Package org.drip.spaces.metric

Class RdBall

java.lang.Object

org.drip.spaces.tensor.RdAggregate

org.drip.spaces.tensor.RdContinuousVector

org.drip.spaces.metric.RdBanach

org.drip.spaces.metric.RdBall

All Implemented Interfaces:

GeneralizedMetricVectorSpace, RdNormed, GeneralizedVector, RdGeneralizedVector

public class RdBall
extends RdBanach

RdBall extends the Continuous R^d 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 Unit Radius RdBall Instance
• RdBall Space Constructor

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
RdBall(R1ContinuousVector[] r1ContinuousVectorArray, RdContinuous rdBorelSigmaMeasure, int pNorm, double normRadius)	RdBall Constructor

Method Summary

Modifier and Type	Method	Description
static RdBall	ClosedUnit(R1ContinuousVector[] aR1CV, RdContinuous distRd, int iPNorm)	Construct a Unit Radius RdBall Instance
double	normRadius()	Retrieve the Radius Norm
boolean	validateInstance(double[] instanceArray)	Validate the Input Instance Array

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

borelMeasureSpaceExpectation, borelSigmaMeasure, pNorm, populationMetricNorm, populationMode, populationSupremumNorm, sampleMetricNorm, sampleSupremumNorm, StandardBanach, SupremumBanach

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

cardinality, hyperVolume, leftDimensionEdge, leftEdge, rightDimensionEdge, rightEdge, Standard

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

dimension, isPredictorBounded, match, subset, vectorSpaces

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

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

dimension, leftDimensionEdge, rightDimensionEdge, vectorSpaces

Constructor Details

RdBall

public RdBall(R1ContinuousVector[] r1ContinuousVectorArray,
RdContinuous rdBorelSigmaMeasure,
int pNorm,
double normRadius)
       throws java.lang.Exception

RdBall Constructor

Parameters:

r1ContinuousVectorArray - Array of Continuous R¹ Vector Spaces

rdBorelSigmaMeasure - The R^d 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 RdBall ClosedUnit(R1ContinuousVector[] aR1CV,
RdContinuous distRd,
int iPNorm)

Construct a Unit Radius RdBall Instance

Parameters:

aR1CV - Array of Continuous R¹ Vector Spaces

distRd - The R^d Borel Sigma Measure

iPNorm - The p-norm of the Space

Returns:

Unit Radius RdBall Instance

normRadius

public double normRadius()

Retrieve the Radius Norm

Returns:

The Radius Norm

validateInstance

public boolean validateInstance(double[] instanceArray)

Description copied from class: RdAggregate

Validate the Input Instance Array

Specified by:

validateInstance in interface RdGeneralizedVector

Overrides:

validateInstance in class RdAggregate

Parameters:

instanceArray - The Input Instance Array

Returns:

TRUE - Instance is a Valid Entry in the Space