Package org.drip.graph.adjacencymatrix

Class GkToR1

java.lang.Object
org.drip.graph.adjacencymatrix.GkToR1
Direct Known Subclasses:
G1ToR1, G2ToR1, GkLinearOperator
public class GkToR1
extends java.lang.Object
GkToR1 implements the Space Map induced by Lk Norm on the R1 Functions over the Vertexes of a Graph. The References are:

  • Dunford, N., and J. Schwartz (1963): Linear Operators II: Spectral Theory: Self-adjoint Operators in the Hilbert Space Wiley Interscience Hoboken NJ
  • Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press Cambridge MA
  • Guo, J. M., Z. W. Wang, and X. Li (2019): Sharp Upper Bounds of the Spectral Radius of a Graph Discrete Mathematics 342 (9) 2559-2563
  • Lax, P. D. (2002): Functional Analysis Wiley Interscience Hoboken NJ
  • Wikipedia (2024): Spectral Radius https://en.wikipedia.org/wiki/Spectral_radius




Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    GkToR1​(R1ToR1 vertexFunction, int k)
    GkToR1 Constructor

  • Method Summary

    Modifier and Type Method Description
    boolean bounded​(Network<java.lang.Double> graphNetwork)
    Indicate if the G2 Map is bounded based on the L2 Metric
    double evaluate​(Network<java.lang.Double> graphNetwork)
    Evaluate the Value across all the Graph Vertexes
    double norm​(Network<java.lang.Double> graphNetwork)
    Evaluate the Norm across all the Graph Vertexes
    R1ToR1 vertexFunction()
    Retrieve the R1 to R1 Vertex Function

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • GkToR1

      public GkToR1​(R1ToR1 vertexFunction, int k) throws java.lang.Exception
      GkToR1 Constructor
      Parameters:
      vertexFunction - R1 to R1 Vertex Function
      k - Norm Exponent
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • vertexFunction

      public R1ToR1 vertexFunction()
      Retrieve the R1 to R1 Vertex Function
      Returns:
      R1 to R1 Vertex Function

    • evaluate

      public double evaluate​(Network<java.lang.Double> graphNetwork) throws java.lang.Exception
      Evaluate the Value across all the Graph Vertexes
      Parameters:
      graphNetwork - Graph Network
      Returns:
      Value across all the Graph Vertexes
      Throws:
      java.lang.Exception - Thrown if the Graph is Invalid

    • norm

      public double norm​(Network<java.lang.Double> graphNetwork) throws java.lang.Exception
      Evaluate the Norm across all the Graph Vertexes
      Parameters:
      graphNetwork - Graph Network
      Returns:
      Norm across all the Graph Vertexes
      Throws:
      java.lang.Exception - Thrown if the Graph is Invalid

    • bounded

      public boolean bounded​(Network<java.lang.Double> graphNetwork) throws java.lang.Exception
      Indicate if the G2 Map is bounded based on the L2 Metric
      Parameters:
      graphNetwork - Graph Network
      Returns:
      TRUE - G2 Map is bounded
      Throws:
      java.lang.Exception - Thrown if the Graph is Invalid