![]() |
Reference documentation for deal.II version 9.6.0
|
#include <deal.II/base/function.h>
Public Types | |
using | time_type |
Public Member Functions | |
ScalarFunctionFromFunctionObject (const std::function< RangeNumberType(const Point< dim > &)> &function_object) | |
virtual RangeNumberType | value (const Point< dim > &p, const unsigned int component=0) const override |
virtual void | vector_value (const Point< dim > &p, Vector< double > &values) const |
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 Tensor< 1, dim, double > | gradient (const Point< dim > &p, const unsigned int component=0) 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 |
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 ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Public Attributes | |
const unsigned int | n_components |
Static Public Attributes | |
static constexpr unsigned int | dimension |
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 | |
const std::function< RangeNumberType(const Point< dim > &)> | function_object |
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 |
Static Private Attributes | |
static std::mutex | mutex |
This class provides a way to convert a scalar function of the kind
into an object of type Function<dim>. Since the argument returns a scalar, the result is clearly a Function object for which function.n_components == 1
. The class works by storing a pointer to the given function and every time function.value(p,component)
is called, calls foo(p)
and returns the corresponding value. It also makes sure that component
is in fact zero, as needs be for scalar functions.
The class provides an easy way to turn a simple global function into something that has the required Function<dim> interface for operations like VectorTools::interpolate_boundary_values() etc., and thereby allows for simpler experimenting without having to write all the boiler plate code of declaring a class that is derived from Function and implementing the Function::value() function. An example of this is given in the results section of step-53.
The class gains additional expressive power because the argument it takes does not have to be a pointer to an actual function. Rather, it is a function object, i.e., it can also be the result of a lambda function or some other object that can be called with a single argument. For example, if you need a Function object that returns the norm of a point, you could write it like so:
and then pass the my_norm_object
around, or you could write it like so:
Similarly, to generate an object that computes the distance to a point q
, we could do this:
or we could write it like so:
The savings in work to write this are apparent.
Finally, these lambda functions can be used as a way to map points in different ways. As an example, let us assume that we have computed the solution to a one-dimensional problem and that that solution resides in the following variables:
We will denote this solution function described by this DoFHandler and vector object by \(u_h(x)\) where \(x\) is a vector with just one component, and consequently is not shown in boldface. Then assume that we want this \(u_h(x)\) to be used as a boundary condition for a 2d problem at the line \(y=0\). Let's say that this line corresponds to boundary indicator 123. If we say that the 2d problem is associated with
then in order to evaluate the boundary conditions for this 2d problem, we would want to call VectorTools::interpolate_boundary_values() via
The question here is what to use as the Function object that can be passed as third argument. It needs to be a Function<2> object, i.e., it receives a 2d input point and is supposed to return the value at that point. What we want it to do is to just take the \(x\) component of the input point and evaluate the 1d solution at that point, knowing that at the boundary with indicator 123, the \(y\) component of the input point must be zero. This all can be achieved via the following function object:
Definition at line 802 of file function.h.
|
inherited |
The scalar-valued real type used for representing time.
Definition at line 168 of file function.h.
|
privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
|
privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
|
explicit |
|
overridevirtual |
Return the value of the function at the given point. Returns the value the function given to the constructor produces for this point.
Reimplemented from Function< dim, double >.
|
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.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
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.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
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.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
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.
|
virtualinherited |
Return the gradient of the specified component of the function at the given point.
Reimplemented in FunctionFromFunctionObjects< dim, RangeNumberType >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::Monomial< dim, Number >, Functions::SymbolicFunction< dim, RangeNumberType >, and VectorFunctionFromTensorFunction< dim, RangeNumberType >.
|
virtualinherited |
Return the gradient of all components of the function at the given point.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
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.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
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.
|
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.
Reimplemented in Functions::ConstantFunction< dim, double >.
|
virtualinherited |
Compute the Laplacian of a given component at point p
.
Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, and Functions::SymbolicFunction< dim, RangeNumberType >.
|
virtualinherited |
Compute the Laplacian of all components at point p
and store them in values
.
|
virtualinherited |
Compute the Laplacian of one component at a set of points.
|
virtualinherited |
Compute the Laplacians of all components at a set of points.
|
virtualinherited |
Compute the Hessian of a given component at point p
, that is the gradient of the gradient of the function.
Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, and Functions::SymbolicFunction< dim, RangeNumberType >.
|
virtualinherited |
Compute the Hessian of all components at point p
and store them in values
.
|
virtualinherited |
Compute the Hessian of one component at a set of points.
|
virtualinherited |
Compute the Hessians of all components at a set of points.
|
virtualinherited |
Return an estimate for the memory consumption, in bytes, of this object.
This function is virtual and can be overloaded by derived classes.
Reimplemented in ComponentSelectFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, RangeNumberType >, and Functions::ConstantFunction< dim, double >.
|
inherited |
Return the value of the time variable.
|
virtualinherited |
Set the time to new_time
, overwriting the old value.
|
virtualinherited |
Advance the time by the given time step delta_t
.
|
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 135 of file subscriptor.cc.
|
inherited |
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
|
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.
|
inlineinherited |
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.
|
inherited |
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.
|
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.
|
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.
Definition at line 52 of file subscriptor.cc.
|
private |
The function object which we call when this class's value() or value_list() functions are called.
Definition at line 825 of file function.h.
Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.
Definition at line 158 of file function.h.
Number of vector components.
Definition at line 163 of file function.h.
|
privateinherited |
Store the present time.
Definition at line 112 of file function_time.h.
|
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 218 of file subscriptor.h.
|
mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
|
mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
|
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 248 of file subscriptor.h.
|
staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable
members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers()
.
Definition at line 271 of file subscriptor.h.