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

It provides the following Functionality:

• NormedR1ToNormedRd Constructor
• Retrieve the Input Metric Vector Space
• Retrieve the Output Metric Vector Space
• Retrieve the Underlying R¹ to R^d Function
• Retrieve the Sample Supremum Norm Array
• Retrieve the Sample Metric Norm Array
• Retrieve the Population ESS (Essential Spectrum) Array

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 Rd Normed Function Spaces

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
R1ToRd	function()	Retrieve the Underlying R1 to Rd 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 generalizedValidatedVector)	Retrieve the Sample Metric Norm Array
double[]	sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)	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()

Retrieve the Input Metric Vector Space

Specified by:

inputMetricVectorSpace in class NormedRxToNormedRd

Returns:

The Input Metric Vector Space

outputMetricVectorSpace

public RdNormed outputMetricVectorSpace()

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 R¹ to R^d Function

Returns:

The Underlying R¹ to R^d Function

sampleSupremumNorm

public double[] sampleSupremumNorm(GeneralizedValidatedVector generalizedValidatedVector)

Retrieve the Sample Supremum Norm Array

Specified by:

sampleSupremumNorm in class NormedRxToNormedRd

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Supremum Norm Array

sampleMetricNorm

public double[] sampleMetricNorm(GeneralizedValidatedVector generalizedValidatedVector)

Retrieve the Sample Metric Norm Array

Specified by:

sampleMetricNorm in class NormedRxToNormedRd

Parameters:

generalizedValidatedVector - The Validated Vector Space Instance

Returns:

The Sample Metric Norm Array

populationESS

public double[] populationESS()

Retrieve the Population ESS (Essential Spectrum) Array

Specified by:

populationESS in class NormedRxToNormedRd

Returns:

The Population ESS (Essential Spectrum) Array