Base class to handle Radial Basis Function with a large set of nodes. More...

Inheritance diagram for bitpit::RBFKernel:

Collaboration diagram for bitpit::RBFKernel:

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Public Member Functions
	RBFKernel ()

	RBFKernel (const RBFKernel &other)

void	activateAllNodes ()

bool	activateNode (const std::vector< int > &)

bool	activateNode (int)

int	addData ()

int	addData (const std::vector< double > &)

void	deactivateAllNodes ()

bool	deactivateNode (const std::vector< int > &)

bool	deactivateNode (int)

void	enablePolynomial (bool enable=true)

double	evalBasis (double)

double	evalBasisPair (int i, int j)

std::vector< double >	evalRBF (const std::array< double, 3 > &)

std::vector< double >	evalRBF (int jnode)

void	fitDataToNodes ()

void	fitDataToNodes (int)

int	getActiveCount ()

std::vector< int >	getActiveSet ()

int	getDataCount ()

RBFBasisFunction	getFunctionType ()

RBFMode	getMode ()

int	getPolynomialDimension ()

int	getPolynomialWeightsCount ()

double	getSupportRadius ()

double	getSupportRadius (int)

const std::vector< std::vector< double > > &	getWeights () const

int	greedy (double)

bool	isActive (int)

void	removeAllData ()

bool	removeData (int)

bool	removeData (std::vector< int > &)

void	setDataToAllNodes (int, const std::vector< double > &)

void	setDataToNode (int, const std::vector< double > &)

void	setFunction (double(&funct)(double))

void	setFunction (RBFBasisFunction)

void	setMode (RBFMode mode)

void	setSupportRadius (const std::vector< double > &)

void	setSupportRadius (double)

int	solve ()

Protected Member Functions
int	addGreedyPoint ()

double	evalError ()

int	solveLSQ ()

void	swap (RBFKernel &x) noexcept

Protected Attributes
std::vector< bool >	m_activeNodes

int	m_maxFields

int	m_nodes

std::vector< int >	m_polyActiveBasis

bool	m_polyEnabled

LinearPolynomial	m_polynomial

std::vector< std::vector< double > >	m_value

std::vector< std::vector< double > >	m_weight

Detailed Description

Base class to handle Radial Basis Function with a large set of nodes.

The class can be used in two different ways:

as interpolator, given a set of external fields
as parameterizator, directly modifying the weights of rbf kernels.

The User can switch between modes, according to its needs. Some internal methods of the class can change their behaviour according to the class mode selected. Please check documentation of each single method to appreciate the differences. Default mode of the class is the "INTERP" RBFMode:: In case of interpolation the contribution of a linear polynomial can be added to regularize the interpolation problem by enabling the polynomial usage.
The actual abstract class does not implement the type of node you want to use; it can be a 3D point or an unstructured mesh. Anyway what you have to do in deriving your own RBF class is to specify a type of node you want to use and implement an evaluator of distances node/node or anywhere point in space/node.

Definition at line 69 of file rbf.hpp.

Constructor & Destructor Documentation

◆ RBFKernel() [1/2]

bitpit::RBFKernel::RBFKernel ( )

Default constructor. RBFBasisFunction is WENDLANDC2 by default. RBFMode is INTERP, by default. Use setFunction and setMode for changing it.

Definition at line 64 of file rbf.cpp.

◆ RBFKernel() [2/2]

bitpit::RBFKernel::RBFKernel ( const RBFKernel & other )

Copy Constructor

Definition at line 87 of file rbf.cpp.

Member Function Documentation

◆ activateAllNodes()

void bitpit::RBFKernel::activateAllNodes ( )

Activate all nodes actually available in your RBFKernel node list. Supported in both modes.

Definition at line 325 of file rbf.cpp.

◆ activateNode() [1/2]

bool bitpit::RBFKernel::activateNode ( const std::vector< int > & list )

Activate a node ensamble in your RBFKernel node list. Supported in both modes.

Parameters

[in] list list of node indices to be activated

Returns: boolean, true if all nodes are activated successfully, false if at least one of them is not

Definition at line 309 of file rbf.cpp.

◆ activateNode() [2/2]

bool bitpit::RBFKernel::activateNode ( int n )

Activate a node in your RBFKernel node list. Supported in both modes.

Parameters

[in] n index of node to be activated

Returns: boolean, true if node is activated successfully, false if not

Definition at line 294 of file rbf.cpp.

◆ addData() [1/2]

int bitpit::RBFKernel::addData ( )

Increment container size for RBFKernel control data.The RBFKernel::fitDataToNodes() method is implicitly called, to ensure dimension consistency between data dimension and number of RBFKernel nodes. Use RBFKernel::setDataToAllNodes to fill them. In INTERP mode, increments and fits fields container, in PARAM mode, the weights one.

Returns: id of virtual data within the class

Examples: RBF_example_00001.cpp.

Definition at line 508 of file rbf.cpp.

◆ addData() [2/2]

int bitpit::RBFKernel::addData ( const std::vector< double > & data )

Adds data attached to RBFKernel nodes to current set, a field to be interpolated in INTERP mode, a RBFKernel weight component in PARAM mode. Note: data vector is added even if its size is different from actual number of RBFKernel nodes. To ensure consistency use fitDataToNodes() method.

Parameters

[in] data values of weight/fields for each RBFKernel node

Returns: id of data within the class

Definition at line 529 of file rbf.cpp.

◆ addGreedyPoint()

int bitpit::RBFKernel::addGreedyPoint ( )

protected

Determines which node has to be added to active set. Supported only in INTERP mode.

Returns: index with max error; if no index available, or dummy call -1 is returned

Definition at line 925 of file rbf.cpp.

◆ deactivateAllNodes()

void bitpit::RBFKernel::deactivateAllNodes ( )

Deactivate all nodes actually available in your RBFKernel node list. Supported in both modes.

Definition at line 368 of file rbf.cpp.

◆ deactivateNode() [1/2]

bool bitpit::RBFKernel::deactivateNode ( const std::vector< int > & list )

Deactivate a node ensamble in your RBFKernel node list. Supported in both modes.

Parameters

[in] list list of node indices to be deactivated

Returns: boolean, true if all nodes are deactivated successfully, false if at least one of them is not

Definition at line 352 of file rbf.cpp.

◆ deactivateNode() [2/2]

bool bitpit::RBFKernel::deactivateNode ( int n )

Deactivate a node in your RBFKernel node list. Supported in both modes.

Parameters

[in] n index of node to be dactivated

Returns: boolean, true if node is activated successfully, false if not

Definition at line 337 of file rbf.cpp.

◆ enablePolynomial()

void bitpit::RBFKernel::enablePolynomial ( bool enable = true )

Enable/disable the use of polynomial term during interpolation.

Parameters

[in] enable true/false to enable/disable polynomial usage term

Definition at line 1117 of file rbf.cpp.

◆ evalBasis()

double bitpit::RBFKernel::evalBasis ( double dist )

Evaluates the basis function. Supported in both modes

Parameters

[in] dist distance

Returns: value of basis function

Definition at line 901 of file rbf.cpp.

◆ evalBasisPair()

double bitpit::RBFKernel::evalBasisPair	(	int	i,
		int	j )

Evaluates the contribution of the node j on the value of the basis at node i

Parameters

[in]	i	point at which the basis function contribution is computed
[in]	j	point from which the basis function contribution is computed

Returns: basis function contribution from j to i

Examples: RBF_example_00001.cpp.

Definition at line 914 of file rbf.cpp.

◆ evalError()

double bitpit::RBFKernel::evalError ( )

protected

Calculates the relative error between rbf interpolation and exact values at nodes. Supported only in INTERP mode.

Returns: max error, if lesser then 0, dummy call triggered.

Definition at line 957 of file rbf.cpp.

◆ evalRBF() [1/2]

std::vector< double > bitpit::RBFKernel::evalRBF ( const std::array< double, 3 > & point )

Evaluates the RBF. Supported in both modes. Its size matches the number of fields/weights attached to RBF.

Parameters

[in] point point where to evaluate the basis

Returns: vector containing interpolated/parameterized values.

Examples: RBF_example_00001.cpp.

Definition at line 614 of file rbf.cpp.

◆ evalRBF() [2/2]

std::vector< double > bitpit::RBFKernel::evalRBF ( int jnode )

Evaluates the RBF on a target RBF node. Supported in both modes. Its size matches the number of fields/weights attached to RBF.

Parameters

[in] jnode index of the RBF node in the node list

Returns: vector containing interpolated/parameterized values.

Definition at line 655 of file rbf.cpp.

◆ fitDataToNodes() [1/2]

void bitpit::RBFKernel::fitDataToNodes ( )

Check dimensions of already available data and resize them to current RBFKernel node list dimension. The method resizes all data structures to current RBFKernel node list dimension and does not destroy any previous stored data within such dimension. Anyway, mismatches definitions could occur. Please use RBFKernel::setDataToAllNodesto load your data again. In RBFMode::PARAM mode data are meant as RBFKernel weights In RBFMode::INTERP mode data are meant as fields to be interpolated

Definition at line 873 of file rbf.cpp.

◆ fitDataToNodes() [2/2]

void bitpit::RBFKernel::fitDataToNodes ( int id )

Check dimensions id-th data and resize it to current RBFKernel node list dimension. The method resizes id-th data structure to current RBFKernel node list dimension and does not destroy any previous stored data within such dimension. Anyway, mismatches definitions could occur. Please use RBFKernel::setDataToAllNodes to load your data again. In RBFMode::PARAM mode data are meant as RBFKernel weights In RBFMode::INTERP mode data are meant as fields to be interpolated

Parameters

[in] id id of data

Definition at line 890 of file rbf.cpp.

◆ getActiveCount()

int bitpit::RBFKernel::getActiveCount ( )

Get the number of active nodes. Supported in both nodes

Returns: number of active nodes

Definition at line 245 of file rbf.cpp.

◆ getActiveSet()

std::vector< int > bitpit::RBFKernel::getActiveSet ( )

Get the indices of the active nodes. Supported in both modes.

Returns: indices of active nodes

Definition at line 259 of file rbf.cpp.

◆ getDataCount()

int bitpit::RBFKernel::getDataCount ( )

Gets the number of data set attached to RBFKernel nodes. In INTERP mode, it is the number of different field that need to be interpolated; In PARAM mode, it identifies the dimension of the weights array for each node.

Returns: number of data

Definition at line 236 of file rbf.cpp.

◆ getFunctionType()

RBFBasisFunction bitpit::RBFKernel::getFunctionType ( )

Gets the type of RBFBasisFunction linked to the class.

Returns: type of RBFBasisFunction linked

Definition at line 225 of file rbf.cpp.

◆ getMode()

RBFMode bitpit::RBFKernel::getMode ( )

Return currently usage mode of your class.

Returns: class mode

Definition at line 427 of file rbf.cpp.

◆ getPolynomialWeightsCount()

int bitpit::RBFKernel::getPolynomialWeightsCount ( )

Returns: The dimension of active polynomial terms

Definition at line 1125 of file rbf.cpp.

◆ getSupportRadius() [1/2]

double bitpit::RBFKernel::getSupportRadius ( )

Return currently set support radius used by the RBFKernel kernel functions. If functions are using a variable support radius, the radius of the first function is returned. Supported in both modes.

Returns: support radius

Definition at line 401 of file rbf.cpp.

◆ getSupportRadius() [2/2]

double bitpit::RBFKernel::getSupportRadius ( int i )

Return currently set support radius used by the ith RBFKernel kernel function. Supported in both modes. It's up to the caller to ensure the function index is valid. Invalid function indexes will lead to undefined beahviour.

Returns: support radius

Definition at line 413 of file rbf.cpp.

◆ getWeights()

const std::vector< std::vector< double > > & bitpit::RBFKernel::getWeights ( ) const

Returns the weights associated to each node.

Returns: vector containing interpolated/parameterized weights.

Definition at line 859 of file rbf.cpp.

◆ greedy()

int bitpit::RBFKernel::greedy ( double tolerance )

Determines effective set of nodes to be used using greedy algorithm and calculate weights on them. Automatically choose which set of RBFKernel nodes is active or not, according to the given tolerance. Supported ONLY in INTERP mode.

Parameters

[in] tolerance error tolerance for adding nodes

Returns: integer error flag . If 0-successfull computation and tolerance met, if 1-errors occurred, not enough nodes, if -1 dummy method call

Definition at line 804 of file rbf.cpp.

◆ isActive()

bool bitpit::RBFKernel::isActive ( int n )

Checks if a node is active. Supported in both modes.

Parameters

[in] n index of node to be checked

Returns: true if active

Definition at line 280 of file rbf.cpp.

◆ removeAllData()

void bitpit::RBFKernel::removeAllData ( )

Remove all data set in RBF list. All fields for interpolation in INTERP mode, or all RBF weights for PARAM mode

Definition at line 599 of file rbf.cpp.

◆ removeData() [1/2]

bool bitpit::RBFKernel::removeData ( int id )

Remove pre-existent data set. Data list is resized and renumbered after extraction. Remove fields to be interpolated in INTERP mode, weights component in PARAM mode.

Parameters

[in] id id of node

Returns: boolean, true if successfully extracted, false otherwise

Definition at line 547 of file rbf.cpp.

◆ removeData() [2/2]

bool bitpit::RBFKernel::removeData ( std::vector< int > & list )

Remove pre-existent set of data. RBF Data list is resized and renumbered after extraction. In PARAM mode data are meant as RBF weights In INTERP mode data are meant as fields to be interpolated

Parameters

[in] list id list of candidates to extraction

Returns: boolean, true if all data set are successfully extracted, false if any of them are not extracted

Definition at line 567 of file rbf.cpp.

◆ setDataToAllNodes()

void bitpit::RBFKernel::setDataToAllNodes	(	int	id,
		const std::vector< double > &	value )

Sets the values of a data set to all currently available nodes. In INTERP mode, set one field to all nodes In PARAM mode, set one weight array component for all nodes.

Parameters

[in]	id	id of data
[in]	value	data values

Definition at line 480 of file rbf.cpp.

◆ setDataToNode()

void bitpit::RBFKernel::setDataToNode	(	int	id,
		const std::vector< double > &	value )

Sets all the type of available data at one node. In INTERP mode, set each field value at the target node In PARAM mode, set the weight coefficient array at node

Parameters

[in]	id	id of node
[in]	value	data values to be set as RBFKernel parameters for the given node

Definition at line 448 of file rbf.cpp.

◆ setFunction() [1/2]

void bitpit::RBFKernel::setFunction ( double(&)(double) bfunc )

Sets the rbf function to a user specified function. Supported in both modes.

Parameters

[in] bfunc basis function to be used

Definition at line 215 of file rbf.cpp.

◆ setFunction() [2/2]

void bitpit::RBFKernel::setFunction ( RBFBasisFunction bfunc )

Sets the rbf function to be used. Supported in both modes.

Parameters

[in] bfunc basis function to be used

Examples: RBF_example_00001.cpp.

Definition at line 125 of file rbf.cpp.

◆ setMode()

void bitpit::RBFKernel::setMode ( RBFMode mode )

Set usage mode of your class.

Parameters

[in] mode class mode. Ref to RBFMode enum

Examples: RBF_example_00001.cpp.

Definition at line 436 of file rbf.cpp.

◆ setSupportRadius() [1/2]

void bitpit::RBFKernel::setSupportRadius ( const std::vector< double > & radius )

Set the support radius of all RBFKernel kernel functions. Supported in both modes.

Parameters

[in] radius support radius

Definition at line 389 of file rbf.cpp.

◆ setSupportRadius() [2/2]

void bitpit::RBFKernel::setSupportRadius ( double radius )

Set the support radius of all RBFKernel kernel functions. Supported in both modes.

Parameters

[in] radius support radius

Examples: RBF_example_00001.cpp.

Definition at line 379 of file rbf.cpp.

◆ solve()

int bitpit::RBFKernel::solve ( )

Calculates the RBF weights using all currently active nodes and just given target fields. Regular LU solver for linear system A*X=B is employed (LAPACKE dgesv). Supported ONLY in INTERP mode.

Returns: integer error flag . If 0-successfull computation, if 1-errors occurred, if -1 dummy method call

Definition at line 699 of file rbf.cpp.

◆ solveLSQ()

int bitpit::RBFKernel::solveLSQ ( )

protected

Calculates the RBFKernel weights using all active nodes and just given target fields. Compute weights as solution of a linear least squares problem (LAPACKE dglsd). Supported ONLY in INTERP mode.

Returns: integer error flag . If 0-successfull computation, if 1-errors occurred , -1 dummy call

Definition at line 999 of file rbf.cpp.

◆ swap()

void bitpit::RBFKernel::swap ( RBFKernel & other )

protectednoexcept

Swap method. Exchange contents of each class member with those corresponding in the argument object.

Parameters

[in] other object to be swapped

Definition at line 103 of file rbf.cpp.

Member Data Documentation

◆ m_activeNodes

std::vector<bool> bitpit::RBFKernel::m_activeNodes

protected

Vector of active/inactive node (m_activeNodes[i] = true/false -> the i-th node is used/not used during RBF evaluation).

Definition at line 104 of file rbf.hpp.

◆ m_maxFields

int bitpit::RBFKernel::m_maxFields

protected

fix the maximum number of fields that can be added to your class

Definition at line 105 of file rbf.hpp.

◆ m_nodes

int bitpit::RBFKernel::m_nodes

protected

Number of RBF nodes.

Definition at line 106 of file rbf.hpp.

◆ m_polyActiveBasis

std::vector<int> bitpit::RBFKernel::m_polyActiveBasis

protected

Active terms of linear polynomial, 0 is constant, i+1 the i-th system coordinate

Definition at line 108 of file rbf.hpp.

◆ m_polyEnabled

bool bitpit::RBFKernel::m_polyEnabled

protected

Enable/disable the use of the linear polynomial term in interpolation

Definition at line 107 of file rbf.hpp.

◆ m_polynomial

LinearPolynomial bitpit::RBFKernel::m_polynomial

protected

Linear polynomial object

Definition at line 109 of file rbf.hpp.

◆ m_value

std::vector<std::vector<double> > bitpit::RBFKernel::m_value

protected

displ value to be interpolated on RBF nodes

Definition at line 102 of file rbf.hpp.

◆ m_weight

std::vector<std::vector<double> > bitpit::RBFKernel::m_weight

protected

weight of your RBF interpolation

Definition at line 103 of file rbf.hpp.

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

src/RBF/rbf.hpp
src/RBF/rbf.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RBFKernel() [1/2]

◆ RBFKernel() [2/2]

Member Function Documentation

◆ activateAllNodes()

◆ activateNode() [1/2]

◆ activateNode() [2/2]

◆ addData() [1/2]

◆ addData() [2/2]

◆ addGreedyPoint()

◆ deactivateAllNodes()

◆ deactivateNode() [1/2]

◆ deactivateNode() [2/2]

◆ enablePolynomial()

◆ evalBasis()

◆ evalBasisPair()

◆ evalError()

◆ evalRBF() [1/2]

◆ evalRBF() [2/2]

◆ fitDataToNodes() [1/2]

◆ fitDataToNodes() [2/2]

◆ getActiveCount()

◆ getActiveSet()

◆ getDataCount()

◆ getFunctionType()

◆ getMode()

◆ getPolynomialWeightsCount()

◆ getSupportRadius() [1/2]

◆ getSupportRadius() [2/2]

◆ getWeights()

◆ greedy()

◆ isActive()

◆ removeAllData()

◆ removeData() [1/2]

◆ removeData() [2/2]

◆ setDataToAllNodes()

◆ setDataToNode()

◆ setFunction() [1/2]

◆ setFunction() [2/2]

◆ setMode()

◆ setSupportRadius() [1/2]

◆ setSupportRadius() [2/2]

◆ solve()

◆ solveLSQ()

◆ swap()

Member Data Documentation

◆ m_activeNodes

◆ m_maxFields

◆ m_nodes

◆ m_polyActiveBasis

◆ m_polyEnabled

◆ m_polynomial

◆ m_value

◆ m_weight