Package org.drip.spaces.metric

Class R1Ball

java.lang.Object

org.drip.spaces.tensor.R1ContinuousVector

org.drip.spaces.metric.R1Field

org.drip.spaces.metric.R1Ball

All Implemented Interfaces:

GeneralizedMetricVectorSpace, R1Normed, GeneralizedVector, R1GeneralizedVector

public class R1Ball
extends R1Field

R1Ball extends the Continuous R¹ Space by enforcing the Closed Bounded Metric. The Reference we've used is:

• Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK

It provides the following Functionality:

• Construct a R1Ball Instance of Unit Radius
• R1Ball Constructor
• Retrieve the Radius Norm

Module	Computational Core Module
Library	Statistical Learning Library
Project	R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package	Hilbert/Banach Normed Metric Spaces

Author:

Lakshmi Krishnamurthy

Field Summary

Fields inherited from interface org.drip.spaces.metric.GeneralizedMetricVectorSpace

EUCLIDEAN_NORM, L2_NORM, LINFINITITY_NORM

Constructor Summary

Constructors

Constructor	Description
R1Ball(double leftEdge, double rightEdge, R1Continuous r1Univariate, int pNorm, double normRadius)	R1Ball Constructor

Method Summary

Modifier and Type	Method	Description
static R1Ball	ClosedUnit(double dblLeftEdge, double dblRightEdge, R1Continuous distR1, int iPNorm)	Construct a R1Ball Instance of Unit Radius
double	normRadius()	Retrieve the Radius Norm
boolean	validateInstance(double instance)	Validate the Input Instance Array

Methods inherited from class org.drip.spaces.metric.R1Field

borelMeasureSpaceExpectation, borelSigmaMeasure, pNorm, populationMetricNorm, populationMode, sampleMetricNorm, Standard, Supremum

Methods inherited from class org.drip.spaces.tensor.R1ContinuousVector

cardinality, hyperVolume, isPredictorBounded, leftEdge, match, rightEdge, Standard, subset

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.drip.spaces.tensor.GeneralizedVector

cardinality, hyperVolume, isPredictorBounded, leftEdge, match, rightEdge, subset

Constructor Details

R1Ball

public R1Ball(double leftEdge,
double rightEdge,
R1Continuous r1Univariate,
int pNorm,
double normRadius)
       throws java.lang.Exception

R1Ball Constructor

Parameters:

leftEdge - The Left Edge

rightEdge - The Right Edge

r1Univariate - The R¹ Borel Sigma Measure

pNorm - The p-norm of the Space

normRadius - Radius Norm of the Unit Ball

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

ClosedUnit

public static final R1Ball ClosedUnit(double dblLeftEdge,
double dblRightEdge,
R1Continuous distR1,
int iPNorm)

Construct a R1Ball Instance of Unit Radius

Parameters:

dblLeftEdge - The Left Edge

dblRightEdge - The Right Edge

distR1 - The R¹ Borel Sigma Measure

iPNorm - The p-norm of the Space

Returns:

R1Ball Instance of Unit Radius

normRadius

public double normRadius()

Retrieve the Radius Norm

Returns:

The Radius Norm

validateInstance

public boolean validateInstance(double instance)

Description copied from class: R1ContinuousVector

Validate the Input Instance Array

Specified by:

validateInstance in interface R1GeneralizedVector

Overrides:

validateInstance in class R1ContinuousVector

Parameters:

instance - The Input Instance Array

Returns:

TRUE - Instance is a Valid Entry in the Space