Package org.drip.numerical.matrix

Class R1SquareEigenized

java.lang.Object

org.drip.numerical.matrix.R1Square

org.drip.numerical.matrix.R1SquareEigenized

public class R1SquareEigenized
extends R1Square

R1SquareEigenized implements an R¹ Square Matrix with its Pre-computed Eigen-values and Eigen-vectors. 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Implementation of R¹ C¹ Matrices

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
R1ToR1	characteristicPolynomial()	Retrieve the Characteristic Polynomial of the Eigenvalues
double	conditionNumberL2()	Compute the L2 Condition Number of the Matrix
double	determinant()	Compute the Determinant of the Matrix
EigenOutput	eigenize()	Eigenize and Extract the Components of the Specified Matrix
EigenOutput	eigenOutput()	Retrieve the Eigen Components and the Eigen Vectors
java.util.Map<java.lang.Double,java.lang.Integer>	eigenValueMultiplicityMap()	Retrieve the Eigenvalue Multiplicity Map
double	spectralRadius()	Compute the Spectral Radius of the Matrix
static R1SquareEigenized	Standard(EigenOutput eigenOutput)	Construct a Standard Instance of R1SquareEigenized from the EigenOutput
EigenOutput	svd()	Perform Singular Value Decomposition and Extract the Components of the Specified Matrix

Methods inherited from class org.drip.numerical.matrix.R1Square

add, defaultConditionNumber, diagonalEntryArray, isNormal, isTriangularizable, multiply, multiply, power, qrDecomposition, r1Grid, rqDecomposition, scale, size, Standard, subtract, svdBasedFrobeniusNorm, trace, transpose

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final R1SquareEigenized Standard(EigenOutput eigenOutput)

Construct a Standard Instance of R1SquareEigenized from the EigenOutput

Parameters:

eigenOutput - The EigenOutput Instance

Returns:

Standard Instance of R1SquareEigenized

eigenOutput

public EigenOutput eigenOutput()

Retrieve the Eigen Components and the Eigen Vectors

Returns:

Eigen Components and the Eigen Vectors

eigenize

public EigenOutput eigenize()

Eigenize and Extract the Components of the Specified Matrix

Overrides:

eigenize in class R1Square

Returns:

The EigenComponents

svd

public EigenOutput svd()

Perform Singular Value Decomposition and Extract the Components of the Specified Matrix

Overrides:

svd in class R1Square

Returns:

The Singular Value Decomposition Components

eigenValueMultiplicityMap

public java.util.Map<java.lang.Double,java.lang.Integer> eigenValueMultiplicityMap()

Retrieve the Eigenvalue Multiplicity Map

Overrides:

eigenValueMultiplicityMap in class R1Square

Returns:

Eigenvalue Multiplicity Map

determinant

public double determinant()
                   throws java.lang.Exception

Compute the Determinant of the Matrix

Overrides:

determinant in class R1Square

Returns:

Determinant of the Matrix

Throws:

java.lang.Exception - Thrown if the Determinant cannot be calculated

conditionNumberL2

public double conditionNumberL2()
                         throws java.lang.Exception

Compute the L₂ Condition Number of the Matrix

Overrides:

conditionNumberL2 in class R1Square

Returns:

L₂ Condition Number of the Matrix

Throws:

java.lang.Exception - Thrown if the Condition Number cannot be calculated

characteristicPolynomial

public R1ToR1 characteristicPolynomial()

Retrieve the Characteristic Polynomial of the Eigenvalues

Overrides:

characteristicPolynomial in class R1Square

Returns:

Characteristic Polynomial of the Eigenvalues

spectralRadius

public double spectralRadius()
                      throws java.lang.Exception

Compute the Spectral Radius of the Matrix

Overrides:

spectralRadius in class R1Square

Returns:

Spectral Radius of the Matrix

Throws:

java.lang.Exception - Thrown if the Spectral Radius cannot be calculated