Package org.drip.numerical.complex

Class C1MatrixUtil

java.lang.Object

org.drip.numerical.complex.C1MatrixUtil

public class C1MatrixUtil
extends java.lang.Object

C1MatrixUtil implements a C¹ Complex Number Matrix 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
C1MatrixUtil()

Method Summary

Modifier and Type	Method	Description
static double	Determinant(C1Cartesian[][] c1Grid)	Determinant of the Input Matrix
static boolean	IsGridValid(C1Cartesian[][] c1Grid)	Indicate the C1 Grid is Valid
static boolean	IsUnitary(C1Cartesian[][] c1Grid)	Indicate if the Input Matrix is Unitary
static boolean	IsVectorValid(C1Cartesian[] c1Vector)	Indicate the C1 Vector is Valid
static C1Cartesian[][]	Product(double[][] r1Grid, C1Cartesian[][] c1Grid)	Compute the Product of the Input Matrices
static C1Cartesian[][]	Product(C1Cartesian[][] c1Grid, double[][] r1Grid)	Compute the Product of the Input Matrices
static C1Cartesian[][]	Product(C1Cartesian[][] c1Grid, C1Cartesian c1)	Compute the Product of the Input Matrix and the Complex Number
static C1Cartesian[][]	Product(C1Cartesian[][] c1GridA, C1Cartesian[][] c1GridB)	Compute the Product of the Input Matrices
static C1Cartesian[][]	Transpose(C1Cartesian[][] c1Grid)	Transpose the specified C1 Square Matrix
static double	UnsafeDeterminant(C1Cartesian[][] c1Grid)	Determinant of the Input Matrix.
static C1Cartesian[][]	UnsafeProduct(double[][] r1GridA, C1Cartesian[][] c1GridB)	Compute the Product of the Input Matrices.
static C1Cartesian[][]	UnsafeProduct(C1Cartesian[][] c1GridA, double[][] r1GridB)	Compute the Product of the Input Matrices.
static C1Cartesian[][]	UnsafeProduct(C1Cartesian[][] c1Grid, C1Cartesian c1)	Compute the Product of the Input Matrix and the Complex Number.
static C1Cartesian[][]	UnsafeProduct(C1Cartesian[][] c1GridA, C1Cartesian[][] c1GridB)	Compute the Product of the Input Matrices.
static C1Cartesian[][]	UnsafeTranspose(C1Cartesian[][] c1Grid)	Transpose the specified C1 Square Matrix.

Methods inherited from class java.lang.Object

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

Constructor Details

C1MatrixUtil

public C1MatrixUtil()

Method Details

UnsafeTranspose

public static final C1Cartesian[][] UnsafeTranspose(C1Cartesian[][] c1Grid)

Transpose the specified C¹ Square Matrix. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

c1Grid - The Input C¹ Matrix Grid

Returns:

The Transpose of the Input C¹ Matrix Grid

UnsafeProduct

public static final C1Cartesian[][] UnsafeProduct(C1Cartesian[][] c1GridA,
C1Cartesian[][] c1GridB)

Compute the Product of the Input Matrices. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

c1GridA - Grid of C¹ A

c1GridB - Grid of C¹ B

Returns:

The Product Matrix

UnsafeProduct

public static final C1Cartesian[][] UnsafeProduct(C1Cartesian[][] c1GridA,
double[][] r1GridB)

Compute the Product of the Input Matrices. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

c1GridA - Grid of C¹

r1GridB - Grid of R¹

Returns:

The Product Matrix

UnsafeProduct

public static final C1Cartesian[][] UnsafeProduct(double[][] r1GridA,
C1Cartesian[][] c1GridB)

Compute the Product of the Input Matrices. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

r1GridA - Grid of R¹

c1GridB - Grid of C¹

Returns:

The Product Matrix

UnsafeProduct

public static final C1Cartesian[][] UnsafeProduct(C1Cartesian[][] c1Grid,
C1Cartesian c1)

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

Parameters:

c1Grid - Grid of C¹

c1 - C¹

Returns:

The Product Matrix

UnsafeDeterminant

public static final double UnsafeDeterminant(C1Cartesian[][] c1Grid)

Determinant of the Input Matrix. Unsafe Methods do not validate the Input Arguments, so use caution in applying these Methods

Parameters:

c1Grid - Grid of C¹ Instances

Returns:

The Determinant

IsVectorValid

public static final boolean IsVectorValid(C1Cartesian[] c1Vector)

Indicate the C¹ Vector is Valid

Parameters:

c1Vector - C¹ Vector

Returns:

TRUE - The C¹ Vector is Valid

IsGridValid

public static final boolean IsGridValid(C1Cartesian[][] c1Grid)

Indicate the C¹ Grid is Valid

Parameters:

c1Grid - C¹ Grid

Returns:

TRUE - The C¹ Grid is Valid

Transpose

public static final C1Cartesian[][] Transpose(C1Cartesian[][] c1Grid)

Transpose the specified C¹ Square Matrix

Parameters:

c1Grid - The Input C¹ Matrix Grid

Returns:

The Transpose of the Input C¹ Matrix Grid

Product

public static final C1Cartesian[][] Product(C1Cartesian[][] c1GridA,
C1Cartesian[][] c1GridB)

Compute the Product of the Input Matrices

Parameters:

c1GridA - Grid of C¹ A

c1GridB - Grid of C¹ B

Returns:

The Product Matrix

Product

public static final C1Cartesian[][] Product(C1Cartesian[][] c1Grid,
double[][] r1Grid)

Compute the Product of the Input Matrices

Parameters:

c1Grid - rid of C¹

r1Grid - Grid of R¹

Returns:

The Product Matrix

Product

public static final C1Cartesian[][] Product(double[][] r1Grid,
C1Cartesian[][] c1Grid)

Compute the Product of the Input Matrices

Parameters:

r1Grid - Grid of R¹

c1Grid - Grid of C¹

Returns:

The Product Matrix

Product

public static final C1Cartesian[][] Product(C1Cartesian[][] c1Grid,
C1Cartesian c1)

Compute the Product of the Input Matrix and the Complex Number

Parameters:

c1Grid - Grid of C¹

c1 - C¹

Returns:

The Product Matrix

Determinant

public static final double Determinant(C1Cartesian[][] c1Grid)
                                throws java.lang.Exception

Determinant of the Input Matrix

Parameters:

c1Grid - Grid of C1Cartesian Instances

Returns:

The Determinant

Throws:

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

IsUnitary

public static final boolean IsUnitary(C1Cartesian[][] c1Grid)
                               throws java.lang.Exception

Indicate if the Input Matrix is Unitary

Parameters:

c1Grid - Grid of C1Cartesian Instances

Returns:

TRUE - Input Matrix is Unitary

Throws:

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