Package org.drip.numerical.complex

Class C1CartesianPhiPsiThetaDelta

java.lang.Object

org.drip.numerical.complex.C1Square

org.drip.numerical.complex.C1CartesianPhiPsiThetaDelta

public class C1CartesianPhiPsiThetaDelta
extends C1Square

C1CartesianPhiPsiThetaDelta implements the type and Functionality associated with a C¹ Square Matrix parameterized by phi, psi, theta, and delta Fields. The References are:

• Fuhr, H., and Z. Rzeszotnik (2018): A Note on Factoring Unitary Matrices Linear Algebra and its Applications 547 32-44
• Horn, R. A., and C. R. Johnson (2013): Matrix Analysis Cambridge University Press Cambridge UK
• Li, C. K., and E. Poon (2002): Additive Decomposition of Real Matrices Linear and Multilinear Algebra 50 (4) 321-326
• Marvian, I. (2022): Restrictions on realizable Unitary Operations imposed by Symmetry and Locality Nature Science 18 (3) 283-289
• Wikipedia (2024): Unitary Matrix https://en.wikipedia.org/wiki/Unitary_matrix

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Implementation of Complex Number Suite

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	alpha()	Calculate Alpha
double	beta()	Calculate Beta
double	delta()	Retrieve Delta
R1SquareRotation2x2	jordanNormalCenter()	Retrieve the Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta
C1Square	jordanNormalLeft()	Retrieve the Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta
C1Square	jordanNormalRight()	Retrieve the Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta
double	phi()	Retrieve Phi
double	psi()	Retrieve Psi
static C1CartesianPhiPsiThetaDelta	Standard(double phi, double psi, double theta, double delta)	Construct a Standard Instance of C1CartesianPhiPsiThetaDelta
double	theta()	Retrieve Theta

Methods inherited from class org.drip.numerical.complex.C1Square

c1Grid, determinant, isUnitary, isUnitDeterminant, product, product, product, Rotation2x2, Rotation2x2, size, slimContract, Standard, transpose

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static C1CartesianPhiPsiThetaDelta Standard(double phi,
double psi,
double theta,
double delta)

Construct a Standard Instance of C1CartesianPhiPsiThetaDelta

Parameters:

phi - "Phi"

psi - "Psi"

theta - "Theta"

delta - "Delta"

Returns:

C1CartesianPhiPsiThetaDelta Instance

phi

public double phi()

Retrieve Phi

Returns:

Phi

psi

public double psi()

Retrieve Psi

Returns:

Psi

theta

public double theta()

Retrieve Theta

Returns:

Theta

delta

public double delta()

Retrieve Delta

Returns:

Delta

jordanNormalLeft

public C1Square jordanNormalLeft()

Retrieve the Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta

jordanNormalCenter

public R1SquareRotation2x2 jordanNormalCenter()

Retrieve the Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta

jordanNormalRight

public C1Square jordanNormalRight()

Retrieve the Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta

alpha

public double alpha()

Calculate Alpha

Returns:

Alpha

beta

public double beta()

Calculate Beta

Returns:

Beta