Package org.drip.spaces.rxtor1

Class NormedRxToNormedR1

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

Direct Known Subclasses:

NormedR1ToNormedR1, NormedRdToNormedR1

public abstract class NormedRxToNormedR1
extends java.lang.Object

NormedRxToNormedR1 is the Abstract Class that exposes f : Normed R^x (x .gte. 1) To Normed R¹ 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 R¹ Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
NormedRxToNormedR1()

Method Summary

Modifier and Type	Method	Description
abstract GeneralizedMetricVectorSpace	inputMetricVectorSpace()	Retrieve the Input Metric Vector Space
abstract R1Normed	outputMetricVectorSpace()	Retrieve the Output Metric Vector Space
double	populationCoveringNumber(double dblCover)	Retrieve the Population Covering Number
abstract double	populationESS()	Retrieve the Population ESS (Essential Spectrum)
abstract double	populationMetricNorm()	Retrieve the Population Metric Norm
double	populationSupremumCoveringNumber(double dblCover)	Retrieve the Population Supremum Covering Number
double	populationSupremumMetricNorm()	Retrieve the Population Supremum Metric Norm
double	sampleCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover)	Retrieve the Sample Covering Number
abstract double	sampleMetricNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Metric Norm
double	sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi, double dblCover)	Retrieve the Sample Supremum Covering Number
abstract double	sampleSupremumNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Supremum Norm

Methods inherited from class java.lang.Object

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

Constructor Details

NormedRxToNormedR1

public NormedRxToNormedR1()

Method Details

inputMetricVectorSpace

public abstract GeneralizedMetricVectorSpace inputMetricVectorSpace()

Retrieve the Input Metric Vector Space

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public abstract R1Normed outputMetricVectorSpace()

Retrieve the Output Metric Vector Space

Returns:

The Output Metric Vector Space

sampleSupremumNorm

public abstract double sampleSupremumNorm(GeneralizedValidatedVector gvvi)
                                   throws java.lang.Exception

Retrieve the Sample Supremum Norm

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm

Throws:

java.lang.Exception - Thrown if the Supremum Norm cannot be computed

sampleMetricNorm

public abstract double sampleMetricNorm(GeneralizedValidatedVector gvvi)
                                 throws java.lang.Exception

Retrieve the Sample Metric Norm

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Metric Norm

Throws:

java.lang.Exception - Thrown if the Sample Metric Norm cannot be computed

sampleCoveringNumber

public double sampleCoveringNumber(GeneralizedValidatedVector gvvi,
double dblCover)
                            throws java.lang.Exception

Retrieve the Sample Covering Number

Parameters:

gvvi - The Validated Vector Space Instance

dblCover - The Cover

Returns:

The Sample Covering Number

Throws:

java.lang.Exception - Thrown if the Sample Covering Number cannot be computed

sampleSupremumCoveringNumber

public double sampleSupremumCoveringNumber(GeneralizedValidatedVector gvvi,
double dblCover)
                                    throws java.lang.Exception

Retrieve the Sample Supremum Covering Number

Parameters:

gvvi - The Validated Vector Space Instance

dblCover - The Cover

Returns:

The Sample Supremum Covering Number

Throws:

java.lang.Exception - Thrown if the Sample Covering Number cannot be computed

populationESS

public abstract double populationESS()
                              throws java.lang.Exception

Retrieve the Population ESS (Essential Spectrum)

Returns:

The Population ESS (Essential Spectrum)

Throws:

java.lang.Exception - Thrown if the Population ESS (Essential Spectrum) cannot be computed

populationMetricNorm

public abstract double populationMetricNorm()
                                     throws java.lang.Exception

Retrieve the Population Metric Norm

Returns:

The Population Metric Norm

Throws:

java.lang.Exception - Thrown if the Population Metric Norm cannot be computed

populationSupremumMetricNorm

public double populationSupremumMetricNorm()
                                    throws java.lang.Exception

Retrieve the Population Supremum Metric Norm

Returns:

The Population Supremum Metric Norm

Throws:

java.lang.Exception - Thrown if the Population Supremum Metric Norm cannot be computed

populationCoveringNumber

public double populationCoveringNumber(double dblCover)
                                throws java.lang.Exception

Retrieve the Population Covering Number

Parameters:

dblCover - The Cover

Returns:

The Population Covering Number

Throws:

java.lang.Exception - Thrown if the Population Covering Number cannot be computed

populationSupremumCoveringNumber

public double populationSupremumCoveringNumber(double dblCover)
                                        throws java.lang.Exception

Retrieve the Population Supremum Covering Number

Parameters:

dblCover - The Cover

Returns:

The Population Supremum Covering Number

Throws:

java.lang.Exception - Thrown if the Population Supremum Covering Number cannot be computed