Package org.drip.numerical.matrix

Class R1Triangular

java.lang.Object
org.drip.numerical.matrix.R1Square
org.drip.numerical.matrix.R1Triangular
public class R1Triangular
extends R1Square
R1Triangular implements the type and Functionality associated with an R1 Triangular 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

  • Field Details

    • LOWER_TRIANGULAR

      public static int LOWER_TRIANGULAR
      Lower Triangular Matrix

    • UPPER_TRIANGULAR

      public static int UPPER_TRIANGULAR
      Upper Triangular Matrix

    • LOWER_AND_UPPER_TRIANGULAR

      public static int LOWER_AND_UPPER_TRIANGULAR
      Lower + Upper Triangular Matrix

    • NON_TRIANGULAR

      public static int NON_TRIANGULAR
      Non Triangular Matrix

  • Method Details

    • Type

      public static final int Type​(double[][] r2Array)
      Retrieve the Triangular Type of the Matrix
      Parameters:
      r2Array - R2 Array
      Returns:
      The Triangular Type

    • Standard

      public static R1Triangular Standard​(double[][] r2Array)
      R1Triangular Constructor
      Parameters:
      r2Array - R2 Array
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • type

      public int type()
      Retrieve the Matrix Type
      Returns:
      Matrix Type

    • isUpper

      public boolean isUpper()
      Indicate if the Matrix is Upper Triangular
      Returns:
      TRUE - Matrix is Upper Triangular

    • isLower

      public boolean isLower()
      Indicate if the Matrix is Lower Triangular
      Returns:
      TRUE - Matrix is Lower Triangular

    • isDiagonal

      public boolean isDiagonal()
      Indicate if the Matrix is Diagonal
      Returns:
      TRUE - Matrix is Diagonal

    • isTriangularizable

      public boolean isTriangularizable()
      Calculate whether the Matrix is "Triangularizable"
      Overrides:
      isTriangularizable in class R1Square
      Returns:
      TRUE - Matrix is "Triangularizable"

    • isUnitriangular

      public boolean isUnitriangular()
      Indicate if the Matrix is Unitriangular
      Returns:
      TRUE - Matrix is Unitriangular

    • isUnit

      public boolean isUnit()
      Indicate if the Matrix is "Unit" Triangular
      Returns:
      TRUE - Matrix is "Unit" Triangular

    • isNormed

      public boolean isNormed()
      Indicate if the Matrix is "Normed" Triangular
      Returns:
      TRUE - Matrix is "Normed" Triangular

    • isUpperUnitriangular

      public boolean isUpperUnitriangular()
      Indicate if the Matrix is Upper Unitriangular
      Returns:
      TRUE - Matrix is Upper Unitriangular

    • isLowerUnitriangular

      public boolean isLowerUnitriangular()
      Indicate if the Matrix is Lower Unitriangular
      Returns:
      TRUE - Matrix is Lower Unitriangular

    • isStrictlyUpper

      public boolean isStrictlyUpper()
      Indicate if the Matrix is Strictly Upper Triangular
      Returns:
      TRUE - Matrix is Strictly Upper Triangular

    • isStrictlyLower

      public boolean isStrictlyLower()
      Indicate if the Matrix is Strictly Lower Triangular
      Returns:
      TRUE - Matrix is Strictly Lower Triangular

    • isAtomicLower

      public boolean isAtomicLower()
      Indicate if the Matrix is Lower "Atomic" Unitriangular
      Returns:
      TRUE - Matrix is Lower "Atomic" Unitriangular

    • isAtomicUpper

      public boolean isAtomicUpper()
      Indicate if the Matrix is Upper "Atomic" Unitriangular
      Returns:
      TRUE - Matrix is Upper "Atomic" Unitriangular

    • isAtomic

      public boolean isAtomic()
      Indicate if the Matrix is "Atomic" Unitriangular
      Returns:
      TRUE - Matrix is "Atomic" Unitriangular

    • isFrobenius

      public boolean isFrobenius()
      Indicate if the Matrix is Frobenius Unitriangular
      Returns:
      TRUE - Matrix is Frobenius Unitriangular

    • isGauss

      public boolean isGauss()
      Indicate if the Matrix is Gauss Unitriangular
      Returns:
      TRUE - Matrix is Gauss Unitriangular

    • isGaussTransformation

      public boolean isGaussTransformation()
      Indicate if the Matrix is Gauss Transformation Unitriangular
      Returns:
      TRUE - Matrix is Gauss Transformation Unitriangular

    • determinant

      public double determinant() throws java.lang.Exception
      Compute the Determinant of the Triangular Matrix
      Overrides:
      determinant in class R1Square
      Returns:
      Determinant of the Triangular Matrix
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • permanent

      public double permanent() throws java.lang.Exception
      Compute the Permanent of the Triangular Matrix
      Returns:
      Permanent of the Triangular Matrix
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • eigenValueMultiplicityMap

      public java.util.Map<java.lang.Double,​java.lang.Integer> eigenValueMultiplicityMap()
      Retrieve the Eigenvalue Multiplicity Map
      Overrides:
      eigenValueMultiplicityMap in class R1Square
      Returns:
      Eigenvalue Multiplicity Map

    • conditionNumberLInfinity

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

    • characteristicPolynomial

      public R1ToR1 characteristicPolynomial()
      Retrieve the Characteristic Polynomial of the Eigenvalues
      Overrides:
      characteristicPolynomial in class R1Square
      Returns:
      Characteristic Polynomial of the Eigenvalues