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 () |
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 |
DeclException0 (ExcInvalidFormula) | |
Static Public Member Functions | |
static DifferenceFormula | get_formula_of_order (const unsigned int ord) |
Private Attributes | |
double | h |
std::vector< Tensor< 1, dim > > | ht |
DifferenceFormula | formula |
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 imployes 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 derivate 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.
enum AutoDerivativeFunction::DifferenceFormula |
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.
virtual AutoDerivativeFunction< dim >::~AutoDerivativeFunction | ( | ) | [virtual] |
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.
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.
Reimplemented in FunctionDerivative< dim >.
virtual 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.
Computes numerical difference quotients using the preset DifferenceFormula.
Reimplemented from Function< dim >.
virtual 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.
Computes numerical difference quotients using the preset DifferenceFormula.
Reimplemented from Function< dim >.
virtual 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.
Computes numerical difference quotients using the preset DifferenceFormula.
Reimplemented from Function< dim >.
virtual 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.
Computes numerical difference quotients using the preset DifferenceFormula.
Reimplemented from Function< dim >.
static DifferenceFormula AutoDerivativeFunction< dim >::get_formula_of_order | ( | const unsigned int | ord | ) | [static] |
Returns a DifferenceFormula of the order ord
at minimum.
AutoDerivativeFunction< dim >::DeclException0 | ( | ExcInvalidFormula | ) |
Exception.
double AutoDerivativeFunction< dim >::h [private] |
Step size of the difference formula. Set by the set_h() function.
Reimplemented in FunctionDerivative< dim >.
std::vector<Tensor<1,dim> > AutoDerivativeFunction< dim >::ht [private] |
Includes the unit vectors scaled by h
.
DifferenceFormula AutoDerivativeFunction< dim >::formula [private] |
Difference formula. Set by the set_formula() function.
Reimplemented in FunctionDerivative< dim >.