* vector. Since handling with vectors is comparatively expensive,
* functions are provided which only ask for a single component of the
* function, which is what you will usually need in case you know that
* your function is scalar-valued.
*
* Access to function objects therefore is through the following
* methods:
* @code
* // access to one component at one point
* double value (const Point<dim> &p,
* const unsigned int component = 0) const;
*
* // return all components at one point
* void vector_value (const Point<dim> &p,
* Vector<double> &value) const;
* @endcode
*
* For more efficiency, there are other functions returning one or all
* components at a list of points at once:
* @code
* // access to one component at several points
* void value_list (const std::vector<Point<dim> > &point_list,
* std::vector<double> &value_list,
* const unsigned int component = 0) const;
*
* // return all components at several points
* void vector_value_list (const std::vector<Point<dim> > &point_list,
* std::vector<Vector<double> > &value_list) const;
* @endcode
*
* Furthermore, there are functions returning the gradient of the
* function at one or several points.
*
* You will usually only overload those functions you need; the
* functions returning several values at a time (value_list(),
* vector_value_list(), and gradient analoga) will call those
* returning only one value (value(), vector_value(), and gradient
* analoga), while those ones will throw an exception when called but
* not overloaded.
*
* Note however, that the functions returning all components of the
* function at one or several points (i.e. vector_value(),
* vector_value_list()), will not call the function returning one
* component at one point repeatedly, once for each point and
* component. The reason is efficiency: this would amount to too many
* virtual function calls. If you have vector-valued functions, you
* should therefore also provide overloads of the virtual functions
* for all components at a time.
*
* Also note, that unless only called a very small number of times,
* you should overload all sets of functions (returning only one
* value, as well as those returning a whole array), since the cost of
* evaluation of a point value is often less than the virtual function
* call itself.
*
*
* Support for time dependant functions can be found in the base
* class FunctionTime.
*
* @note if the functions you are dealing with have sizes which
* are a priori known (for example, <tt>dim</tt> elements), you might
* consider using the TensorFunction class instead.
*
* @ingroup functions
* @author Wolfgang Bangerth, 1998, 1999
*/
template <int dim>
class Function : public FunctionTime,
public Subscriptor
{
public:
/**
* Export the value of the
* template parameter as a static
* member constant. Sometimes
* useful for some expression
* template programming.
*/
static const unsigned int dimension = dim;
/**
* Number of vector components.
*/
const unsigned int n_components;
/**
* Constructor. May take an
* initial value for the number
* of components (which defaults
* to one, i.e. a scalar
* function), and the time
* variable, which defaults to
* zero.
*/
Function (const unsigned int n_components = 1,
const double initial_time = 0.0);
/**
* Virtual destructor; absolutely
* necessary in this case.
*
* This destructor is declared
* pure virtual, such that
* objects of this class cannot
* be created. Since all the
* other virtual functions have a
* pseudo-implementation to avoid
* overhead in derived classes,
* this is the best place to do
* this.
*
* Nevertheless, since derived
* classes want to call the
* destructor of a base class,
* the destructor is implemented
* (despite it being pure
* virtual).
*
* Note: Compaq's cxx compiler
* does not allow defining a
* function that was declared
* pure. It simply refuses to
* instantiate the function when
* it later sees it, but also
* does not generate a respective
* function itself, which then
* leads to linker errors
* claiming that the destructor
* of this class is missing. We
* therefore only make the
* function abstract if the
* compiler can handle this.
*/
virtual ~Function ()
#ifndef DEAL_II_IMPLEMENTED_PURE_FUNCTION_BUG
= 0
#endif
;
/**
* Assignment operator. This is
* here only so that you can have
* objects of derived classes in
* containers, or assign them
* otherwise. It will raise an
* exception if the object from
* which you assign has a
* different number of components
* than the one being assigned
* to.
*/
Function & operator= (const Function &f);
/**
* 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 a
* given point.
*
* <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;
/**
* Set <tt>values</tt> to the point
* values of the specified
* component of the function at
* the <tt>points</tt>. It is assumed
* that <tt>values</tt> already has the
* right size, i.e. the same
* size as the <tt>points</tt> array.
*
* Be default, this function
* repeatedly calls value() for
* each point separately, to
* fill the output array.
*/
virtual void value_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component = 0) const;
/**
* Set <tt>values</tt> to the point
* values of the function at the
* <tt>points</tt>. It is assumed that
* <tt>values</tt> already has the right
* size, i.e. the same size as
* the <tt>points</tt> array, and that
* all elements be vectors with
* the same number of components
* as this function has.
*
* Be default, this function
* repeatedly calls vector_value() for
* each point separately, to
* fill the output array.
*/
virtual void vector_value_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
/**
* Return the gradient of the
* specified component of the
* function at the given point.
*/
virtual Tensor<1,dim> gradient (const Point<dim> &p,
const unsigned int component = 0) const;
/**
* Return the gradient of all
* components of the
* function at the given point.
*/
virtual void vector_gradient (const Point<dim> &p,
std::vector<Tensor<1,dim> > &gradients) const;
/**
* Set <tt>gradients</tt> to the
* gradients of the specified
* component of the function at
* the <tt>points</tt>. It is assumed
* that <tt>gradients</tt> already has the
* right size, i.e. the same
* size as the <tt>points</tt> array.
*/
virtual void gradient_list (const std::vector<Point<dim> > &points,
std::vector<Tensor<1,dim> > &gradients,
const unsigned int component = 0) const;
/**
* Set <tt>gradients</tt> to the gradients of
* the function at the <tt>points</tt>,
* for all components.
* It is assumed that <tt>gradients</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt> array.
*
* The outer loop over
* <tt>gradients</tt> is over the points
* in the list, the inner loop
* over the different components
* of the function.
*/
virtual void vector_gradient_list (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const;
/**
* Compute the Laplacian of a
* given component at point <tt>p</tt>.
*/
virtual double laplacian (const Point<dim> &p,
const unsigned int component = 0) const;
/**
* Compute the Laplacian of all
* components at point <tt>p</tt> and
* store them in <tt>values</tt>.
*/
virtual void vector_laplacian (const Point<dim> &p,
Vector<double> &values) const;
/**
* Compute the Laplacian of one
* component at a set of points.
*/
virtual void laplacian_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component = 0) const;
/**
* Compute the Laplacians of all
* components at a set of points.
*/
virtual void vector_laplacian_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
/**
* Determine an estimate for
* the memory consumption (in
* bytes) of this
* object. Since sometimes
* the size of objects can
* not be determined exactly
* (for example: what is the
* memory consumption of an
* STL <tt>std::map</tt> type with a
* certain number of
* elements?), this is only
* an estimate. however often
* quite close to the true
* value.
*/
unsigned int memory_consumption () const;
};
/**
* Provide a function which always returns zero. Obviously, also the
* derivates of this function are zero. Also, it returns zero on all
* components in case the function is not a scalar one, which can be
* obtained by passing the constructor the appropriate number of
* components.
*
* This function is of use when you want to implement homogeneous boundary
* conditions, or zero initial conditions.
*
* @ingroup functions
* @author Wolfgang Bangerth, 1998, 1999
*/
template <int dim>
class ZeroFunction : public Function<dim>
{
public:
/**
* Constructor. The number of
* components is preset to one.
*/
ZeroFunction (const unsigned int n_components = 1);
/**
* Virtual destructor; absolutely
* necessary in this case.
*/
virtual ~ZeroFunction ();
/**
* Return the value of the function
* at the given point for one
* component.
*/
virtual double value (const Point<dim> &p,
const unsigned int component) const;
/**
* Return the value of the function
* at the given point for all
* components.
*/
virtual void vector_value (const Point<dim> &p,
Vector<double> &return_value) const;
/**
* Set <tt>values</tt> to the point values
* of the function at the <tt>points</tt>,
* for the given component.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt>
* array.
*/
virtual void value_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component = 0) const;
/**
* Set <tt>values</tt> to the point values
* of the function at the <tt>points</tt>,
* for all components.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt>
* array.
*/
virtual void vector_value_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
/**
* Return the gradient of the function
* at the given point, for the
* given component.
*/
virtual Tensor<1,dim> gradient (const Point<dim> &p,
const unsigned int component = 0) const;
/**
* Return the gradient of the
* specified component of the
* function at the given point,
* for all components.
*/
virtual void vector_gradient (const Point<dim> &p,
std::vector<Tensor<1,dim> > &gradients) const;
/**
* Set <tt>gradients</tt> to the gradients of
* the function at the <tt>points</tt>,
* for the given component.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt> array.
*/
virtual void gradient_list (const std::vector<Point<dim> > &points,
std::vector<Tensor<1,dim> > &gradients,
const unsigned int component = 0) const;
/**
* Set <tt>gradients</tt> to the gradients of
* the function at the <tt>points</tt>,
* for all components.
* It is assumed that <tt>gradients</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt> array.
*
* The outer loop over
* <tt>gradients</tt> is over the points
* in the list, the inner loop
* over the different components
* of the function.
*/
virtual void vector_gradient_list (const std::vector<Point<dim> > &points,
std::vector<std::vector<Tensor<1,dim> > > &gradients) const;
};
/**
* Provide a function which always returns the constant value
* handed to the constructor.
*
* Obviously, the derivates of this
* function are zero, which is why we derive this class from
* <tt>ZeroFunction</tt>: we then only have to overload the value functions,
* not all the derivatives. In some way, it would be more obvious to
* do the derivation in the opposite direction, i.e. let
* <tt>ZeroFunction</tt> be a more specialized version of <tt>ConstantFunction</tt>;
* however, this would be less efficient, since we could not make
* use of the fact that the function value of the <tt>ZeroFunction</tt> is
* known at compile time and need not be looked up somewhere in
* memory.
*
* You can pass to the constructor an integer denoting the number of
* components this function shall have. It defaults to one. If it is
* greater than one, then the function will return the constant value
* in all its components, which might not be overly useful a feature
* in most cases, however.
*
* @ingroup functions
* @author Wolfgang Bangerth, 1998, 1999
*/
template <int dim>
class ConstantFunction : public ZeroFunction<dim>
{
public:
/**
* Constructor; takes the constant function
* value as an argument. The number of
* components is preset to one.
*/
ConstantFunction (const double value,
const unsigned int n_components = 1);
/**
* Virtual destructor; absolutely
* necessary in this case.
*/
virtual ~ConstantFunction ();
/**
* Return the value of the function
* at the given point for one
* component.
*/
virtual double value (const Point<dim> &p,
const unsigned int component) const;
/**
* Return the value of the function
* at the given point for all
* components.
*/
virtual void vector_value (const Point<dim> &p,
Vector<double> &return_value) const;
/**
* Set <tt>values</tt> to the point values
* of the function at the <tt>points</tt>,
* for the given component.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt>
* array.
*/
virtual void value_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component = 0) const;
/**
* Set <tt>values</tt> to the point values
* of the function at the <tt>points</tt>,
* for all components.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt>
* array.
*/
virtual void vector_value_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
/**
* Determine an estimate for
* the memory consumption (in
* bytes) of this
* object. Since sometimes
* the size of objects can
* not be determined exactly
* (for example: what is the
* memory consumption of an
* STL <tt>std::map</tt> type with a
* certain number of
* elements?), this is only
* an estimate. however often
* quite close to the true
* value.
*/
unsigned int memory_consumption () const;
protected:
/**
* Store the constant function value.
*/
const double function_value;
};
/**
* This is a constant vector-valued function, in which one or more
* components of the vector have a constant value and all other
* components are zero. It is especially useful as a weight function
* for <tt>VectorTools::integrate_difference</tt>, where it allows to
* integrate only one or a few vector components, rather than the
* entire vector-valued solution. See the step-20
* tutorial program for a detailed explanation.
*
* @ingroup functions
* @author Guido Kanschat, 2000, Wolfgang Bangerth 2006
*/
template <int dim>
class ComponentSelectFunction : public ConstantFunction<dim>
{
public:
/**
* Constructor if only a single
* component shall be
* non-zero. Arguments denote the
* component selected, the value
* for that component and the
* total number of vector
* components.
*/
ComponentSelectFunction (const unsigned int selected,
const double value,
const unsigned int n_components);
/**
* Constructor. As before, but
* the value for the selected
* component is assumed to be
* one. In essence, this function
* then works as a mask.
*/
ComponentSelectFunction (const unsigned int selected,
const unsigned int n_components);
/**
* Constructor if multiple
* components shall have
* non-zero, unit values
* (i.e. this should be a mask
* for multiple components). The
* first argument denotes a
* half-open interval of
* components (for example
* std::pair(0,dim) for the first
* dim components), and the
* second argument is the total
* number of vector components.
*/
ComponentSelectFunction (const std::pair<unsigned int, unsigned int> &selected,
const unsigned int n_components);
/**
* Return the value of the function
* at the given point for all
* components.
*/
virtual void vector_value (const Point<dim> &p,
Vector<double> &return_value) const;
/**
* Set <tt>values</tt> to the point values
* of the function at the <tt>points</tt>,
* for all components.
* It is assumed that <tt>values</tt>
* already has the right size, i.e.
* the same size as the <tt>points</tt>
* array.
*/
virtual void vector_value_list (const std::vector<Point<dim> > &points,
std::vector<Vector<double> > &values) const;
/**
* Determine an estimate for
* the memory consumption (in
* bytes) of this
* object. Since sometimes
* the size of objects can
* not be determined exactly
* (for example: what is the
* memory consumption of an
* STL <tt>std::map</tt> type with a
* certain number of
* elements?), this is only
* an estimate. however often
* quite close to the true
* value.
*/
unsigned int memory_consumption () const;
protected:
/**
* Half-open interval of the
* indices of selected
* components.
*/
const std::pair<unsigned int,unsigned int> selected_components;
};
DEAL_II_NAMESPACE_CLOSE
#endif
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