Package org.drip.spaces.metric

Class R1CombinatorialBall

java.lang.Object

org.drip.spaces.tensor.R1CombinatorialVector

org.drip.spaces.metric.R1Combinatorial

org.drip.spaces.metric.R1CombinatorialBall

All Implemented Interfaces:

GeneralizedMetricVectorSpace, R1Normed, GeneralizedVector, R1GeneralizedVector

public class R1CombinatorialBall
extends R1Combinatorial

R1CombinatorialBall extends the Combinatorial R¹ Banach 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 R1CombinatorialBall Instance of Unit Radius
• R1CombinatorialBall 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
R1CombinatorialBall(java.util.List<java.lang.Double> elementSpaceList, R1Univariate r1Distribution, int pNorm, double normRadius)	R1CombinatorialBall Constructor

Method Summary

Modifier and Type	Method	Description
static R1CombinatorialBall	ClosedUnit(java.util.List<java.lang.Double> lsElementSpace, R1Univariate distR1, int iPNorm)	Construct a R1CombinatorialBall Instance of Unit Radius
double	normRadius()	Retrieve the Radius Norm
boolean	validateInstance(double instance)	Validate the Input Instance Ordinate

Methods inherited from class org.drip.spaces.metric.R1Combinatorial

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

Methods inherited from class org.drip.spaces.tensor.R1CombinatorialVector

cardinality, elementSpace, hyperVolume, isPredictorBounded, leftEdge, match, rightEdge, 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

R1CombinatorialBall

public R1CombinatorialBall(java.util.List<java.lang.Double> elementSpaceList,
R1Univariate r1Distribution,
int pNorm,
double normRadius)
                    throws java.lang.Exception

R1CombinatorialBall Constructor

Parameters:

elementSpaceList - The List Space of Elements

r1Distribution - 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 R1CombinatorialBall ClosedUnit(java.util.List<java.lang.Double> lsElementSpace,
R1Univariate distR1,
int iPNorm)

Construct a R1CombinatorialBall Instance of Unit Radius

Parameters:

lsElementSpace - The List Space of Elements

distR1 - The R¹ Borel Sigma Measure

iPNorm - The p-norm of the Space

Returns:

R1CombinatorialBall 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: R1CombinatorialVector

Validate the Input Instance Ordinate

Specified by:

validateInstance in interface R1GeneralizedVector

Overrides:

validateInstance in class R1CombinatorialVector

Parameters:

instance - The Input Instance Ordinate

Returns:

TRUE - Instance Ordinate is a Valid Entry in the Space