Documentation of 'edu.princeton.cs.algs4.GaussJordanElimination' Java class
GaussJordanElimination
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edu.princeton.cs.algs4

Class GaussJordanElimination


  • public class GaussJordanElimination
extends java.lang.Object
    The GaussJordanElimination data type provides methods to solve a linear system of equations Ax = b, where A is an n-by-n matrix and b is a length n vector. If no solution exists, it finds a solution y to yA = 0, yb ≠ 0, which which serves as a certificate of infeasibility.

    This implementation uses Gauss-Jordan elimination with partial pivoting. See GaussianElimination for an implementation that uses Gaussian elimination (but does not provide the certificate of infeasibility). For an industrial-strength numerical linear algebra library, see JAMA.

    For additional documentation, see Section 9.9 Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

    • Constructor Summary

      Constructors 
      Constructor and Description
      GaussJordanElimination(double[][] A, double[] b)
      Solves the linear system of equations Ax = b, where A is an n-by-n matrix and b is a length n vector.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double[] dual()
      Returns a solution to the linear system of equations yA = 0, yb ≠ 0.
      boolean isFeasible()
      Returns true if there exists a solution to the linear system of equations Ax = b.
      static void main(java.lang.String[] args)
      Unit tests the GaussJordanElimination data type.
      double[] primal()
      Returns a solution to the linear system of equations Ax = b.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • GaussJordanElimination

        public GaussJordanElimination(double[][] A,
                              double[] b)
        Solves the linear system of equations Ax = b, where A is an n-by-n matrix and b is a length n vector.
        Parameters:
        A - the n-by-n constraint matrix
        b - the length n right-hand-side vector

    • Method Detail

      • primal

        public double[] primal()
        Returns a solution to the linear system of equations Ax = b.
        Returns:
        a solution x to the linear system of equations Ax = b; null if no such solution

      • dual

        public double[] dual()
        Returns a solution to the linear system of equations yA = 0, yb ≠ 0.
        Returns:
        a solution y to the linear system of equations yA = 0, yb ≠ 0; null if no such solution

      • isFeasible

        public boolean isFeasible()
        Returns true if there exists a solution to the linear system of equations Ax = b.
        Returns:
        true if there exists a solution to the linear system of equations Ax = b; false otherwise

      • main

        public static void main(java.lang.String[] args)
        Unit tests the GaussJordanElimination data type.
        Parameters:
        args - the command-line arguments
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