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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/auto_derivative_function.h>
Public Types | |
enum | DifferenceFormula { Euler , UpwindEuler , FourthOrder } |
using | time_type |
Public Member Functions | |
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 |
virtual RangeNumberType | value (const Point< dim > &p, const unsigned int component=0) 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_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, RangeNumberType > > &gradients, const unsigned int component=0) const |
virtual void | vector_gradients (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const |
virtual void | vector_gradient_list (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 DifferenceFormula | get_formula_of_order (const unsigned int ord) |
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 = dim |
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 |
Static Private Attributes | |
static std::mutex | mutex |
This class automatically computes the gradient of a function by employing numerical difference quotients. This only, if the user function does not provide the gradient function himself.
The following example of an user defined function overloads and implements only the value() function but not the gradient() function. If the gradient() function is invoked then the gradient function implemented by the AutoDerivativeFunction is called, where the latter function employs numerical difference quotients.
If the user overloads and implements also the gradient function, then, of course, the users gradient function is called.
Note, that the usage of the value() and gradient() functions explained above, also applies to the value_list() and gradient_list() functions as well as to the vector valued versions of these functions, see e.g. vector_value(), vector_gradient(), vector_value_list() and vector_gradient_list().
The gradient() and gradient_list() functions make use of the Function::value() function. The vector_gradient() and vector_gradient_list() make use of the Function::vector_value() function. Make sure that the user defined function implements the value() function and the vector_value() function, respectively.
Furthermore note, that an object of this class does not represent the derivative of a function, like FunctionDerivative, that gives a directional derivative by calling the value() function. In fact, this class (the AutoDerivativeFunction class) can substitute the Function class as base class for user defined classes. This class implements the gradient() functions for automatic computation of numerical difference quotients and serves as intermediate class between the base Function class and the user defined function class.
Definition at line 81 of file auto_derivative_function.h.
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inherited |
The scalar-valued real type used for representing time.
Definition at line 168 of file function.h.
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
enum AutoDerivativeFunction::DifferenceFormula |
Names of difference formulas.
Definition at line 87 of file auto_derivative_function.h.
AutoDerivativeFunction< dim >::AutoDerivativeFunction | ( | const double | h, |
const unsigned int | n_components = 1, | ||
const double | initial_time = 0.0 ) |
Constructor. 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 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.
h
can be changed later using the set_h() function.
Sets DifferenceFormula formula
to the default Euler
formula of the set_formula() function. Change this preset formula by calling the set_formula() function.
Definition at line 25 of file auto_derivative_function.cc.
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overridevirtualdefault |
Virtual destructor; absolutely necessary in this case.
void AutoDerivativeFunction< dim >::set_formula | ( | const DifferenceFormula | formula = Euler | ) |
Choose the difference formula. See the enum DifferenceFormula for available choices.
Definition at line 42 of file auto_derivative_function.cc.
void AutoDerivativeFunction< dim >::set_h | ( | const double | h | ) |
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 64 of file auto_derivative_function.cc.
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overridevirtual |
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 74 of file auto_derivative_function.cc.
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overridevirtual |
Return the gradient of all components of the function at the given point.
Compute numerical difference quotients using the preset DifferenceFormula.
Definition at line 126 of file auto_derivative_function.cc.
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overridevirtual |
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 203 of file auto_derivative_function.cc.
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overridevirtual |
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 267 of file auto_derivative_function.cc.
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static |
Return a DifferenceFormula of the order ord
at minimum.
Definition at line 335 of file auto_derivative_function.cc.
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virtualinherited |
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 in FunctionDerivative< dim >, FunctionFromFunctionObjects< dim, RangeNumberType >, FunctionParser< dim >, Functions::Bessel1< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CoordinateRestriction< dim >, Functions::CosineFunction< dim >, Functions::CosineGradFunction< dim >, Functions::CSpline< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionCinfty< dim >, Functions::CutOffFunctionLinfty< dim >, Functions::CutOffFunctionTensorProduct< dim >, Functions::CutOffFunctionW1< dim >, Functions::ExpFunction< dim >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, Functions::FourierCosineFunction< dim >, Functions::FourierCosineSum< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::IncrementalFunction< dim, RangeNumberType >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::JumpFunction< dim >, Functions::Monomial< dim, Number >, Functions::ParsedFunction< dim >, Functions::PillowFunction< dim >, Functions::Polynomial< dim >, Functions::Q1WedgeFunction< dim >, Functions::SignedDistance::Ellipsoid< dim >, Functions::SignedDistance::Plane< dim >, Functions::SignedDistance::Rectangle< dim >, Functions::SignedDistance::Sphere< dim >, Functions::SignedDistance::ZalesakDisk< dim >, Functions::SlitSingularityFunction< dim >, Functions::Spherical< dim >, Functions::SquareFunction< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, NonMatching::internal::DiscreteQuadratureGeneratorImplementation::RefSpaceFEFieldFunction< dim, VectorType >, ScalarFunctionFromFunctionObject< dim, RangeNumberType >, VectorFunctionFromScalarFunctionObject< dim, RangeNumberType >, and VectorFunctionFromTensorFunction< dim, RangeNumberType >.
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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 >.
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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 >.
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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 >.
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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.
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virtualinherited |
Return the gradient of all components of the function at the given point.
Reimplemented in Functions::ConstantFunction< dim, double >.
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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 >.
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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.
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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 >.
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virtualinherited |
Compute the Laplacian of a given component at point p
.
Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CosineFunction< dim >, Functions::CosineGradFunction< dim >, Functions::CSpline< dim >, Functions::ExpFunction< dim >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::FourierCosineFunction< dim >, Functions::FourierCosineSum< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::JumpFunction< dim >, Functions::PillowFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::SquareFunction< dim >, and Functions::SymbolicFunction< dim, RangeNumberType >.
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virtualinherited |
Compute the Laplacian of all components at point p
and store them in values
.
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virtualinherited |
Compute the Laplacian of one component at a set of points.
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virtualinherited |
Compute the Laplacians of all components at a set of points.
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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::CoordinateRestriction< dim >, Functions::CosineFunction< dim >, Functions::CSpline< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::SignedDistance::Plane< dim >, Functions::SignedDistance::Sphere< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, and NonMatching::internal::DiscreteQuadratureGeneratorImplementation::RefSpaceFEFieldFunction< dim, VectorType >.
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virtualinherited |
Compute the Hessian of all components at point p
and store them in values
.
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virtualinherited |
Compute the Hessian of one component at a set of points.
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virtualinherited |
Compute the Hessians of all components at a set of points.
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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 >, FunctionDerivative< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::CSpline< dim >, Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::JumpFunction< dim >, Functions::Polynomial< dim >, and Functions::Spherical< dim >.
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inherited |
Return the value of the time variable.
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virtualinherited |
Set the time to new_time
, overwriting the old value.
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virtualinherited |
Advance the time by the given time step delta_t
.
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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.
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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.
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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.
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inlineinherited |
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.
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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.
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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.
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private |
Step size of the difference formula. Set by the set_h() function.
Definition at line 222 of file auto_derivative_function.h.
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private |
Includes the unit vectors scaled by h
.
Definition at line 227 of file auto_derivative_function.h.
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private |
Difference formula. Set by the set_formula() function.
Definition at line 232 of file auto_derivative_function.h.
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staticconstexprinherited |
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.
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inherited |
Number of vector components.
Definition at line 163 of file function.h.
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privateinherited |
Store the present time.
Definition at line 112 of file function_time.h.
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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.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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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.
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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.
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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.