Class RdContinuousBall

All Implemented Interfaces:
GeneralizedMetricVectorSpace, RdNormed, GeneralizedVector, RdGeneralizedVector

public class RdContinuousBall
extends RdContinuousBanach
RdContinuousBall extends the Continuous Rd Banach Space by enforcing the Closed Bounded Metric. 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:
  • Construct a Unit Radius RdContinuousBall Instance
  • RdContinuousBall Space Constructor

Module Computational Core Module
Library Statistical Learning Library
Project R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package Hilbert/Banach Normed Metric Spaces
Author:
Lakshmi Krishnamurthy
  • Constructor Details

    • RdContinuousBall

      public RdContinuousBall​(R1ContinuousVector[] r1ContinuousVectorArray, Rd rdBorelSigmaMeasure, int pNorm, double normRadius) throws java.lang.Exception
      RdContinuousBall Constructor
      Parameters:
      r1ContinuousVectorArray - Array of Continuous R1 Vector Spaces
      rdBorelSigmaMeasure - The Rd Borel Sigma Measure
      pNorm - The p-norm of the Space
      normRadius - Radius Norm of the Unit Ball
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid
  • Method Details

    • ClosedUnit

      public static final RdContinuousBall ClosedUnit​(R1ContinuousVector[] aR1CV, Rd distRd, int iPNorm)
      Construct a Unit Radius RdContinuousBall Instance
      Parameters:
      aR1CV - Array of Continuous R1 Vector Spaces
      distRd - The Rd Borel Sigma Measure
      iPNorm - The p-norm of the Space
      Returns:
      Unit Radius RdContinuousBall Instance
    • normRadius

      public double normRadius()
      Retrieve the Radius Norm
      Returns:
      The Radius Norm
    • validateInstance

      public boolean validateInstance​(double[] instanceArray)
      Description copied from class: RdAggregate
      Validate the Input Instance Array
      Specified by:
      validateInstance in interface RdGeneralizedVector
      Overrides:
      validateInstance in class RdAggregate
      Parameters:
      instanceArray - The Input Instance Array
      Returns:
      TRUE - Instance is a Valid Entry in the Space