Package org.drip.spaces.rxtor1

Class NormedR1ContinuousToR1Continuous

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedR1ToNormedR1

org.drip.spaces.rxtor1.NormedR1ContinuousToR1Continuous

Direct Known Subclasses:

RegularizerR1ContinuousToR1Continuous

public class NormedR1ContinuousToR1Continuous
extends NormedR1ToNormedR1

NormedR1ContinuousToR1Continuous implements the f : Validated Normed R¹ Continuous to Validated Normed R¹ Continuous 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:

• NormedR1ContinuousToR1Continuous Function Space Constructor
• Retrieve the Population Metric Norm

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

Constructor Summary

Constructors

Constructor	Description
NormedR1ContinuousToR1Continuous(R1Continuous r1ContinuousInput, R1Continuous r1ContinuousOutput, R1ToR1 r1ToR1Function)	NormedR1ContinuousToR1Continuous Function Space Constructor

Method Summary

Modifier and Type	Method	Description
double	populationMetricNorm()	Retrieve the Population Metric Norm

Methods inherited from class org.drip.spaces.rxtor1.NormedR1ToNormedR1

function, inputMetricVectorSpace, outputMetricVectorSpace, populationESS, sampleMetricNorm, sampleSupremumNorm

Methods inherited from class org.drip.spaces.rxtor1.NormedRxToNormedR1

populationCoveringNumber, populationSupremumCoveringNumber, populationSupremumMetricNorm, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

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

Constructor Details

NormedR1ContinuousToR1Continuous

public NormedR1ContinuousToR1Continuous(R1Continuous r1ContinuousInput,
R1Continuous r1ContinuousOutput,
R1ToR1 r1ToR1Function)
                                 throws java.lang.Exception

NormedR1ContinuousToR1Continuous Function Space Constructor

Parameters:

r1ContinuousInput - The R¹ Input Metric Vector Space

r1ContinuousOutput - The R¹ Output Metric Vector Space

r1ToR1Function - The R¹ To R¹ Function

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

populationMetricNorm

public double populationMetricNorm()
                            throws java.lang.Exception

Retrieve the Population Metric Norm

Specified by:

populationMetricNorm in class NormedRxToNormedR1

Returns:

The Population Metric Norm

Throws:

java.lang.Exception - Thrown if the Population Metric Norm cannot be computed