sot::Shepard Class Reference

Shepard's method More...

#include <shepard.h>

Inheritance diagram for sot::Shepard:

Public Member Functions
	Shepard (int maxPoints, int dim, double p)
	Constructor. More...
int	dim () const
	Method for getting the number of dimensions. More...
int	numPoints () const
	Method for getting the current number of points. More...
vec	X (int i) const
	Method for getting current point number i (0 is the first) More...
mat	X () const
	Method for getting the current points. More...
double	fX (int i) const
	Method for getting the value of current point number i (0 is the first) More...
vec	fX () const
	Method for getting the values of the current points. More...
void	addPoint (const vec &point, double funVal)
	Method for adding a point with a known value. More...
void	addPoints (const mat &points, const vec &funVals)
	Method for adding multiple points with known values. More...
double	eval (const vec &point) const
	Method for evaluating the surrogate model at a point. More...
double	eval (const vec &point, const vec &dists) const
	Method for evaluating the surrogate at multiple points. More...
vec	evals (const mat &points) const
	Method for evaluating the surrogate at multiple points. More...
vec	evals (const mat &points, const mat &dists) const
	Method for evaluating the surrogate at multiple points. More...
vec	deriv (const vec &point) const
	Method for evaluating the kNN derivative at one point (not implemented) More...
void	reset ()
	Method for resetting the surrogate model.
void	fit ()
	Fits the interpolant (does nothing)

Protected Attributes
double	mp
double	mDistTol = 1e-10
int	mMaxPoints
int	mNumPoints
int	mDim
mat	mX
mat	mfX

Detailed Description

Shepard's method

Shepard's method, also known as Inverse Distance Weighting (IMW), assigns function values to unknown points as a weighted average of the values available at the known points. The weights are given by \( w_i(x) = \|x-x_i\|^{-p/2}\) which makes it clear that points close to \(x\) are weighted higher.

Author

David Eriksson, dme65.nosp@m.@cor.nosp@m.nell..nosp@m.edu

Constructor & Destructor Documentation

sot::Shepard::Shepard ( int  maxPoints, int  dim, double  p  )

inline

Constructor.

Parameters

maxPoints	Capacity
dim	Number of dimensions
p	Value of the exponent, 2 is a common choice

Member Function Documentation

void sot::Shepard::addPoint ( const vec &  point, double  funVal  )

inlinevirtual

Method for adding a point with a known value.

Parameters

point	Point to be added
funVal	Function value at point

Exceptions

std::logic_error

if one point is supplied or if capacity is exceeded

Implements sot::Surrogate.

void sot::Shepard::addPoints ( const mat &  points, const vec &  funVals  )

inlinevirtual

Method for adding multiple points with known values.

Parameters

points	Points to be added
funVals	Function values at the points

Exceptions

std::logic_error

if one point is supplied or if capacity is exceeded

Implements sot::Surrogate.

vec sot::Shepard::deriv ( const vec &  point ) const

inlinevirtual

Method for evaluating the kNN derivative at one point (not implemented)

Exceptions

std::logic_error

Not available for Shepard

Implements sot::Surrogate.

int sot::Shepard::dim ( ) const

inlinevirtual

Method for getting the number of dimensions.

Returns

Number of dimensions

Implements sot::Surrogate.

double sot::Shepard::eval ( const vec &  point ) const

inlinevirtual

Method for evaluating the surrogate model at a point.

Parameters

point

Point for which to evaluate the surrogate

Returns

Value of the surrogate model at the point

Implements sot::Surrogate.

double sot::Shepard::eval ( const vec &  point, const vec &  dists  ) const

inlinevirtual

Method for evaluating the surrogate at multiple points.

Parameters

point	Points for which to evaluate the surrogate model
dists	Distances between the interpolation nodes and point

Returns

Values of the surrogate model at the points

Implements sot::Surrogate.

vec sot::Shepard::evals ( const mat &  points ) const

inlinevirtual

Method for evaluating the surrogate at multiple points.

Parameters

points

Points for which to evaluate the surrogate model

Returns

Values of the surrogate model at the points

Implements sot::Surrogate.

vec sot::Shepard::evals ( const mat &  points, const mat &  dists  ) const

inlinevirtual

Method for evaluating the surrogate at multiple points.

Parameters

points	Points for which to evaluate the surrogate model
dists	Distances between the interpolation nodes and the points

Returns

Values of the surrogate model at the points

Implements sot::Surrogate.

double sot::Shepard::fX ( int  i ) const

inlinevirtual

Method for getting the value of current point number i (0 is the first)

Returns

Value of point number i

Implements sot::Surrogate.

vec sot::Shepard::fX ( ) const

inlinevirtual

Method for getting the values of the current points.

Returns

Values of current points

Implements sot::Surrogate.

int sot::Shepard::numPoints ( ) const

inlinevirtual

Method for getting the current number of points.

Returns

Current number of points

Implements sot::Surrogate.

vec sot::Shepard::X ( int  i ) const

inlinevirtual

Method for getting current point number i (0 is the first)

Returns

Point number i

Implements sot::Surrogate.

mat sot::Shepard::X ( ) const

inlinevirtual

Method for getting the current points.

Returns

Current points

Implements sot::Surrogate.

Member Data Documentation

int sot::Shepard::mDim

protected

Number of dimensions

double sot::Shepard::mDistTol = 1e-10

protected

Distance tolerance for distinguishing points

mat sot::Shepard::mfX

protected

Current point values

int sot::Shepard::mMaxPoints

protected

Capacity

int sot::Shepard::mNumPoints

protected

Current number of points

double sot::Shepard::mp

protected

Value of the exponent p

mat sot::Shepard::mX

protected

Current points

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

• include/sot_bits/shepard.h