Class MatrixMeasure

java.lang.Object
dev.nm.algebra.linear.matrix.doubles.operation.MatrixMeasure

public class MatrixMeasure extends Object
A measure, μ, of a matrix, A, is a map from the Matrix space to the Real line. That is,
μ: A -> R
  • Constructor Summary

    Constructors
    Constructor
    Description
     
  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    Compute the determinant of a matrix.
    static double
    Compute the Frobenius norm, i.e., the sqrt of the sum of squares of all elements of a matrix.
    static double
    Compute the maximal entry in a matrix.
    static double
    Compute the minimal entry in a matrix.
    static int
    Deprecated.
    Not supported yet.
    static int
    Compute the numerical rank of a matrix.
    static int
    rank(Matrix A, double epsilon)
    Compute the numerical rank of a matrix.
    static double
    Compute the sum of the diagonal elements, i.e., the trace of a matrix.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Constructor Details

    • MatrixMeasure

      public MatrixMeasure()
  • Method Details

    • rank

      public static int rank(Matrix A, double epsilon)
      Compute the numerical rank of a matrix. Ignore all singular values smaller than a threshold.
      Parameters:
      A - a matrix
      epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
      Returns:
      the numerical rank of A
      See Also:
    • rank

      public static int rank(Matrix A)
      Compute the numerical rank of a matrix. Ignore all singular values less than a threshold.
      Parameters:
      A - a matrix
      Returns:
      the numerical rank of A
    • nullity

      @Deprecated public static int nullity(Matrix A)
      Deprecated.
      Not supported yet.
      Compute the nullity of a matrix.
      Parameters:
      A - a matrix
      Returns:
      the nullity of A
      See Also:
    • det

      public static double det(Matrix A)
      Compute the determinant of a matrix.
      Parameters:
      A - a matrix
      Returns:
      the determinant of A
      See Also:
    • tr

      public static double tr(Matrix A)
      Compute the sum of the diagonal elements, i.e., the trace of a matrix.
      Parameters:
      A - a matrix
      Returns:
      the trace of A
      See Also:
    • Frobenius

      public static double Frobenius(Matrix A)
      Compute the Frobenius norm, i.e., the sqrt of the sum of squares of all elements of a matrix.
      Parameters:
      A - a matrix
      Returns:
      the sqrt of sum of squares of all elements in A
      See Also:
    • max

      public static double max(Matrix A)
      Compute the maximal entry in a matrix.
      Parameters:
      A - a matrix
      Returns:
      the maximal entry
    • min

      public static double min(Matrix A)
      Compute the minimal entry in a matrix.
      Parameters:
      A - a matrix
      Returns:
      the minimal entry