Package org.drip.numerical.matrixnorm

Class R1SquareConsistencyValidator

java.lang.Object

org.drip.numerical.matrixnorm.R1SquareConsistencyValidator

public class R1SquareConsistencyValidator
extends java.lang.Object

R1SquareConsistencyValidator contains the Consistency Validation Checks for the Norm Evaluator of a R¹ Square 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
R1SquareConsistencyValidator(boolean positiveValued, boolean definite, boolean absolutelyHomogeneous, boolean matrixMatrixSubAdditive, boolean matrixMatrixSubMultiplicative, boolean matrixVectorSubMultiplicative)	R1SquareConsistencyValidator Constructor

Method Summary

Modifier and Type	Method	Description
boolean	absolutelyHomogeneous()	Indicate if the Norm is Absolutely Homogeneous
static boolean	AbsolutelyHomogeneous(double norm, double alpha, double alphaNorm)	Indicate if the Norm is Absolutely Homogeneous
boolean	definite()	Indicate if the Norm is Definite
static boolean	Definite(double norm, double[][] r1Grid)	Indicate if the Norm is Definite
boolean	matrixMatrixSubAdditive()	Indicate if the Norm is Matrix-Matrix Sub-additive
static boolean	MatrixMatrixSubAdditive(double normA, double normB, double normAPlusB)	Indicate if the Norm is Matrix-Matrix Sub-additive
boolean	matrixMatrixSubMultiplicative()	Indicate if the Norm is Matrix-Matrix Sub-multiplicative
static boolean	MatrixMatrixSubMultiplicative(double normA, double normB, double normAB)	Indicate if the Norm is Matrix-Matrix Sub-multiplicative
boolean	matrixVectorSubMultiplicative()	Indicate if the Norm is Matrix-Vector Sub-multiplicative
static boolean	MatrixVectorSubMultiplicative(double normA, double normX, double normAX)	Indicate if the Norm is Matrix-Vector Sub-multiplicative
boolean	positiveValued()	Indicate if the Norm is Positive Valued
static boolean	PositiveValued(double norm)	Indicate if the Norm is Positive Valued
static R1SquareConsistencyValidator	Standard(double normA, double[][] a, double normB, double alphaNormA, double alpha, double normAPlusB, double normAB, double normV, double normAV)	Construct a Standard Instance of R1SquareConsistencyValidator
boolean	validate()	Check if the Validation has been successful

Methods inherited from class java.lang.Object

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

Constructor Details

R1SquareConsistencyValidator

public R1SquareConsistencyValidator(boolean positiveValued,
boolean definite,
boolean absolutelyHomogeneous,
boolean matrixMatrixSubAdditive,
boolean matrixMatrixSubMultiplicative,
boolean matrixVectorSubMultiplicative)

R1SquareConsistencyValidator Constructor

Parameters:

positiveValued - TRUE - Norm is Positive Valued

definite - TRUE - Norm is Definite

absolutelyHomogeneous - TRUE - Norm is Absolutely Homogeneous

matrixMatrixSubAdditive - TRUE - Norm is Matrix-Matrix Sub-additive

matrixMatrixSubMultiplicative - TRUE - Norm is Matrix-Matrix Sub-multiplicative

matrixVectorSubMultiplicative - TRUE - Norm is Matrix-Vector Sub-multiplicative

Method Details

PositiveValued

public static final boolean PositiveValued(double norm)

Indicate if the Norm is Positive Valued

Parameters:

norm - Norm

Returns:

TRUE - Norm is Positive Valued

Definite

public static final boolean Definite(double norm,
double[][] r1Grid)

Indicate if the Norm is Definite

Parameters:

norm - Norm

r1Grid - R¹ Square Matrix

Returns:

TRUE - Norm is Definite

AbsolutelyHomogeneous

public static final boolean AbsolutelyHomogeneous(double norm,
double alpha,
double alphaNorm)

Indicate if the Norm is Absolutely Homogeneous

Parameters:

norm - Norm

alpha - Alpha

alphaNorm - Alpha Norm

Returns:

TRUE - Norm is Absolutely Homogeneous

MatrixMatrixSubAdditive

public static final boolean MatrixMatrixSubAdditive(double normA,
double normB,
double normAPlusB)

Indicate if the Norm is Matrix-Matrix Sub-additive

Parameters:

normA - Norm of Matrix A

normB - Norm of Matrix B

normAPlusB - Norm of Matrix A Plus B

Returns:

TRUE - Norm is Matrix-Matrix Sub-additive

MatrixMatrixSubMultiplicative

public static final boolean MatrixMatrixSubMultiplicative(double normA,
double normB,
double normAB)

Indicate if the Norm is Matrix-Matrix Sub-multiplicative

Parameters:

normA - Norm of Matrix A

normB - Norm of Matrix B

normAB - Norm of Matrix A.B

Returns:

TRUE - Norm is Matrix-Matrix Sub-multiplicative

MatrixVectorSubMultiplicative

public static final boolean MatrixVectorSubMultiplicative(double normA,
double normX,
double normAX)

Indicate if the Norm is Matrix-Vector Sub-multiplicative

Parameters:

normA - Norm of Matrix A

normX - Norm of Vector X

normAX - Norm of Matrix A.X

Returns:

TRUE - Norm is Matrix-Vector Sub-multiplicative

Standard

public static final R1SquareConsistencyValidator Standard(double normA,
double[][] a,
double normB,
double alphaNormA,
double alpha,
double normAPlusB,
double normAB,
double normV,
double normAV)

Construct a Standard Instance of R1SquareConsistencyValidator

Parameters:

normA - Norm of Matrix A

a - Matrix A

normB - Norm of Matrix B

alphaNormA - Norm of Alpha-Matrix A

alpha - Alpha

normAPlusB - Norm of A and B Matrix-Matrix Sum

normAB - Norm of A and B Matrix-Matrix Product

normV - Norm of Vector V

normAV - Norm of A and V Matrix-Vector Product

Returns:

Standard Instance of R1SquareConsistencyValidator

positiveValued

public boolean positiveValued()

Indicate if the Norm is Positive Valued

Returns:

TRUE - Norm is Positive Valued

definite

public boolean definite()

Indicate if the Norm is Definite

Returns:

TRUE - Norm is Definite

absolutelyHomogeneous

public boolean absolutelyHomogeneous()

Indicate if the Norm is Absolutely Homogeneous

Returns:

TRUE - Norm is Absolutely Homogeneous

matrixMatrixSubAdditive

public boolean matrixMatrixSubAdditive()

Indicate if the Norm is Matrix-Matrix Sub-additive

Returns:

TRUE - Norm is Matrix-Matrix Sub-additive

matrixMatrixSubMultiplicative

public boolean matrixMatrixSubMultiplicative()

Indicate if the Norm is Matrix-Matrix Sub-multiplicative

Returns:

TRUE - Norm is Matrix-Matrix Sub-multiplicative

matrixVectorSubMultiplicative

public boolean matrixVectorSubMultiplicative()

Indicate if the Norm is Matrix-Vector Sub-multiplicative

Returns:

TRUE - Norm is Matrix-Vector Sub-multiplicative

validate

public boolean validate()

Check if the Validation has been successful

Returns:

TRUE - The Validation has been successful