Package org.drip.spaces.rxtord

Class NormedR1ToNormedRd

java.lang.Object

org.drip.spaces.rxtord.NormedRxToNormedRd

org.drip.spaces.rxtord.NormedR1ToNormedRd

Direct Known Subclasses:

NormedR1CombinatorialToRdContinuous, NormedR1ContinuousToRdContinuous

public abstract class NormedR1ToNormedRd
extends NormedRxToNormedRd

NormedR1ToNormedRd is the Abstract Class underlying the f : Validated Normed R¹ 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

• 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 R^d Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
R1ToRd	function()	Retrieve the Underlying R1ToRd Function
R1Normed	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[]	sampleMetricNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Metric Norm Array
double[]	sampleSupremumNorm(GeneralizedValidatedVector gvvi)	Retrieve the Sample Supremum Norm Array

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

populationCoveringNumber, populationMetricNorm, populationSupremumCoveringNumber, populationSupremumNorm, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

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

Method Details

inputMetricVectorSpace

public R1Normed inputMetricVectorSpace()

Description copied from class: NormedRxToNormedRd

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedRd

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public RdNormed outputMetricVectorSpace()

Description copied from class: NormedRxToNormedRd

Retrieve the Output Metric Vector Space

Specified by:

outputMetricVectorSpace in class NormedRxToNormedRd

Returns:

The Output Metric Vector Space

function

public R1ToRd function()

Retrieve the Underlying R1ToRd Function

Returns:

The Underlying R1ToR1 Function

sampleSupremumNorm

public double[] sampleSupremumNorm(GeneralizedValidatedVector gvvi)

Description copied from class: NormedRxToNormedRd

Retrieve the Sample Supremum Norm Array

Specified by:

sampleSupremumNorm in class NormedRxToNormedRd

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm Array

sampleMetricNorm

public double[] sampleMetricNorm(GeneralizedValidatedVector gvvi)

Description copied from class: NormedRxToNormedRd

Retrieve the Sample Metric Norm Array

Specified by:

sampleMetricNorm in class NormedRxToNormedRd

Parameters:

gvvi - The Validated Vector Space Instance

Returns:

The Sample Metric Norm Array

populationESS

public double[] populationESS()

Description copied from class: NormedRxToNormedRd

Retrieve the Population ESS (Essential Spectrum) Array

Specified by:

populationESS in class NormedRxToNormedRd

Returns:

The Population ESS (Essential Spectrum) Array