Package org.drip.spaces.cover

Class CarlStephaniNormedBounds

java.lang.Object
org.drip.spaces.cover.CarlStephaniNormedBounds
public class CarlStephaniNormedBounds
extends java.lang.Object
CarlStephaniNormedBounds contains the Normed Bounds that result from the Convolution Product of 2 Normed Rx To Normed Rx Function Spaces. The References are:

  • Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operators in Banach Spaces Annals of the Fourier Institute 35 (3) 79-118
  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK
  • Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory ACM New York
It provides the following Functionality:
  • ZombieMatrix Constructor
  • Retrieve the Uninfected Cell Set
  • Retrieve the Row Count
  • Retrieve the Column Count
  • Compute the Period for Full Infection

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

  • Constructor Summary

    Constructors
    Constructor Description
    CarlStephaniNormedBounds​(double entropyBoundNormA, double entropyBoundNormB)
    CarlStephaniNormedBounds Constructor

  • Method Summary

    Modifier and Type Method Description
    double entropyBoundNormA()
    Retrieve the Entropy Bound using the Function Class Norm A
    double entropyBoundNormB()
    Retrieve the Entropy Bound using the Function Class Norm B
    double minimumUpperBound()
    Retrieve the Minimum Upper Entropy Bound

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • CarlStephaniNormedBounds

      public CarlStephaniNormedBounds​(double entropyBoundNormA, double entropyBoundNormB) throws java.lang.Exception
      CarlStephaniNormedBounds Constructor
      Parameters:
      entropyBoundNormA - The Entropy Bound using the Function Class Norm A
      entropyBoundNormB - The Entropy Bound using the Function Class Norm B
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • entropyBoundNormA

      public double entropyBoundNormA()
      Retrieve the Entropy Bound using the Function Class Norm A
      Returns:
      The Entropy Bound using the Function Class Norm A

    • entropyBoundNormB

      public double entropyBoundNormB()
      Retrieve the Entropy Bound using the Function Class Norm B
      Returns:
      The Entropy Bound using the Function Class Norm B

    • minimumUpperBound

      public double minimumUpperBound()
      Retrieve the Minimum Upper Entropy Bound
      Returns:
      The Minimum Upper Entropy Bound