Package org.drip.numerical.matrixnorm

Class FrobeniusEvaluator

java.lang.Object
org.drip.numerical.matrixnorm.R1SquareEvaluator
org.drip.numerical.matrixnorm.EntryWiseEvaluator
org.drip.numerical.matrixnorm.FrobeniusEvaluator
public class FrobeniusEvaluator
extends EntryWiseEvaluator
FrobeniusEvaluator computes the Entry-wise L2, 2 Norm of the Entries of the R1 Square Matrix. The References are:

  • Alon, N., and A. Naor (2004): Approximating the Cut-norm via Grothendieck Inequality Proceedings of the 36th Annual ACM Symposium on Theory of Computing STOC’04 ACM Chicago IL
  • Golub, G. H., and C. F. van Loan (1996): Matrix Computations 3rd Edition Johns Hopkins University Press Baltimore MD
  • Horn, R. A., and C. R. Johnson (2013): Matrix Analysis 2nd Edition Cambridge University Press Cambridge UK
  • Lazslo, L. (2012): Large Networks and Graph Limits American Mathematical Society Providence RI
  • Wikipedia (2024): Matrix Norm https://en.wikipedia.org/wiki/Matrix_norm




Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    FrobeniusEvaluator()
    FrobeniusEvaluator Constructor

  • Method Summary

    Modifier and Type Method Description
    double norm​(R1Square r1Square)
    Compute the Norm of the R1 Square Matrix
    double svdNorm​(R1Square r1Square)
    Compute the SVD-based Norm of the R1 Square Matrix
    double traceNorm​(R1Square r1Square)
    Compute the Trace-based Norm of the R1 Square Matrix

    Methods inherited from class org.drip.numerical.matrixnorm.EntryWiseEvaluator

    L2_1, Lp_p, p, q

    Methods inherited from class org.drip.numerical.matrixnorm.R1SquareEvaluator

    validator

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • FrobeniusEvaluator

      public FrobeniusEvaluator() throws java.lang.Exception
      FrobeniusEvaluator Constructor
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • norm

      public double norm​(R1Square r1Square) throws java.lang.Exception
      Compute the Norm of the R1 Square Matrix
      Overrides:
      norm in class EntryWiseEvaluator
      Parameters:
      r1Square - R1 Square Matrix
      Returns:
      Norm of the R1 Square Matrix
      Throws:
      java.lang.Exception - Thrown if the Norm cannot be calculated

    • traceNorm

      public double traceNorm​(R1Square r1Square) throws java.lang.Exception
      Compute the Trace-based Norm of the R1 Square Matrix
      Parameters:
      r1Square - R1 Square Matrix
      Returns:
      Trace-based Norm of the R1 Square Matrix
      Throws:
      java.lang.Exception - Thrown if the Norm cannot be calculated

    • svdNorm

      public double svdNorm​(R1Square r1Square) throws java.lang.Exception
      Compute the SVD-based Norm of the R1 Square Matrix
      Parameters:
      r1Square - R1 Square Matrix
      Returns:
      SVD-based Norm of the R1 Square Matrix
      Throws:
      java.lang.Exception - Thrown if the Norm cannot be calculated