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

Inheritance diagram for Functions::InterpolatedUniformGridData< dim >:

Public Member Functions
	InterpolatedUniformGridData (const std::array< std::pair< double, double >, dim > &interval_endpoints, const std::array< unsigned int, dim > &n_subintervals, const Table< dim, double > &data_values)

virtual double	value (const Point< dim > &p, const unsigned int component=0) const

Public Member Functions inherited from Function< dim >
	Function (const unsigned int n_components=1, const double initial_time=0.0)

virtual	~Function ()=0

Function &	operator= (const Function &f)

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 Tensor< 1, dim, double >	gradient (const Point< dim > &p, const unsigned int component=0) 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 &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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)

Private Attributes
const std::array< std::pair< double, double >, dim >	interval_endpoints

const std::array< unsigned int, dim >	n_subintervals

const Table< dim, double >	data_values

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

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 Functions::InterpolatedUniformGridData< dim >

A scalar function that computes its values by (bi-, tri-)linear interpolation from a set of point data that are arranged on a uniformly spaced tensor product mesh. In other words, considering the three- dimensional case, let there be points \(x_0,\ldots, x_{K-1}\) that result from a uniform subdivision of the interval \([x_0,x_{K-1}]\) into \(K-1\) sub-intervals of size \(\Delta x = (x_{K-1}-x_0)/(K-1)\), and similarly \(y_0,\ldots,y_{L-1}\), \(z_1,\ldots,z_{M-1}\). Also consider 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 you have a problem where the points \(x_i\) are not equally spaced (e.g., they result from a computation on a graded mesh that is denser closer to one boundary), then use the InterpolatedTensorProductGridData 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 this class is discussed in step-53.

Author: Wolfgang Bangerth, 2013

Definition at line 1229 of file function_lib.h.

Constructor & Destructor Documentation

◆ InterpolatedUniformGridData()

template<int dim>

Functions::InterpolatedUniformGridData< dim >::InterpolatedUniformGridData	(	const std::array< std::pair< double, double >, dim > &	interval_endpoints,
		const std::array< unsigned int, dim > &	n_subintervals,
		const Table< dim, double > &	data_values
	)

Constructor

Parameters

interval_endpoints	The left and right end points of the (uniformly subdivided) intervals in each of the coordinate directions.
n_subintervals	The number of subintervals in each coordinate direction. A value of one for a coordinate means that the interval is considered as one subinterval consisting of the entire range. A value of two means that there are two subintervals each with one half of the range, etc.
data_values	A dim-dimensional table of data at each of the mesh points defined by the coordinate arrays above. 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 2530 of file function_lib.cc.

Member Function Documentation

◆ value()

template<int dim>

double Functions::InterpolatedUniformGridData< dim >::value	(	const Point< dim > &	p,
		const unsigned int	component = `0`
	)		const

virtual

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 2554 of file function_lib.cc.

Member Data Documentation

◆ interval_endpoints

template<int dim>

const std::array<std::pair<double,double>,dim> Functions::InterpolatedUniformGridData< dim >::interval_endpoints

private

The set of interval endpoints in each of the coordinate directions.

Definition at line 1269 of file function_lib.h.

◆ n_subintervals

template<int dim>

const std::array<unsigned int,dim> Functions::InterpolatedUniformGridData< dim >::n_subintervals

private

The number of subintervals in each of the coordinate directions.

Definition at line 1274 of file function_lib.h.

◆ data_values

template<int dim>

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

private

The data that is to be interpolated.

Definition at line 1279 of file function_lib.h.

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

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

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim> class Functions::InterpolatedUniformGridData< dim >

Constructor & Destructor Documentation

◆ InterpolatedUniformGridData()

Member Function Documentation

◆ value()

Member Data Documentation

◆ interval_endpoints

◆ n_subintervals

◆ data_values

template<int dim>
class Functions::InterpolatedUniformGridData< dim >