Package org.ejml.dense.row.misc

Class NaiveDeterminant

java.lang.Object
org.ejml.dense.row.misc.NaiveDeterminant
public class NaiveDeterminant extends Object
Computes the determinant using different very simple and computationally expensive algorithms.

  • Constructor Summary

    Constructors
    Constructor
    Description
    NaiveDeterminant()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    leibniz(org.ejml.data.DMatrixRMaj mat)
    Computes the determinant of the matrix using Leibniz's formula
    static double
    recursive(org.ejml.data.DMatrixRMaj mat)
    A simple and inefficient algorithm for computing the determinant.
    static float
    recursive(org.ejml.data.FMatrixRMaj mat)
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • NaiveDeterminant

      public NaiveDeterminant()

  • Method Details

    • leibniz

      public static double leibniz(org.ejml.data.DMatrixRMaj mat)

      Computes the determinant of the matrix using Leibniz's formula

      A direct implementation of Leibniz determinant equation. This is of little practical use because of its slow runtime of O(n!) where n is the width of the matrix. LU decomposition should be used instead. One advantage of Leibniz's equation is how simplistic it is.

      det(A) = Sum( σ in Sn ; sgn(σ) Prod( i = 1 to n ; ai,σ(i)) )

      • sgn is the sign function of permutations. +1 or -1 for even and odd permutations
      • a set of permutations. if n=3 then the possible permutations are (1,2,3) (1,3,2), (3,2,1), ... etc
      Parameters:
      mat - The matrix whose determinant is computed.
      Returns:
      The value of the determinant

    • recursive

      public static double recursive(org.ejml.data.DMatrixRMaj mat)

      A simple and inefficient algorithm for computing the determinant. This should never be used. It is at least two orders of magnitude slower than DeterminantFromMinor_DDRM. This is included to provide a point of comparison for other algorithms.

      Parameters:
      mat - The matrix that the determinant is to be computed from
      Returns:
      The determinant.

    • recursive

      public static float recursive(org.ejml.data.FMatrixRMaj mat)