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

• 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

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 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 Details

function

public RdToR1 function()

Retrieve the Underlying RdToR1 Function

Returns:

The Underlying RdToR1 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

inputMetricVectorSpace

public RdNormed inputMetricVectorSpace()

Description copied from class: NormedRxToNormedR1

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedR1

Returns:

The Input Metric Vector Space

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