Package org.drip.spaces.rxtor1

Class NormedRdToNormedR1

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedRdToNormedR1

Direct Known Subclasses:

EigenFunctionRdToR1, NormedRdCombinatorialToR1Continuous, NormedRdContinuousToR1Continuous

public abstract class NormedRdToNormedR1
extends NormedRxToNormedR1

NormedRdToNormedR1 is the Abstract Class underlying the f : Validated Normed R^d To Validated Normed R¹ 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 RdToR1 Function
• Retrieve the Sample Supremum Norm
• Retrieve the Sample Metric Norm
• Retrieve the Population ESS (Essential Spectrum)
• Retrieve the Input Metric Vector Space
• Retrieve the Output Metric Vector Space

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 R1 Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
RdToR1	function()	Retrieve the Underlying RdToR1 Function
RdNormed	inputMetricVectorSpace()	Retrieve the Input Metric Vector Space
R1Normed	outputMetricVectorSpace()	Retrieve the Output Metric Vector Space
double	populationESS()	Retrieve the Population ESS (Essential Spectrum)
double	sampleMetricNorm(GeneralizedValidatedVector generalizedValidatedVector)	Retrieve the Sample Metric Norm
double	sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)	Retrieve the Sample Supremum Norm

Methods inherited from class org.drip.spaces.rxtor1.NormedRxToNormedR1

populationCoveringNumber, populationMetricNorm, populationSupremumCoveringNumber, populationSupremumMetricNorm, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

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

Method Details

function

public RdToR1 function()

Retrieve the Underlying RdToR1 Function

Returns:

The Underlying RdToR1 Function

sampleSupremumNorm

public double sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)
                          throws java.lang.Exception

Retrieve the Sample Supremum Norm

Specified by:

sampleSupremumNorm in class NormedRxToNormedR1

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm

Throws:

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

sampleMetricNorm

public double sampleMetricNorm(GeneralizedValidatedVector generalizedValidatedVector)
                        throws java.lang.Exception

Retrieve the Sample Metric Norm

Specified by:

sampleMetricNorm in class NormedRxToNormedR1

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Metric Norm

Throws:

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

populationESS

public double populationESS()
                     throws java.lang.Exception

Retrieve the Population ESS (Essential Spectrum)

Specified by:

populationESS in class NormedRxToNormedR1

Returns:

The Population ESS (Essential Spectrum)

Throws:

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

inputMetricVectorSpace

public RdNormed inputMetricVectorSpace()

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public R1Normed outputMetricVectorSpace()

Retrieve the Output Metric Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Output Metric Vector Space