Package org.drip.numerical.complex

Class C1Util

java.lang.Object

org.drip.numerical.complex.C1Util

public class C1Util
extends java.lang.Object

C1Util implements a C¹ Complex Number Manipulation Utilities. 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

Constructor Summary

Constructors

Constructor	Description
C1Util()

Method Summary

Modifier and Type	Method	Description
static C1Cartesian	Add(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Add the 2 Complex Numbers
static C1Cartesian	Divide(C1Cartesian numeratorC1, C1Cartesian denominatorC1)	Divide the Numerator Complex Number by the Denominator Complex Number
static double	DotProduct(C1Cartesian a, C1Cartesian e)	Dot Product of Complex Numbers A and E
static C1Cartesian	Exponentiate(C1Cartesian complexNumber)	Exponentiate the Complex Number
static C1Cartesian	Logarithm(C1Cartesian complexNumber)	Compute Logarithm of the Complex Number
static C1Cartesian	Multiply(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Multiply the 2 Complex Numbers
static C1Cartesian	Scale(C1Cartesian cartesianC1, double scale)	Scale the Complex Number with the factor
static C1Cartesian	Scale(C1Cartesian cartesianC1, C1Cartesian cartesianC1Scale)	Scale the Complex Number with the factor
static C1Cartesian	Square(C1Cartesian c1)	Square the Complex Number
static C1Cartesian	SquareRoot(C1Cartesian complexNumber)	Compute the Square Root of the Complex Number
static C1Cartesian	Subtract(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Subtract the Second Complex Number from the First
static C1Cartesian	UnsafeAdd(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Add the 2 Complex Numbers.
static C1Cartesian	UnsafeDivide(C1Cartesian numeratorC1, C1Cartesian denominatorC1)	Divide the Numerator Complex Number by the Denominator Complex Number.
static double	UnsafeDotProduct(C1Cartesian a, C1Cartesian e)	Dot Product of Complex Numbers A and E.
static C1Cartesian	UnsafeExponentiate(C1Cartesian complexNumber)	Exponentiate the Complex Number.
static C1Cartesian	UnsafeLogarithm(C1Cartesian complexNumber)	Compute Logarithm of the Complex Number.
static C1Cartesian	UnsafeProduct(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Multiply the 2 Complex Numbers.
static C1Cartesian	UnsafeScale(C1Cartesian cartesianC1, double scale)	Scale the Complex Number with the factor.
static C1Cartesian	UnsafeScale(C1Cartesian cartesianC1, C1Cartesian cartesianC1Scale)	Scale the Complex Number with the factor.
static C1Cartesian	UnsafeSquare(C1Cartesian c1)	Square the Complex Number.
static C1Cartesian	UnsafeSquareRoot(C1Cartesian complexNumber)	Compute the Square Root of the Complex Number.
static C1Cartesian	UnsafeSubtract(C1Cartesian firstCartesianC1, C1Cartesian secondCartesianC1)	Subtract the Second Complex Number from the First.

Methods inherited from class java.lang.Object

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

Constructor Details

C1Util

public C1Util()

Method Details

UnsafeAdd

public static final C1Cartesian UnsafeAdd(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Add the 2 Complex Numbers. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The Complex Number instance that is a sum of the two

UnsafeScale

public static final C1Cartesian UnsafeScale(C1Cartesian cartesianC1,
double scale)

Scale the Complex Number with the factor. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

cartesianC1 - The Complex Number

scale - The Scaling Factor

Returns:

The Scaled Complex Number

UnsafeScale

public static final C1Cartesian UnsafeScale(C1Cartesian cartesianC1,
C1Cartesian cartesianC1Scale)

Scale the Complex Number with the factor. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

cartesianC1 - The Complex Number

cartesianC1Scale - The Complex Scaling Factor

Returns:

The Scaled Complex Number

UnsafeSubtract

public static final C1Cartesian UnsafeSubtract(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Subtract the Second Complex Number from the First. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The "Difference" Complex Number

UnsafeProduct

public static final C1Cartesian UnsafeProduct(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Multiply the 2 Complex Numbers. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The Complex Number instance that is a product of the two

UnsafeDivide

public static final C1Cartesian UnsafeDivide(C1Cartesian numeratorC1,
C1Cartesian denominatorC1)

Divide the Numerator Complex Number by the Denominator Complex Number. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

numeratorC1 - The Numerator Complex Number

denominatorC1 - The Denominator Complex Number

Returns:

The "Divided" Complex Number

UnsafeSquare

public static final C1Cartesian UnsafeSquare(C1Cartesian c1)

Square the Complex Number. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

c1 - The Complex Number

Returns:

The Squared Complex Number Instance

UnsafeSquareRoot

public static final C1Cartesian UnsafeSquareRoot(C1Cartesian complexNumber)

Compute the Square Root of the Complex Number. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

complexNumber - The Complex Number

Returns:

The Square Root Complex Number Instance

UnsafeExponentiate

public static final C1Cartesian UnsafeExponentiate(C1Cartesian complexNumber)

Exponentiate the Complex Number. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

complexNumber - The Complex Number

Returns:

The Exponentiated Complex Number Instance

UnsafeLogarithm

public static final C1Cartesian UnsafeLogarithm(C1Cartesian complexNumber)

Compute Logarithm of the Complex Number. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

complexNumber - The Complex Number

Returns:

The Complex Number Logarithm Instance

UnsafeDotProduct

public static final double UnsafeDotProduct(C1Cartesian a,
C1Cartesian e)

Dot Product of Complex Numbers A and E. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

a - First C¹

e - Second C¹

Returns:

The Dot Product

Add

public static final C1Cartesian Add(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Add the 2 Complex Numbers

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The Complex Number instance that is a sum of the two

Scale

public static final C1Cartesian Scale(C1Cartesian cartesianC1,
double scale)

Scale the Complex Number with the factor

Parameters:

cartesianC1 - The Complex Number

scale - The Scaling Factor

Returns:

The Scaled Complex Number

Scale

public static final C1Cartesian Scale(C1Cartesian cartesianC1,
C1Cartesian cartesianC1Scale)

Scale the Complex Number with the factor

Parameters:

cartesianC1 - The Complex Number

cartesianC1Scale - The ComplexScaling Factor

Returns:

The Scaled Complex Number

Subtract

public static final C1Cartesian Subtract(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Subtract the Second Complex Number from the First

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The "Difference" Complex Number

Multiply

public static final C1Cartesian Multiply(C1Cartesian firstCartesianC1,
C1Cartesian secondCartesianC1)

Multiply the 2 Complex Numbers

Parameters:

firstCartesianC1 - The First Complex Number

secondCartesianC1 - The Second Complex Number

Returns:

The Complex Number instance that is a product of the two

Divide

public static final C1Cartesian Divide(C1Cartesian numeratorC1,
C1Cartesian denominatorC1)

Divide the Numerator Complex Number by the Denominator Complex Number

Parameters:

numeratorC1 - The Numerator Complex Number

denominatorC1 - The Denominator Complex Number

Returns:

The "Divided" Complex Number

Square

public static final C1Cartesian Square(C1Cartesian c1)

Square the Complex Number

Parameters:

c1 - The Complex Number

Returns:

The Squared Complex Number Instance

SquareRoot

public static final C1Cartesian SquareRoot(C1Cartesian complexNumber)

Compute the Square Root of the Complex Number

Parameters:

complexNumber - The Complex Number

Returns:

The Square Root Complex Number Instance

Exponentiate

public static final C1Cartesian Exponentiate(C1Cartesian complexNumber)

Exponentiate the Complex Number

Parameters:

complexNumber - The Complex Number

Returns:

The Exponentiated Complex Number Instance

Logarithm

public static final C1Cartesian Logarithm(C1Cartesian complexNumber)

Compute Logarithm of the Complex Number

Parameters:

complexNumber - The Complex Number

Returns:

The Complex Number Logarithm Instance

DotProduct

public static final double DotProduct(C1Cartesian a,
C1Cartesian e)
                               throws java.lang.Exception

Dot Product of Complex Numbers A and E

Parameters:

a - First C¹

e - Second C¹

Returns:

The Dot Product

Throws:

java.lang.Exception - Thrown if the Dot Product Cannot be computed