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

Inheritance diagram for Functions::InterpolatedTensorProductGridData< dim >:

Public Types
using	time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::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)

Public Attributes
const unsigned int	n_components

Static Public Attributes
static const 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 Attributes
numbers::NumberTraits< double >::real_type	time

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

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

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

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

void	check_no_subscribers () const noexcept

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.

Dealing with large data sets

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:

const unsigned int N=..., M=...;     // table sizes, assumed known
Table<2,double>    data_table;
const unsigned int root_rank = 0;
 
if (Utilities::MPI::this_mpi_process(mpi_communicator) == root_rank)
{
  data_table.resize (N,M);
 
  std::ifstream input_file ("data_file.dat");
  ...;                               // read the data from the file
}
 
// Now distribute to all processes
data_table.replicate_across_communicator (mpi_communicator, root_rank);
 
// Set up the x- and y-coordinates of the points stored in the
// data table
std::array<std::vector<double>, dim> coordinate_values;
...;                                 // do what needs to be done
 
// And finally set up the interpolation object. The calls
// to std::move() make sure that the tables are moved into
// the memory space of the InterpolateTensorProductGridData
// object:
InterpolatedTensorProductGridData<2>
      interpolation_function (std::move(coordinate_values),
                              std::move(data_table));

Definition at line 1453 of file function_lib.h.

Member Typedef Documentation

◆ time_type

template<int dim, typename RangeNumberType = double>

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

inherited

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

Constructor & Destructor Documentation

◆ InterpolatedTensorProductGridData() [1/2]

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 2492 of file function_lib.cc.

◆ InterpolatedTensorProductGridData() [2/2]

template<int dim>

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.

Definition at line 2519 of file function_lib.cc.

Member Function Documentation

◆ 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, RangeNumberType >.

Definition at line 2606 of file function_lib.cc.

◆ gradient()

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, RangeNumberType >.

Definition at line 2637 of file function_lib.cc.

◆ memory_consumption()

template<int dim>

std::size_t Functions::InterpolatedTensorProductGridData< dim >::memory_consumption

overridevirtual

Return an estimate for the memory consumption, in bytes, of this object.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 2584 of file function_lib.cc.

◆ get_data()

template<int dim>

const Table< dim, double > & Functions::InterpolatedTensorProductGridData< dim >::get_data

Return a reference to the internally stored data.

Definition at line 2597 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 2547 of file function_lib.cc.

◆ vector_value()

template<int dim, typename RangeNumberType = double>

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

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ value_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::value_list	(	const std::vector< Point< dim > > &	points,
		std::vector< RangeNumberType > &	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.

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ vector_value_list()

template<int dim, typename RangeNumberType = double>

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

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ vector_values()

template<int dim, typename RangeNumberType = double>

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

◆ vector_gradient()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ gradient_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::gradient_list	(	const std::vector< Point< dim > > &	points,
		std::vector< Tensor< 1, dim, RangeNumberType > > &	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.

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ vector_gradients()

template<int dim, typename RangeNumberType = double>

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

◆ vector_gradient_list()

template<int dim, typename RangeNumberType = double>

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

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ laplacian()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

Compute the Laplacian of a given component at point p.

◆ vector_laplacian()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ laplacian_list()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ vector_laplacian_list()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

Reimplemented in Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ hessian()

template<int dim, typename RangeNumberType = double>

virtual SymmetricTensor< 2, dim, RangeNumberType > Function< dim, RangeNumberType >::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::LevelSet::Plane< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::CosineFunction< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::CoordinateRestriction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, and Functions::LevelSet::Sphere< dim >.

◆ vector_hessian()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

◆ hessian_list()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

◆ vector_hessian_list()

template<int dim, typename RangeNumberType = double>

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

virtualinherited

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

◆ get_time()

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::get_time ( ) const

inherited

Return the value of the time variable.

◆ set_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::set_time ( const numbers::NumberTraits< double >::real_type new_time )

virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::advance_time ( const numbers::NumberTraits< double >::real_type delta_t )

virtualinherited

Advance the time by the given time step delta_t.

Member Data Documentation

◆ coordinate_values

template<int dim>

const std::array<std::vector<double>, dim> Functions::InterpolatedTensorProductGridData< dim >::coordinate_values

protected

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

Definition at line 1540 of file function_lib.h.

◆ data_values

template<int dim>

const Table<dim, double> Functions::InterpolatedTensorProductGridData< dim >::data_values

protected

The data that is to be interpolated.

Definition at line 1545 of file function_lib.h.

◆ dimension

template<int dim, typename RangeNumberType = double>

const unsigned int Function< dim, RangeNumberType >::dimension = dim

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

template<int dim, typename RangeNumberType = double>

const unsigned int Function< dim, RangeNumberType >::n_components

inherited

Number of vector components.

Definition at line 164 of file function.h.

◆ time

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::time

privateinherited

Store the present time.

Definition at line 113 of file function_time.h.

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

include/deal.II/base/function_lib.h
source/base/function_lib.cc

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Subscriptor functionality

Detailed Description

Dealing with large data sets

Member Typedef Documentation

◆ time_type

Constructor & Destructor Documentation

◆ InterpolatedTensorProductGridData() [1/2]

◆ InterpolatedTensorProductGridData() [2/2]

Member Function Documentation

◆ value()

◆ gradient()

◆ memory_consumption()

◆ get_data()

◆ table_index_of_point()

◆ vector_value()

◆ value_list()

◆ vector_value_list()

◆ vector_values()

◆ vector_gradient()

◆ gradient_list()

◆ vector_gradients()

◆ vector_gradient_list()

◆ laplacian()

◆ vector_laplacian()

◆ laplacian_list()

◆ vector_laplacian_list()

◆ hessian()

◆ vector_hessian()

◆ hessian_list()

◆ vector_hessian_list()

◆ get_time()

◆ set_time()

◆ advance_time()

Member Data Documentation

◆ coordinate_values

◆ data_values

◆ dimension

◆ n_components

◆ time