Package org.drip.spaces.rxtor1

Class NormedR1ToNormedR1

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedR1ToNormedR1

Direct Known Subclasses:

NormedR1CombinatorialToR1Continuous, NormedR1ContinuousToR1Continuous

public abstract class NormedR1ToNormedR1
extends NormedRxToNormedR1

NormedR1ToNormedR1 is the Abstract Class underlying the f : Validated Normed R¹ 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 R1ToR1 Function
• Retrieve the Sample Supremum Norm
• Retrieve the Sample Metric Norm
• Retrieve the Population ESS (Essential Spectrum)
• Retrieve the Output Metric Vector Space
• Retrieve the Input 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
R1ToR1	function()	Retrieve the Underlying R1ToR1 Function
R1Normed	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 R1ToR1 function()

Retrieve the Underlying R1ToR1 Function

Returns:

The Underlying R1ToR1 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

outputMetricVectorSpace

public R1Normed outputMetricVectorSpace()

Retrieve the Output Metric Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Output Metric Vector Space

inputMetricVectorSpace

public R1Normed inputMetricVectorSpace()

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Input Metric Vector Space