Package org.drip.spaces.functionclass

Class NormedRxToNormedR1Finite

java.lang.Object
org.drip.spaces.functionclass.NormedRxToNormedRxFinite
org.drip.spaces.functionclass.NormedRxToNormedR1Finite
Direct Known Subclasses:
NormedR1ToNormedR1Finite, NormedRdToNormedR1Finite
public class NormedRxToNormedR1Finite
extends NormedRxToNormedRxFinite
NormedRxToNormedR1Finite implements the Class F with f E f : Normed Rx To Normed R1 Space of Finite Functions. 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 Array of Function Spaces in the Class
  • Estimate for the Function Class Population Covering Number
  • Estimate for the Function Class Population Supremum Covering Number
  • Estimate for the Scale-Sensitive Sample Covering Number for the specified Cover Size
  • Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size

Module Computational Core Module
Library Statistical Learning Library
Project R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package Normed Finite Spaces Function Class
Author:
Lakshmi Krishnamurthy

  • Method Details

    • agnosticCoveringNumberBounds

      public FunctionClassCoveringBounds agnosticCoveringNumberBounds()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Agnostic Covering Number Upper/Lower Bounds for the Function Class
      Specified by:
      agnosticCoveringNumberBounds in class NormedRxToNormedRxFinite
      Returns:
      The Agnostic Covering Number Upper/Lower Bounds for the Function Class

    • inputMetricVectorSpace

      public GeneralizedMetricVectorSpace inputMetricVectorSpace()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Input Vector Space
      Specified by:
      inputMetricVectorSpace in class NormedRxToNormedRxFinite
      Returns:
      The Input Vector Space

    • outputMetricVectorSpace

      public R1Normed outputMetricVectorSpace()
      Description copied from class: NormedRxToNormedRxFinite
      Retrieve the Output Vector Space
      Specified by:
      outputMetricVectorSpace in class NormedRxToNormedRxFinite
      Returns:
      The Output Vector Space

    • functionSpaces

      public NormedRxToNormedR1[] functionSpaces()
      Retrieve the Array of Function Spaces in the Class
      Returns:
      The Array of Function Spaces in the Class

    • populationCoveringNumber

      public double populationCoveringNumber​(double cover) throws java.lang.Exception
      Estimate for the Function Class Population Covering Number
      Parameters:
      cover - The Size of the Cover
      Returns:
      Function Class Population Covering Number Estimate
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • populationSupremumCoveringNumber

      public double populationSupremumCoveringNumber​(double cover) throws java.lang.Exception
      Estimate for the Function Class Population Supremum Covering Number
      Parameters:
      cover - The Size of the Cover
      Returns:
      Function Class Population Supremum Covering Number Estimate
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • sampleCoveringNumber

      public double sampleCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover) throws java.lang.Exception
      Estimate for the Scale-Sensitive Sample Covering Number for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      cover - The Size of the Cover
      Returns:
      The Scale-Sensitive Sample Covering Number for the specified Cover Size
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • sampleSupremumCoveringNumber

      public double sampleSupremumCoveringNumber​(GeneralizedValidatedVector generalizedValidatedVector, double cover) throws java.lang.Exception
      Estimate for the Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size
      Parameters:
      generalizedValidatedVector - The Validated Instance Vector Sequence
      cover - The Size of the Cover
      Returns:
      The Scale-Sensitive Sample Supremum Covering Number for the specified Cover Size
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • operatorPopulationMetricNorm

      public double operatorPopulationMetricNorm() throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Population Metric Norm
      Specified by:
      operatorPopulationMetricNorm in class NormedRxToNormedRxFinite
      Returns:
      The Operator Population Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Norm cannot be computed

    • operatorPopulationSupremumNorm

      public double operatorPopulationSupremumNorm() throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Population Supremum Norm
      Specified by:
      operatorPopulationSupremumNorm in class NormedRxToNormedRxFinite
      Returns:
      The Operator Population Supremum Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Population Supremum Norm cannot be computed

    • operatorSampleMetricNorm

      public double operatorSampleMetricNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Sample Metric Norm
      Specified by:
      operatorSampleMetricNorm in class NormedRxToNormedRxFinite
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Operator Sample Metric Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Norm cannot be computed

    • operatorSampleSupremumNorm

      public double operatorSampleSupremumNorm​(GeneralizedValidatedVector generalizedValidatedVector) throws java.lang.Exception
      Description copied from class: NormedRxToNormedRxFinite
      Compute the Operator Sample Supremum Norm
      Specified by:
      operatorSampleSupremumNorm in class NormedRxToNormedRxFinite
      Parameters:
      generalizedValidatedVector - The Validated Vector Space Instance
      Returns:
      The Operator Sample Supremum Norm
      Throws:
      java.lang.Exception - Thrown if the Operator Sample Supremum Norm cannot be computed