Package org.drip.spaces.rxtor1

Class NormedRdContinuousToR1Continuous

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedRdToNormedR1

org.drip.spaces.rxtor1.NormedRdContinuousToR1Continuous

Direct Known Subclasses:

RegularizerRdContinuousToR1Continuous

public class NormedRdContinuousToR1Continuous
extends NormedRdToNormedR1

NormedRdContinuousToR1Continuous implements the f : Validated Normed R^d 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:

• NormedRdContinuousToR1Continuous 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
NormedRdContinuousToR1Continuous(RdContinuousBanach rdContinuousBanachInput, R1Continuous r1ContinuousOutput, RdToR1 rdToR1Function)	NormedRdContinuousToR1Continuous 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.NormedRdToNormedR1

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

NormedRdContinuousToR1Continuous

public NormedRdContinuousToR1Continuous(RdContinuousBanach rdContinuousBanachInput,
R1Continuous r1ContinuousOutput,
RdToR1 rdToR1Function)
                                 throws java.lang.Exception

NormedRdContinuousToR1Continuous Function Space Constructor

Parameters:

rdContinuousBanachInput - The Continuous R^d Input Banach Metric Vector Space

r1ContinuousOutput - The Continuous R¹ Output Metric Vector Space

rdToR1Function - The R^d 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