Package org.drip.spaces.metric

Class RdCombinatorialHilbert

java.lang.Object

org.drip.spaces.tensor.RdAggregate

org.drip.spaces.tensor.RdCombinatorialVector

org.drip.spaces.metric.RdCombinatorialBanach

org.drip.spaces.metric.RdCombinatorialHilbert

All Implemented Interfaces:

GeneralizedMetricVectorSpace, RdNormed, GeneralizedVector, RdGeneralizedVector

public class RdCombinatorialHilbert
extends RdCombinatorialBanach

RdCombinatorialHilbert implements the Bounded/Unbounded, Combinatorial l₂ R^d Spaces. The Reference we've used is:

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

• RdCombinatorialHilbert 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
RdCombinatorialHilbert(R1CombinatorialVector[] r1CombinatorialVectorArray, Rd rdDistribution)	RdCombinatorialHilbert Space Constructor

Method Summary

Modifier and Type	Method	Description
double	sampleMetricNorm(double[] xArray)	Compute the Metric Norm of the Sample

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

borelMeasureSpaceExpectation, borelSigmaMeasure, pNorm, populationMetricNorm, populationMode, populationSupremumNorm, sampleSupremumNorm

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

cardinality, hyperVolume, iterator, leftDimensionEdge, leftEdge, rightDimensionEdge, rightEdge

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

dimension, isPredictorBounded, match, subset, validateInstance, 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, validateInstance, vectorSpaces

Constructor Details

RdCombinatorialHilbert

public RdCombinatorialHilbert(R1CombinatorialVector[] r1CombinatorialVectorArray,
Rd rdDistribution)
                       throws java.lang.Exception

RdCombinatorialHilbert Space Constructor

Parameters:

r1CombinatorialVectorArray - Array of Combinatorial R¹ Vector Spaces

rdDistribution - The R^d Borel Sigma Measure

Throws:

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

Method Details

sampleMetricNorm

public double sampleMetricNorm(double[] xArray)
                        throws java.lang.Exception

Description copied from interface: RdNormed

Compute the Metric Norm of the Sample

Specified by:

sampleMetricNorm in interface RdNormed

Overrides:

sampleMetricNorm in class RdCombinatorialBanach

Parameters:

xArray - The Sample

Returns:

The Metric Norm of the Sample

Throws:

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