Package org.drip.numerical.matrix

Class R1Square

java.lang.Object
org.drip.numerical.matrix.R1Square
Direct Known Subclasses:
R1SquareEigenized, R1SquareRotation2x2, R1Triangular, R1Tridiagonal
public class R1Square
extends java.lang.Object
R1Square implements the type and Functionality associated with a R1Square Matrix. The References are:

  • Axler, S. J. (1997): Linear Algebra Done Right 2nd Edition Springer New York NY
  • Bernstein, D. S. (2009): Matrix Mathematics: Theory, Facts, and Formulas 2nd Edition Princeton University Press Princeton NJ
  • Herstein, I. N. (1975): Topics in Algebra 2nd Edition Wiley New York NY
  • Prasolov, V. V. (1994): Topics in Algebra American Mathematical Society Providence RI
  • Wikipedia (2024): Triangular Matrix https://en.wikipedia.org/wiki/Triangular_matrix




Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    R1Square add​(R1Square squareMatrixOther)
    Compute the Addition with the other Square Matrix
    R1ToR1 characteristicPolynomial()
    Retrieve the Characteristic Polynomial of the Eigenvalues
    double conditionNumberL2()
    Compute the L2 Condition Number of the Matrix
    double defaultConditionNumber()
    Compute the Default Condition Number of the Matrix
    double determinant()
    Compute the Determinant of the Matrix
    double[] diagonalEntryArray()
    Retrieve the Array of Diagonal Entries
    EigenOutput eigenize()
    Eigenize and Extract the Components of the Specified Matrix
    java.util.Map<java.lang.Double,​java.lang.Integer> eigenValueMultiplicityMap()
    Retrieve the Eigenvalue Multiplicity Map
    boolean isNormal()
    Calculate whether the Matrix is "Normal"
    boolean isTriangularizable()
    Calculate whether the Matrix is "Triangularizable"
    R1Square multiply​(double[] r1Array)
    Compute the Product with the Vector
    R1Square multiply​(R1Square squareMatrixOther)
    Compute the Product with the other Square Matrix
    R1Square power​(int k)
    Compute the kth Power
    QR qrDecomposition()
    Generate the QR Decomposition of the Square Matrix
    double[][] r1Grid()
    Retrieve R1 Grid
    QR rqDecomposition()
    Generate the RQ Decomposition of the Square Matrix
    R1Square scale​(double scale)
    Scale the Square Matrix
    int size()
    Retrieve the Size of the Square Matrix
    double spectralRadius()
    Compute the Spectral Radius of the Matrix
    static R1Square Standard​(double[][] r1Grid)
    Construct a Standard Instance of R1Square
    R1Square subtract​(R1Square squareMatrixOther)
    Compute the Subtraction with the other Square Matrix
    EigenOutput svd()
    Perform Singular Value Decomposition and Extract the Components of the Specified Matrix
    double svdBasedFrobeniusNorm()
    Compute the Frobenius Norm of the Eigenvalues
    double trace()
    Compute the Trace
    R1Square 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 R1Square Standard​(double[][] r1Grid)
      Construct a Standard Instance of R1Square
      Parameters:
      r1Grid - R1 Grid
      Returns:
      Standard Instance of R1Square

    • r1Grid

      public double[][] r1Grid()
      Retrieve R1 Grid
      Returns:
      R1 Grid

    • size

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

    • trace

      public double trace()
      Compute the Trace
      Returns:
      The Trace

    • transpose

      public R1Square transpose()
      Transpose the Square Matrix
      Returns:
      The Transposed Square Matrix

    • add

      public R1Square add​(R1Square squareMatrixOther)
      Compute the Addition with the other Square Matrix
      Parameters:
      squareMatrixOther - "Other" Square Matrix
      Returns:
      Resulting Matrix

    • scale

      public R1Square scale​(double scale)
      Scale the Square Matrix
      Parameters:
      scale - Scalar to Scale by
      Returns:
      Resulting Matrix

    • subtract

      public R1Square subtract​(R1Square squareMatrixOther)
      Compute the Subtraction with the other Square Matrix
      Parameters:
      squareMatrixOther - "Other" Square Matrix
      Returns:
      Resulting Matrix

    • multiply

      public R1Square multiply​(R1Square squareMatrixOther)
      Compute the Product with the other Square Matrix
      Parameters:
      squareMatrixOther - "Other" Square Matrix
      Returns:
      Resulting Matrix

    • multiply

      public R1Square multiply​(double[] r1Array)
      Compute the Product with the Vector
      Parameters:
      r1Array - Vector Array
      Returns:
      Resulting Matrix

    • isNormal

      public boolean isNormal()
      Calculate whether the Matrix is "Normal"
      Returns:
      TRUE - Matrix is "Normal"

    • isTriangularizable

      public boolean isTriangularizable()
      Calculate whether the Matrix is "Triangularizable"
      Returns:
      TRUE - Matrix is "Triangularizable"

    • qrDecomposition

      public QR qrDecomposition()
      Generate the QR Decomposition of the Square Matrix
      Returns:
      QR Decomposition

    • rqDecomposition

      public QR rqDecomposition()
      Generate the RQ Decomposition of the Square Matrix
      Returns:
      RQ Decomposition

    • eigenize

      public EigenOutput eigenize()
      Eigenize and Extract the Components of the Specified Matrix
      Returns:
      The EigenComponents

    • svd

      public EigenOutput svd()
      Perform Singular Value Decomposition and Extract the Components of the Specified Matrix
      Returns:
      The Singular Value Decomposition Components

    • svdBasedFrobeniusNorm

      public double svdBasedFrobeniusNorm() throws java.lang.Exception
      Compute the Frobenius Norm of the Eigenvalues
      Returns:
      Frobenius Norm of the Eigenvalues
      Throws:
      java.lang.Exception - Thrown if the R1 Square Matrix cannot be eigenized

    • diagonalEntryArray

      public double[] diagonalEntryArray()
      Retrieve the Array of Diagonal Entries
      Returns:
      Array of Diagonal Entries

    • power

      public R1Square power​(int k)
      Compute the kth Power
      Parameters:
      k - Power k
      Returns:
      kth Power

    • eigenValueMultiplicityMap

      public java.util.Map<java.lang.Double,​java.lang.Integer> eigenValueMultiplicityMap()
      Retrieve the Eigenvalue Multiplicity Map
      Returns:
      Eigenvalue Multiplicity Map

    • determinant

      public double determinant() throws java.lang.Exception
      Compute the Determinant of the Matrix
      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
      Returns:
      L2 Condition Number of the Matrix
      Throws:
      java.lang.Exception - Thrown if the Condition Number cannot be calculated

    • defaultConditionNumber

      public double defaultConditionNumber() throws java.lang.Exception
      Compute the Default Condition Number of the Matrix
      Returns:
      Default Condition Number of the Matrix
      Throws:
      java.lang.Exception - Thrown if the Default Condition Number cannot be calculated

    • characteristicPolynomial

      public R1ToR1 characteristicPolynomial()
      Retrieve the Characteristic Polynomial of the Eigenvalues
      Returns:
      Characteristic Polynomial of the Eigenvalues

    • spectralRadius

      public double spectralRadius() throws java.lang.Exception
      Compute the Spectral Radius of the Matrix
      Returns:
      Spectral Radius of the Matrix
      Throws:
      java.lang.Exception - Thrown if the Spectral Radius cannot be calculated