GaussianElimination (Algorithms 4/e)

Object
- edu.princeton.cs.algs4.GaussianElimination

```
public class GaussianElimination
extends 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.
This computes correct results if all arithmetic performed is without floating-point rounding error or arithmetic overflow. In practice, there will be floating-point rounding error; partial pivoting helps prevent accumulated floating-point rounding errors from growing out of control (though it does not provide any guarantees).
For additional documentation, see Section 9.9 Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.

Author:

Robert Sedgewick, 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

All Methods Static Methods Instance Methods Concrete Methods
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(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 Object
clone, equals, finalize, 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:
    
    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(String[] args)
```
    Unit tests the GaussianElimination data type.
    
    Parameters:
    
    args - the command-line arguments