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 R^1 To Validated Normed R^1 Function Spaces. The Reference we've used is: - Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators, Cambridge University Press, Cambridge UK.

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method and 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 gvvi) Retrieve the Sample Metric Norm
double	sampleSupremumNorm(GeneralizedValidatedVector gvvi) 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 Detail

function

public R1ToR1 function()

Retrieve the Underlying R1ToR1 Function

Returns:

The Underlying R1ToR1 Function

sampleSupremumNorm

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

Description copied from class: NormedRxToNormedR1

Retrieve the Sample Supremum Norm

Specified by:

sampleSupremumNorm in class NormedRxToNormedR1

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

Description copied from class: NormedRxToNormedR1

Retrieve the Sample Metric Norm

Specified by:

sampleMetricNorm in class NormedRxToNormedR1

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

populationESS

public double populationESS()
                     throws java.lang.Exception

Description copied from class: NormedRxToNormedR1

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()

Description copied from class: NormedRxToNormedR1

Retrieve the Output Metric Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Output Metric Vector Space

inputMetricVectorSpace

public R1Normed inputMetricVectorSpace()

Description copied from class: NormedRxToNormedR1

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Input Metric Vector Space