Package org.drip.numerical.complex

Class C1Square

java.lang.Object
org.drip.numerical.complex.C1Square
Direct Known Subclasses:
C1CartesianFuhrRzeszotnik, C1CartesianPhiAB, C1CartesianPhiAlphaBetaTheta, C1CartesianPhiPsiThetaDelta, UnitaryMatrix
public class C1Square
extends java.lang.Object
C1Square implements the type and Functionality associated with a C1Square Matrix. 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




Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    C1Cartesian[][] c1Grid()
    Retrieve C1 Array
    double determinant()
    Determinant of with the "Other"
    boolean isUnitary()
    Indicate if the Determinant is 1
    boolean isUnitDeterminant()
    Indicate if the Determinant is 1
    C1Square product​(C1Cartesian c1)
    Compute the Product of the Input Matrix and the Complex Number
    C1Square product​(C1Square squareMatrixOther)
    Compute the Product with the other Square Matrix
    C1Square product​(R1Square r1Square)
    Compute the Product with the other Square Matrix
    static C1Square Rotation2x2​(double theta)
    Construct a 2x2 Rotation C1 Matrix
    static C1Square Rotation2x2​(double theta1, double theta2)
    Construct a 2x2 Rotation C1 Matrix
    int size()
    Retrieve the Size of the Square Matrix
    C1Square slimContract()
    Contract the Square C1Cartesian by one Row/Column
    static C1Square Standard​(C1Cartesian[][] c1Grid)
    Construct a Standard Instance of C1Square
    C1Cartesian[][] transpose()
    Transpose the Square Matrix

    Methods inherited from class java.lang.Object

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

  • Method Details

    • Standard

      public static C1Square Standard​(C1Cartesian[][] c1Grid)
      Construct a Standard Instance of C1Square
      Parameters:
      c1Grid - Grid of C1Cartesian Elements
      Returns:
      C1Square Instance

    • Rotation2x2

      public static final C1Square Rotation2x2​(double theta)
      Construct a 2x2 Rotation C1 Matrix
      Parameters:
      theta - The Rotation Angle
      Returns:
      2x2 Rotation C1 Matrix

    • Rotation2x2

      public static final C1Square Rotation2x2​(double theta1, double theta2)
      Construct a 2x2 Rotation C1 Matrix
      Parameters:
      theta1 - The Left Rotation Angle
      theta2 - The Right Rotation Angle
      Returns:
      2x2 Rotation C1 Matrix

    • c1Grid

      public C1Cartesian[][] c1Grid()
      Retrieve C1 Array
      Returns:
      C1 Array

    • size

      public int size()
      Retrieve the Size of the Square Matrix
      Returns:
      Size of the Square Matrix

    • product

      public C1Square product​(C1Square squareMatrixOther)
      Compute the Product with the other Square Matrix
      Parameters:
      squareMatrixOther - "Other" Square Matrix
      Returns:
      Resulting Product

    • transpose

      public C1Cartesian[][] transpose()
      Transpose the Square Matrix
      Returns:
      The Transpose of the Matrix Grid

    • slimContract

      public C1Square slimContract()
      Contract the Square C1Cartesian by one Row/Column
      Returns:
      New C1Square

    • determinant

      public double determinant()
      Determinant of with the "Other"
      Returns:
      The Determinant

    • isUnitDeterminant

      public boolean isUnitDeterminant()
      Indicate if the Determinant is 1
      Returns:
      TRUE - Determinant is 1

    • isUnitary

      public boolean isUnitary()
      Indicate if the Determinant is 1
      Returns:
      TRUE - Determinant is 1

    • product

      public C1Square product​(R1Square r1Square)
      Compute the Product with the other Square Matrix
      Parameters:
      r1Square - R1 Square Matrix
      Returns:
      Resulting Product

    • product

      public C1Square product​(C1Cartesian c1)
      Compute the Product of the Input Matrix and the Complex Number
      Parameters:
      c1 - C1
      Returns:
      The Product C1Square