Reference documentation for deal.II version 9.2.0
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#include <deal.II/base/function_lib.h>
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 override |
virtual Tensor< 1, dim > | gradient (const Point< dim > &p, const unsigned int component=0) const override |
Public Member Functions inherited from Function< dim > | |
Function (const unsigned int n_components=1, const time_type initial_time=0.0) | |
Function (const Function &f)=default | |
virtual | ~Function () override=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 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< numbers::NumberTraits< double >::real_type > | |
FunctionTime (const numbers::NumberTraits< double >::real_type initial_time=numbers::NumberTraits< double >::real_type(0.0)) | |
virtual | ~FunctionTime ()=default |
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 Member Functions inherited from Subscriptor | |
Subscriptor () | |
Subscriptor (const Subscriptor &) | |
Subscriptor (Subscriptor &&) noexcept | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
Subscriptor & | operator= (Subscriptor &&) noexcept |
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) |
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 | |
Public Types inherited from Function< dim > | |
using | time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type |
Public Types inherited from FunctionTime< numbers::NumberTraits< double >::real_type > | |
using | time_type = numbers::NumberTraits< double >::real_type |
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 |
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.
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.)
Definition at line 1530 of file function_lib.h.
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
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 2603 of file function_lib.cc.
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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 >.
Definition at line 2627 of file function_lib.cc.
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overridevirtual |
Compute the gradient 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 >.
Definition at line 2676 of file function_lib.cc.
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private |
The set of interval endpoints in each of the coordinate directions.
Definition at line 1584 of file function_lib.h.
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private |
The number of subintervals in each of the coordinate directions.
Definition at line 1589 of file function_lib.h.
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private |
The data that is to be interpolated.
Definition at line 1594 of file function_lib.h.