![]() |
Reference documentation for deal.II version 9.6.0
|
#include <deal.II/base/function_lib.h>
Public Types | |
using | time_type |
Public Member Functions | |
InterpolatedTensorProductGridData (const std::array< std::vector< double >, dim > &coordinate_values, const Table< dim, double > &data_values) | |
InterpolatedTensorProductGridData (std::array< std::vector< double >, dim > &&coordinate_values, Table< dim, double > &&data_values) | |
virtual double | value (const Point< dim > &p, const unsigned int component=0) const override |
virtual Tensor< 1, dim > | gradient (const Point< dim > &p, const unsigned int component=0) const override |
virtual std::size_t | memory_consumption () const override |
const Table< dim, double > & | get_data () 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 |
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 = dim |
Protected Member Functions | |
TableIndices< dim > | table_index_of_point (const Point< dim > &p) const |
Protected Attributes | |
const std::array< std::vector< double >, dim > | coordinate_values |
const Table< dim, double > | data_values |
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 | |
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 |
A scalar function that computes its values by (bi-, tri-)linear interpolation from a set of point data that are arranged on a possibly non-uniform tensor product mesh. In other words, considering the three-dimensional case, let there be points \(x_0,\ldots, x_{K-1}\), \(y_0,\ldots,y_{L-1}\), \(z_1,\ldots,z_{M-1}\), and data \(d_{klm}\) defined at point \((x_k,y_l,z_m)^T\), then evaluating the function at a point \(\mathbf x=(x,y,z)\) will find the box so that \(x_k\le x\le x_{k+1}, y_l\le y\le y_{l+1}, z_m\le z\le z_{m+1}\), and do a trilinear interpolation of the data on this cell. Similar operations are done in lower dimensions.
This class is most often used for either evaluating coefficients or right hand sides that are provided experimentally at a number of points inside the domain, or for comparing outputs of a solution on a finite element mesh against previously obtained data defined on a grid.
If a point is requested outside the box defined by the end points of the coordinate arrays, then the function is assumed to simply extend by constant values beyond the last data point in each coordinate direction. (The class does not throw an error if a point lies outside the box since it frequently happens that a point lies just outside the box by an amount on the order of numerical roundoff.)
This class is often used to interpolate data provided by fairly large data tables that are expensive to read from disk, and that take a large amount of memory when replicated on every process of parallel (MPI) programs.
The Table class can help with amortizing this cost by using shared memory to store the data only as often as necessary – see the documentation of the TableBase class. Once one has obtained such a Table object that uses shared memory to store the data only as often as is necessary, one has to avoid that the current class copies the table into its own member variable. Rather, it is necessary to use the move constructor of this class to take over ownership of the table and its shared memory space. This can be achieved using the following extension of the code snippet shown in the documentation of the TableBase class:
Definition at line 1452 of file function_lib.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.
Functions::InterpolatedTensorProductGridData< dim >::InterpolatedTensorProductGridData | ( | const std::array< std::vector< double >, dim > & | coordinate_values, |
const Table< dim, double > & | data_values ) |
Constructor to initialize this class instance with the data given in data_values
.
coordinate_values | An array of dim arrays. Each of the inner arrays contains the coordinate values \(x_0,\ldots, x_{K-1}\) and similarly for the other coordinate directions. These arrays need not have the same size. Obviously, we need dim such arrays for a dim-dimensional function object. The coordinate values within this array are assumed to be strictly ascending to allow for efficient lookup. |
data_values | A dim-dimensional table of data at each of the mesh points defined by the coordinate arrays above. The data passed in is copied into internal data structures. Note that the Table class has a number of conversion constructors that allow converting other data types into a table where you specify this argument. |
Definition at line 2491 of file function_lib.cc.
Functions::InterpolatedTensorProductGridData< dim >::InterpolatedTensorProductGridData | ( | std::array< std::vector< double >, dim > && | coordinate_values, |
Table< dim, double > && | data_values ) |
Like the previous constructor, but take the arguments as rvalue references and move, instead of copy the data. This is often useful in cases where the data stored in these tables is large and the information used to initialize the current object is no longer needed separately. In other words, there is no need to keep the original object from which this object could copy its information, but it might as well take over ("move") the data.
Moving data also enables using tables that are located in shared memory between multiple MPI processes, rather than copying the data from shared memory into local memory whenever one creates an InterpolatedTensorProductGridData object. See the TableBase::replicate_across_communicator() function on how to share a data set between multiple processes.
Definition at line 2518 of file function_lib.cc.
|
overridevirtual |
Compute the value of the function set by bilinear interpolation of the given data set.
p | The point at which the function is to be evaluated. |
component | The vector component. Since this function is scalar, only zero is a valid argument here. |
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 2605 of file function_lib.cc.
|
overridevirtual |
Compute the gradient of the function defined by bilinear interpolation of the given data set.
p | The point at which the function gradient is to be evaluated. |
component | The vector component. Since this function is scalar, only zero is a valid argument here. |
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 2636 of file function_lib.cc.
|
overridevirtual |
Return an estimate for the memory consumption, in bytes, of this object.
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 2583 of file function_lib.cc.
const Table< dim, double > & Functions::InterpolatedTensorProductGridData< dim >::get_data | ( | ) | const |
Return a reference to the internally stored data.
Definition at line 2596 of file function_lib.cc.
|
protected |
Find the index in the table of the rectangle containing an input point
Definition at line 2546 of file function_lib.cc.
|
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 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::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 >.
|
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::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 >.
|
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.
|
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.
|
protected |
The set of coordinate values in each of the coordinate directions.
Definition at line 1546 of file function_lib.h.
|
protected |
The data that is to be interpolated.
Definition at line 1551 of file function_lib.h.
|
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.
|
inherited |
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.