Reference documentation for deal.II version Git 1dafe5d 2017-11-23 14:01:03 +0100
Public Types | Public Member Functions | Static Public Member Functions | Private Attributes | List of all members
AutoDerivativeFunction< dim > Class Template Reference

#include <deal.II/base/auto_derivative_function.h>

Inheritance diagram for AutoDerivativeFunction< dim >:
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Public Types

enum  DifferenceFormula { Euler, UpwindEuler, FourthOrder }
 

Public Member Functions

 AutoDerivativeFunction (const double h, const unsigned int n_components=1, const double initial_time=0.0)
 
virtual ~AutoDerivativeFunction ()=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
 
virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim > > &gradients) const
 
virtual void gradient_list (const std::vector< Point< dim > > &points, std::vector< Tensor< 1, dim > > &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
 
- Public Member Functions inherited from Function< dim >
 Function (const unsigned int n_components=1, const doubleinitial_time=0.0)
 
virtual ~Function ()=0
 
Functionoperator= (const Function &f)
 
virtual double value (const Point< dim > &p, const unsigned int component=0) const
 
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 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
 
std::size_t memory_consumption () const
 
- Public Member Functions inherited from FunctionTime< Number >
 FunctionTime (const Number initial_time=Number(0.0))
 
virtual ~FunctionTime ()=default
 
Number get_time () const
 
virtual void set_time (const Number new_time)
 
virtual void advance_time (const Number delta_t)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=nullptr) const
 
void unsubscribe (const char *identifier=nullptr) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Static Public Member Functions

static DifferenceFormula get_formula_of_order (const unsigned int ord)
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 

Private Attributes

double h
 
std::vector< Tensor< 1, dim > > ht
 
DifferenceFormula formula
 

Additional Inherited Members

- Public Attributes inherited from Function< dim >
const unsigned int n_components
 
- Static Public Attributes inherited from Function< dim >
static const unsigned int dimension
 

Detailed Description

template<int dim>
class AutoDerivativeFunction< dim >

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.

class UserFunction: public AutoDerivativeFunction
{ // access to one component at one point
double value (const Point<dim> &p, const
unsigned int component = 0) const
{ // Implementation .... };
} user_function;
// gradient by employing difference quotients.
Tensor<1,dim> grad=user_function.gradient(some_point);

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.

Author
Ralf Hartmann, 2001

Definition at line 76 of file auto_derivative_function.h.

Constructor & Destructor Documentation

template<int dim>
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 26 of file auto_derivative_function.cc.

template<int dim>
virtual AutoDerivativeFunction< dim >::~AutoDerivativeFunction ( )
virtualdefault

Virtual destructor; absolutely necessary in this case.

Member Function Documentation

template<int dim>
void AutoDerivativeFunction< dim >::set_formula ( const DifferenceFormula  formula = Euler)

Choose the difference formula. See the enum DifferenceFormula for available choices.

Definition at line 43 of file auto_derivative_function.cc.

template<int dim>
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.

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

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 >.

Definition at line 74 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
virtual

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

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 128 of file auto_derivative_function.cc.

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
virtual

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

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 266 of file auto_derivative_function.cc.

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

Return a DifferenceFormula of the order ord at minimum.

Definition at line 332 of file auto_derivative_function.cc.

Member Data Documentation

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

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

Definition at line 213 of file auto_derivative_function.h.

template<int dim>
std::vector<Tensor<1,dim> > AutoDerivativeFunction< dim >::ht
private

Includes the unit vectors scaled by h.

Definition at line 218 of file auto_derivative_function.h.

template<int dim>
DifferenceFormula AutoDerivativeFunction< dim >::formula
private

Difference formula. Set by the set_formula() function.

Definition at line 223 of file auto_derivative_function.h.


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