Package org.drip.spaces.rxtor1

Class NormedRxToNormedR1

java.lang.Object
org.drip.spaces.rxtor1.NormedRxToNormedR1
Direct Known Subclasses:
NormedR1ToNormedR1, NormedRdToNormedR1
public abstract class NormedRxToNormedR1
extends java.lang.Object
NormedRxToNormedR1 is the Abstract Class that exposes f : Normed Rx (x .gte. 1) To Normed R1 Function Space. 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:
  • Retrieve the Input Metric Vector Space
  • Retrieve the Output Metric Vector Space
  • Retrieve the Sample Supremum Norm
  • Retrieve the Sample Metric Norm
  • Retrieve the Sample Covering Number
  • Retrieve the Sample Supremum Covering Number
  • Retrieve the Population ESS (Essential Spectrum)
  • Retrieve the Population Metric Norm
  • Retrieve the Population Supremum Metric Norm
  • Retrieve the Population Covering Number
  • Retrieve the Population Supremum Covering Number

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 Details

    • NormedRxToNormedR1

      public NormedRxToNormedR1()

  • Method Details

    • inputMetricVectorSpace

      public abstract GeneralizedMetricVectorSpace inputMetricVectorSpace()
      Retrieve the Input Metric Vector Space
      Returns:
      The Input Metric Vector Space

    • outputMetricVectorSpace

      public abstract R1Normed outputMetricVectorSpace()
      Retrieve the Output Metric Vector Space
      Returns:
      The Output Metric Vector Space

    • sampleSupremumNorm

      public abstract double sampleSupremumNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Retrieve the Sample Supremum Norm
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Supremum Norm
      Throws:
      java.lang.Exception - Thrown if the Supremum Norm cannot be computed

    • sampleMetricNorm

      public abstract double sampleMetricNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Retrieve the Sample Metric Norm
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Sample Metric Norm cannot be computed

    • sampleCoveringNumber

      public double sampleCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover) throws java.lang.Exception
      Retrieve the Sample Covering Number
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      cover - The Cover
      Returns:
      The Sample Covering Number
      Throws:
      java.lang.Exception - Thrown if the Sample Covering Number cannot be computed

    • sampleSupremumCoveringNumber

      public double sampleSupremumCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover) throws java.lang.Exception
      Retrieve the Sample Supremum Covering Number
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      cover - The Cover
      Returns:
      The Sample Supremum Covering Number
      Throws:
      java.lang.Exception - Thrown if the Sample Covering Number cannot be computed

    • populationESS

      public abstract double populationESS() throws java.lang.Exception
      Retrieve the Population ESS (Essential Spectrum)
      Returns:
      The Population ESS (Essential Spectrum)
      Throws:
      java.lang.Exception - Thrown if the Population ESS (Essential Spectrum) cannot be computed

    • populationMetricNorm

      public abstract double populationMetricNorm() throws java.lang.Exception
      Retrieve the Population Metric Norm
      Returns:
      The Population Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Population Metric Norm cannot be computed

    • populationSupremumMetricNorm

      public double populationSupremumMetricNorm() throws java.lang.Exception
      Retrieve the Population Supremum Metric Norm
      Returns:
      The Population Supremum Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Population Supremum Metric Norm cannot be computed

    • populationCoveringNumber

      public double populationCoveringNumber​(double cover) throws java.lang.Exception
      Retrieve the Population Covering Number
      Parameters:
      cover - The Cover
      Returns:
      The Population Covering Number
      Throws:
      java.lang.Exception - Thrown if the Population Covering Number cannot be computed

    • populationSupremumCoveringNumber

      public double populationSupremumCoveringNumber​(double cover) throws java.lang.Exception
      Retrieve the Population Supremum Covering Number
      Parameters:
      cover - The Cover
      Returns:
      The Population Supremum Covering Number
      Throws:
      java.lang.Exception - Thrown if the Population Supremum Covering Number cannot be computed