Reference documentation for deal.II version 9.4.1
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Functions::InterpolatedUniformGridData< dim > Class Template Reference

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

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

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

## 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)

InterpolatedUniformGridData (std::array< std::pair< double, double >, dim > &&interval_endpoints, std::array< unsigned int, dim > &&n_subintervals, 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

Number get_time () const

virtual void set_time (const Number new_time)

virtual void advance_time (const Number delta_t)

## Public Attributes

const unsigned int n_components

## Static Public Attributes

static constexpr unsigned int dimension = dim

## 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

Number time

## Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

std::atomic< unsigned intcounter

std::map< std::string, unsigned intcounter_map

std::vector< std::atomic< bool > * > validity_pointers

const std::type_info * object_info

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)

using map_value_type = decltype(counter_map)::value_type

using map_iterator = decltype(counter_map)::iterator

static std::mutex mutex

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

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

void check_no_subscribers () const noexcept

## 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.

### Dealing with large data sets

This class supports the same facilities for dealing with large data sets as the InterpolatedTensorProductGridData class. See there for more information and example codes.

Definition at line 1593 of file function_lib.h.

## ◆ time_type

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

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

## ◆ InterpolatedUniformGridData() [1/2]

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 2666 of file function_lib.cc.

## ◆ InterpolatedUniformGridData() [2/2]

template<int dim>
 Functions::InterpolatedUniformGridData< dim >::InterpolatedUniformGridData ( std::array< std::pair< double, double >, dim > && interval_endpoints, std::array< unsigned int, dim > && n_subintervals, 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 2690 of file function_lib.cc.

## ◆ value()

template<int dim>
 double Functions::InterpolatedUniformGridData< 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 2716 of file function_lib.cc.

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

Compute the gradient 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 gradient of the interpolated function at this point. If the point lies outside the set of coordinates, the function is extended by a constant whose gradient is then of course zero.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 2765 of file function_lib.cc.

## ◆ memory_consumption()

template<int dim>
 std::size_t Functions::InterpolatedUniformGridData< dim >::memory_consumption
overridevirtual

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

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 2816 of file function_lib.cc.

## ◆ get_data()

template<int dim>
 const Table< dim, double > & Functions::InterpolatedUniformGridData< dim >::get_data

Return a reference to the internally stored data.

Definition at line 2826 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.

## ◆ 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.

## ◆ 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.

## ◆ 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.

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.

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.

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.

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.

## ◆ laplacian()

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

## ◆ 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, VectorType, spacedim >.

## ◆ 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, VectorType, spacedim >.

## ◆ 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, VectorType, spacedim >.

## ◆ 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.

## ◆ 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()

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.

## ◆ interval_endpoints

template<int dim>
 const std::array, dim> Functions::InterpolatedUniformGridData< dim >::interval_endpoints
private

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

Definition at line 1673 of file function_lib.h.

## ◆ n_subintervals

template<int dim>
 const std::array Functions::InterpolatedUniformGridData< dim >::n_subintervals
private

The number of subintervals in each of the coordinate directions.

Definition at line 1678 of file function_lib.h.

## ◆ data_values

template<int dim>
 const Table Functions::InterpolatedUniformGridData< dim >::data_values
private

The data that is to be interpolated.

Definition at line 1683 of file function_lib.h.

## ◆ dimension

template<int dim, typename RangeNumberType = double>
 constexpr unsigned int Function< dim, RangeNumberType >::dimension = dim
staticconstexprinherited

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

template<typename Number = double>
 Number FunctionTime< Number >::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: