Reference documentation for deal.II version Git 040c6ad7d4 2020-09-26 18:01:03 +0200
Functions::InterpolatedTensorProductGridData< dim > Class Template Reference

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

Inheritance diagram for Functions::InterpolatedTensorProductGridData< dim >:
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## Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type

## Public Member Functions

InterpolatedTensorProductGridData (const std::array< std::vector< double >, dim > &coordinate_values, const 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 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, doublehessian (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

Number get_time () const

virtual void set_time (const Number new_time)

virtual void advance_time (const Number 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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Public Attributes

const unsigned int n_components

## Static Public Attributes

static const unsigned int dimension

## 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, doubledata_values

## Detailed Description

### template<int dim> class Functions::InterpolatedTensorProductGridData< dim >

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.

Note
If the points $$x_i$$ are actually equally spaced on an interval $$[x_0,x_1]$$ and the same is true for the other data points in higher dimensions, you should use the InterpolatedUniformGridData class instead.

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.)

Note
The use of the related class InterpolatedUniformGridData is discussed in step-53.

Definition at line 1386 of file function_lib.h.

## ◆ time_type

 using Function< dim, double >::time_type = typename FunctionTime< typename numbers::NumberTraits::real_type>::time_type
inherited

The scalar-valued real type used for representing time.

Definition at line 170 of file function.h.

## ◆ InterpolatedTensorProductGridData()

template<int dim>
 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.

Parameters
 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 2478 of file function_lib.cc.

## ◆ value()

template<int dim>
 double Functions::InterpolatedTensorProductGridData< dim >::value ( const Point< dim > & p, const unsigned int component = 0 ) const
overridevirtual

Compute the value of the function set by bilinear interpolation of the given data set.

Parameters
 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.
Returns
The interpolated value at this point. If the point lies outside the set of coordinates, the function is extended by a constant.

Reimplemented from Function< dim >.

Definition at line 2543 of file function_lib.cc.

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

Compute the gradient of the function defined by bilinear interpolation of the given data set.

Parameters
 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.
Returns
The value of the gradient of the interpolated function at this point. If the point lies outside the set of coordinates, the function is extended by a constant and so its gradient is extended by 0.

Reimplemented from Function< dim >.

Definition at line 2574 of file function_lib.cc.

## ◆ table_index_of_point()

template<int dim>
 TableIndices< dim > Functions::InterpolatedTensorProductGridData< dim >::table_index_of_point ( const Point< dim > & p ) const
protected

Find the index in the table of the rectangle containing an input point

Definition at line 2506 of file function_lib.cc.

## ◆ vector_value()

 virtual void Function< dim, double >::vector_value ( const Point< dim > & p, Vector< double > & values ) const
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.

## ◆ value_list()

 virtual void Function< dim, double >::value_list ( const std::vector< Point< dim >> & points, std::vector< double > & values, const unsigned int component = 0 ) const
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.

## ◆ vector_value_list()

 virtual void Function< dim, double >::vector_value_list ( const std::vector< Point< dim >> & points, std::vector< Vector< double >> & values ) const
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.

## ◆ vector_values()

 virtual void Function< dim, double >::vector_values ( const std::vector< Point< dim >> & points, std::vector< std::vector< double >> & values ) const
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.

 virtual void Function< dim, double >::vector_gradient ( const Point< dim > & p, std::vector< Tensor< 1, dim, double >> & gradients ) const
virtualinherited

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

 virtual void Function< dim, double >::gradient_list ( const std::vector< Point< dim >> & points, std::vector< Tensor< 1, dim, double >> & gradients, const unsigned int component = 0 ) const
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.

 virtual void Function< dim, double >::vector_gradients ( const std::vector< Point< dim >> & points, std::vector< std::vector< Tensor< 1, dim, double >>> & gradients ) const
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.

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

## ◆ laplacian()

 virtual double Function< dim, double >::laplacian ( const Point< dim > & p, const unsigned int component = 0 ) const
virtualinherited

Compute the Laplacian of a given component at point p.

## ◆ vector_laplacian()

 virtual void Function< dim, double >::vector_laplacian ( const Point< dim > & p, Vector< double > & values ) const
virtualinherited

Compute the Laplacian of all components at point p and store them in values.

## ◆ laplacian_list()

 virtual void Function< dim, double >::laplacian_list ( const std::vector< Point< dim >> & points, std::vector< double > & values, const unsigned int component = 0 ) const
virtualinherited

Compute the Laplacian of one component at a set of points.

## ◆ vector_laplacian_list()

 virtual void Function< dim, double >::vector_laplacian_list ( const std::vector< Point< dim >> & points, std::vector< Vector< double >> & values ) const
virtualinherited

Compute the Laplacians of all components at a set of points.

Reimplemented in Functions::FlowFunction< dim >, and Functions::FlowFunction< 2 >.

## ◆ hessian()

 virtual SymmetricTensor<2, dim, double > Function< dim, double >::hessian ( const Point< dim > & p, const unsigned int component = 0 ) const
virtualinherited

Compute the Hessian of a given component at point p, that is the gradient of the gradient of the function.

Reimplemented in Functions::CosineFunction< dim >, Functions::CSpline< dim >, and Functions::Spherical< dim >.

## ◆ vector_hessian()

 virtual void Function< dim, double >::vector_hessian ( const Point< dim > & p, std::vector< SymmetricTensor< 2, dim, double >> & values ) const
virtualinherited

Compute the Hessian of all components at point p and store them in values.

## ◆ hessian_list()

 virtual void Function< dim, double >::hessian_list ( const std::vector< Point< dim >> & points, std::vector< SymmetricTensor< 2, dim, double >> & values, const unsigned int component = 0 ) const
virtualinherited

Compute the Hessian of one component at a set of points.

## ◆ vector_hessian_list()

 virtual void Function< dim, double >::vector_hessian_list ( const std::vector< Point< dim >> & points, std::vector< std::vector< SymmetricTensor< 2, dim, double >>> & values ) const
virtualinherited

Compute the Hessians of all components at a set of points.

## ◆ memory_consumption()

 std::size_t Function< dim, double >::memory_consumption ( ) const
inherited

Return an estimate for the memory consumption, in bytes, of this object. This is not exact (but will usually be close) because calculating the memory usage of trees (e.g., std::map) is difficult.

## ◆ get_time()

template<typename Number = double>
 Number FunctionTime< Number >::get_time ( ) const
inherited

Return the value of the time variable.

## ◆ set_time()

template<typename Number = double>
 virtual void FunctionTime< Number >::set_time ( const Number new_time )
virtualinherited

Set the time to new_time, overwriting the old value.

template<typename Number = double>
 virtual void FunctionTime< Number >::advance_time ( const Number delta_t )
virtualinherited

Advance the time by the given time step delta_t.

## ◆ subscribe()

 void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
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 136 of file subscriptor.cc.

## ◆ unsubscribe()

 void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

## ◆ n_subscriptions()

 unsigned int Subscriptor::n_subscriptions ( ) const
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.

## ◆ list_subscribers() [1/2]

template<typename StreamType >
 void Subscriptor::list_subscribers ( StreamType & stream ) const
inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

## ◆ list_subscribers() [2/2]

 void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

## ◆ serialize()

template<class Archive >
 void Subscriptor::serialize ( Archive & ar, const unsigned int version )
inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization.

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.

## ◆ coordinate_values

template<int dim>
 const std::array, dim> Functions::InterpolatedTensorProductGridData< dim >::coordinate_values
protected

The set of coordinate values in each of the coordinate directions.

Definition at line 1448 of file function_lib.h.

## ◆ data_values

template<int dim>
 const Table Functions::InterpolatedTensorProductGridData< dim >::data_values
protected

The data that is to be interpolated.

Definition at line 1453 of file function_lib.h.

## ◆ dimension

 const unsigned int Function< dim, double >::dimension
staticinherited

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 159 of file function.h.

## ◆ n_components

 const unsigned int Function< dim, double >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.

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