Package org.drip.numerical.matrixnorm

Class EntryWiseEvaluator

java.lang.Object

org.drip.numerical.matrixnorm.R1SquareEvaluator

org.drip.numerical.matrixnorm.EntryWiseEvaluator

Direct Known Subclasses:

FrobeniusEvaluator, MaxInfinityInfinityEvaluator

public class EntryWiseEvaluator
extends R1SquareEvaluator

EntryWiseEvaluator computes the Entry-wise Norm of a R¹Square Matrix. The References are:

• Alon, N., and A. Naor (2004): Approximating the Cut-norm via Grothendieck Inequality Proceedings of the 36^th Annual ACM Symposium on Theory of Computing STOC’04 ACM Chicago IL
• Golub, G. H., and C. F. van Loan (1996): Matrix Computations 3^rd Edition Johns Hopkins University Press Baltimore MD
• Horn, R. A., and C. R. Johnson (2013): Matrix Analysis 2^nd 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Implementation of Matrix Norm Variants

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
EntryWiseEvaluator(int p, int q)	EntryWiseEvaluator Constructor

Method Summary

Modifier and Type	Method	Description
static EntryWiseEvaluator	L2_1()	Construct a L2, 1 Instance of EntryWiseEvaluator
static EntryWiseEvaluator	Lp_p(int p)	Construct a Lp, p Instance of EntryWiseEvaluator
double	norm(R1Square r1Square)	Compute the Norm of the R1Square Matrix
int	p()	Retrieve the p Norm
int	q()	Retrieve the q Norm

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

EntryWiseEvaluator

public EntryWiseEvaluator(int p,
int q)
                   throws java.lang.Exception

EntryWiseEvaluator Constructor

Parameters:

p - p Norm

q - q Norm

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

L2_1

public static final EntryWiseEvaluator L2_1()

Construct a L_{2, 1} Instance of EntryWiseEvaluator

Returns:

L_{2, 1} Instance of EntryWiseEvaluator

Lp_p

public static final EntryWiseEvaluator Lp_p(int p)

Construct a L_{p, p} Instance of EntryWiseEvaluator

Parameters:

p - p Norm

Returns:

L_{p, p} Instance of EntryWiseEvaluator

p

public int p()

Retrieve the p Norm

Returns:

p Norm

q

public int q()

Retrieve the q Norm

Returns:

q Norm

norm

public double norm(R1Square r1Square)
            throws java.lang.Exception

Compute the Norm of the R¹Square Matrix

Specified by:

norm in class R1SquareEvaluator

Parameters:

r1Square - R¹Square Matrix

Returns:

Norm of the R¹Square Matrix

Throws:

java.lang.Exception