Interface R1Normed

All Superinterfaces:
GeneralizedMetricVectorSpace, GeneralizedVector, R1GeneralizedVector
All Known Implementing Classes:
R1Combinatorial, R1CombinatorialBall, R1Continuous, R1ContinuousBall

public interface R1Normed
extends GeneralizedMetricVectorSpace, R1GeneralizedVector
R1Normed Abstract Class implements the Normed, Bounded/Unbounded Continuous/Combinatorial lp Rd Spaces. 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 Borel Sigma R1 Probability Measure
  • Compute the Metric Norm of the Sample
  • Retrieve the Population Mode
  • Compute the Borel Measure Expectation for the specified R1 To R1 Function over the full Input Space

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
  • Method Details

    • borelSigmaMeasure

      R1Univariate borelSigmaMeasure()
      Retrieve the Borel Sigma R1 Probability Measure
      Returns:
      The Borel Sigma R1 Probability Measure
    • sampleMetricNorm

      double sampleMetricNorm​(double x) throws java.lang.Exception
      Compute the Metric Norm of the Sample
      Parameters:
      x - The Sample
      Returns:
      The Metric Norm of the Sample
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid
    • populationMode

      double populationMode() throws java.lang.Exception
      Retrieve the Population Mode
      Returns:
      The Population Mode
      Throws:
      java.lang.Exception - Thrown if the Population Mode cannot be calculated
    • borelMeasureSpaceExpectation

      double borelMeasureSpaceExpectation​(R1ToR1 r1ToR1Function) throws java.lang.Exception
      Compute the Borel Measure Expectation for the specified R1 To R1 Function over the full Input Space
      Parameters:
      r1ToR1Function - R1 To R1 Function Instance
      Returns:
      The Borel Measure Expectation for the specified R1 To R1 Function over `the full Input Space
      Throws:
      java.lang.Exception - Thrown if the Population Mode cannot be calculated