Package org.drip.spaces.rxtord

Class NormedRxToNormedRd

java.lang.Object
org.drip.spaces.rxtord.NormedRxToNormedRd
Direct Known Subclasses:
NormedR1ToNormedRd, NormedRdToNormedRd
public abstract class NormedRxToNormedRd
extends java.lang.Object
NormedRxToNormedRd is the Abstract Class that exposes f : Normed Rx (x .gte. 1) to Normed Rd 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 Array
  • Retrieve the Sample Metric Norm Array
  • Retrieve the Sample Covering Number Array
  • Retrieve the Sample Supremum Covering Number Array
  • Retrieve the Population ESS (Essential Spectrum) Array
  • Retrieve the Population Metric Norm Array
  • Retrieve the Population Supremum Norm Array
  • Retrieve the Population Covering Number Array
  • Retrieve the Population Supremum Covering Number 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

  • Constructor Details

    • NormedRxToNormedRd

      public NormedRxToNormedRd()

  • Method Details

    • inputMetricVectorSpace

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

    • outputMetricVectorSpace

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

    • sampleSupremumNorm

      public abstract double[] sampleSupremumNorm​(GeneralizedValidatedVector generalizedValidatedVector)
      Retrieve the Sample Supremum Norm Array
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Supremum Norm Array

    • sampleMetricNorm

      public abstract double[] sampleMetricNorm​(GeneralizedValidatedVector generalizedValidatedVector)
      Retrieve the Sample Metric Norm Array
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Sample Metric Norm Array

    • sampleCoveringNumber

      public double[] sampleCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover)
      Retrieve the Sample Covering Number Array
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      cover - The Cover
      Returns:
      The Sample Covering Number Array

    • sampleSupremumCoveringNumber

      public double[] sampleSupremumCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover)
      Retrieve the Sample Supremum Covering Number Array
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      cover - The Cover
      Returns:
      The Sample Supremum Covering Number Array

    • populationESS

      public abstract double[] populationESS()
      Retrieve the Population ESS (Essential Spectrum) Array
      Returns:
      The Population ESS (Essential Spectrum) Array

    • populationMetricNorm

      public abstract double[] populationMetricNorm()
      Retrieve the Population Metric Norm Array
      Returns:
      The Population Metric Norm Array

    • populationSupremumNorm

      public double[] populationSupremumNorm()
      Retrieve the Population Supremum Norm Array
      Returns:
      The Population Supremum Norm Array

    • populationCoveringNumber

      public double[] populationCoveringNumber​(double cover)
      Retrieve the Population Covering Number Array
      Parameters:
      cover - The Cover
      Returns:
      The Population Covering Number Array

    • populationSupremumCoveringNumber

      public double[] populationSupremumCoveringNumber​(double cover)
      Retrieve the Population Supremum Covering Number Array
      Parameters:
      cover - The Cover
      Returns:
      The Population Supremum Covering Number Array