Package org.drip.spaces.rxtord

Class NormedRdToNormedRd

java.lang.Object

org.drip.spaces.rxtord.NormedRxToNormedRd

org.drip.spaces.rxtord.NormedRdToNormedRd

Direct Known Subclasses:

NormedRdCombinatorialToRdContinuous, NormedRdContinuousToRdContinuous

public abstract class NormedRdToNormedRd
extends NormedRxToNormedRd

NormedRdToNormedRd is the Abstract Class underlying the f : Validated Normed R^d to Validated Normed R^d Function 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

It provides the following Functionality:

• Retrieve the Underlying RdToRd Function
• Retrieve the Population R^d ESS (Essential Spectrum) Array
• Retrieve the Population R^d Supremum Norm
• Retrieve the Input Metric Vector Space
• Retrieve the Output Metric Vector Space
• Retrieve the Sample Supremum Norm Array
• Retrieve the Sample Metric Norm Array
• Retrieve the Population ESS (Essential Spectrum) Array
• Retrieve the Population Supremum Norm Array

Module	Computational Core Module
Library	Statistical Learning Library
Project	R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package	Rx To Rd Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
RdToRd	function()	Retrieve the Underlying RdToRd Function
RdNormed	inputMetricVectorSpace()	Retrieve the Input Metric Vector Space
RdNormed	outputMetricVectorSpace()	Retrieve the Output Metric Vector Space
double[]	populationESS()	Retrieve the Population ESS (Essential Spectrum) Array
double[]	populationRdESS()	Retrieve the Population Rd ESS (Essential Spectrum) Array
double[]	populationRdSupremumNorm()	Retrieve the Population Rd Supremum Norm
double[]	populationSupremumNorm()	Retrieve the Population Supremum Norm Array
double[]	sampleMetricNorm(GeneralizedValidatedVector generalizedValidatedVector)	Retrieve the Sample Metric Norm Array
double[]	sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)	Retrieve the Sample Supremum Norm Array

Methods inherited from class org.drip.spaces.rxtord.NormedRxToNormedRd

populationCoveringNumber, populationMetricNorm, populationSupremumCoveringNumber, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

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

Method Details

function

public RdToRd function()

Retrieve the Underlying RdToRd Function

Returns:

The Underlying RdToRd Function

populationRdESS

public double[] populationRdESS()

Retrieve the Population R^d ESS (Essential Spectrum) Array

Returns:

The Population R^d ESS (Essential Spectrum) Array

populationRdSupremumNorm

public double[] populationRdSupremumNorm()

Retrieve the Population R^d Supremum Norm

Returns:

The Population R^d Supremum Norm

inputMetricVectorSpace

public RdNormed inputMetricVectorSpace()

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedRd

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public RdNormed outputMetricVectorSpace()

Retrieve the Output Metric Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedRd

Returns:

The Output Metric Vector Space

sampleSupremumNorm

public double[] sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)

Retrieve the Sample Supremum Norm Array

Specified by:

sampleSupremumNorm in class NormedRxToNormedRd

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm Array

sampleMetricNorm

public double[] sampleMetricNorm(GeneralizedValidatedVector generalizedValidatedVector)

Retrieve the Sample Metric Norm Array

Specified by:

sampleMetricNorm in class NormedRxToNormedRd

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Metric Norm Array

populationESS

public double[] populationESS()

Retrieve the Population ESS (Essential Spectrum) Array

Specified by:

populationESS in class NormedRxToNormedRd

Returns:

The Population ESS (Essential Spectrum) Array

populationSupremumNorm

public double[] populationSupremumNorm()

Retrieve the Population Supremum Norm Array

Overrides:

populationSupremumNorm in class NormedRxToNormedRd

Returns:

The Population Supremum Norm Array