Package org.drip.spaces.rxtord

Class NormedRxToNormedRd

java.lang.Object

org.drip.spaces.rxtord.NormedRxToNormedRd

Direct Known Subclasses:

NormedR1ToNormedRd, NormedRdToNormedRd

public abstract class NormedRxToNormedRd
extends java.lang.Object

NormedRxToNormedRd is the Abstract Class that exposes f : Normed R^x (x .gte. 1) To Normed R^d Function Space. The Reference we've used is:

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

• Module = Computational Core Module
• Library = Statistical Learning Library
• Project = R¹ and R^d Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
• Package = R^x To R^d Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
NormedRxToNormedRd()

Method Summary

Modifier and Type	Method	Description
abstract GeneralizedMetricVectorSpace	inputMetricVectorSpace()	Retrieve the Input Metric Vector Space
abstract RdNormed	outputMetricVectorSpace()	Retrieve the Output Metric Vector Space
double[]	populationCoveringNumber(double dblCover)	Retrieve the Population Covering Number Array
abstract double[]	populationESS()	Retrieve the Population ESS (Essential Spectrum) Array
abstract double[]	populationMetricNorm()	Retrieve the Population Metric Norm Array
double[]	populationSupremumCoveringNumber(double dblCover)	Retrieve the Population Supremum Covering Number Array
double[]	populationSupremumNorm()	Retrieve the Population Supremum Norm Array
double[]	sampleCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover)	Retrieve the Sample Covering Number Array
abstract double[]	sampleMetricNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Metric Norm Array
double[]	sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover)	Retrieve the Sample Supremum Covering Number Array
abstract double[]	sampleSupremumNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Supremum Norm Array

Methods inherited from class java.lang.Object

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

Constructor Details

NormedRxToNormedRd

public NormedRxToNormedRd()

Method Details

inputMetricVectorSpace

public abstract GeneralizedMetricVectorSpace inputMetricVectorSpace()

Retrieve the Input Metric Vector Space

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public abstract RdNormed outputMetricVectorSpace()

Retrieve the Output Metric Vector Space

Returns:

The Output Metric Vector Space

sampleSupremumNorm

public abstract double[] sampleSupremumNorm(GeneralizedValidatedVector gvvi)

Retrieve the Sample Supremum Norm Array

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm Array

sampleMetricNorm

public abstract double[] sampleMetricNorm(GeneralizedValidatedVector gvvi)

Retrieve the Sample Metric Norm Array

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Metric Norm Array

sampleCoveringNumber

public double[] sampleCoveringNumber(GeneralizedValidatedVector gvvi,
double dblCover)

Retrieve the Sample Covering Number Array

Parameters:

gvvi - The Validated Vector Space Instance

dblCover - The Cover

Returns:

The Sample Covering Number Array

sampleSupremumCoveringNumber

public double[] sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi,
double dblCover)

Retrieve the Sample Supremum Covering Number Array

Parameters:

gvvi - The Validated Vector Space Instance

dblCover - The Cover

Returns:

The Sample Supremum Covering Number Array

populationESS

public abstract double[] populationESS()

Retrieve the Population ESS (Essential Spectrum) Array

Returns:

The Population ESS (Essential Spectrum) Array

populationMetricNorm

public abstract double[] populationMetricNorm()

Retrieve the Population Metric Norm Array

Returns:

The Population Metric Norm Array

populationSupremumNorm

public double[] populationSupremumNorm()

Retrieve the Population Supremum Norm Array

Returns:

The Population Supremum Norm Array

populationCoveringNumber

public double[] populationCoveringNumber(double dblCover)

Retrieve the Population Covering Number Array

Parameters:

dblCover - The Cover

Returns:

The Population Covering Number Array

populationSupremumCoveringNumber

public double[] populationSupremumCoveringNumber(double dblCover)

Retrieve the Population Supremum Covering Number Array

Parameters:

dblCover - The Cover

Returns:

The Population Supremum Covering Number Array