edu.princeton.cs.algs4

Class GaussianElimination

java.lang.Object

edu.princeton.cs.algs4.GaussianElimination

public class GaussianElimination
extends java.lang.Object

The GaussianElimination data type provides methods to solve a linear system of equations Ax = b, where A is an m-by-n matrix and b is a length n vector.

This is a bare-bones implementation that uses Gaussian elimination with partial pivoting. See GaussianEliminationLite.java for a stripped-down version that assumes the matrix A is square and nonsingular. See GaussJordanElimination for an alternate implementation that uses Gauss-Jordan elimination. 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
GaussianElimination(double[][] A, double[] b) Solves the linear system of equations Ax = b, where A is an m-by-n matrix and b is a length m vector.

Method Summary

Modifier and Type	Method and Description
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 GaussianElimination 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

GaussianElimination

public GaussianElimination(double[][] A,
                           double[] b)

Solves the linear system of equations Ax = b, where A is an m-by-n matrix and b is a length m vector.

Parameters:

A - the m-by-n constraint matrix

b - the length m right-hand-side vector

Throws:

java.lang.IllegalArgumentException - if the dimensions disagree, i.e., the length of b does not equal m

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

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 GaussianElimination data type.

Parameters:

args - the command-line arguments