# GaussianElimination.java

Below is the syntax highlighted version of GaussianElimination.java from §9.5 Numerical Solutions to Differential Equations.

```/******************************************************************************
*  Compilation:  javac GaussianElimination.java
*  Execution:    java GaussianElimination
*
*  Gaussian elimination with partial pivoting.
*
*  % java GaussianElimination
*  -1.0
*  2.0
*  2.0
*
******************************************************************************/

public class GaussianElimination {
private static final double EPSILON = 1e-10;

// Gaussian elimination with partial pivoting
public static double[] lsolve(double[][] A, double[] b) {
int n = b.length;

for (int p = 0; p < n; p++) {

// find pivot row and swap
int max = p;
for (int i = p + 1; i < n; i++) {
if (Math.abs(A[i][p]) > Math.abs(A[max][p])) {
max = i;
}
}
double[] temp = A[p]; A[p] = A[max]; A[max] = temp;
double   t    = b[p]; b[p] = b[max]; b[max] = t;

// singular or nearly singular
if (Math.abs(A[p][p]) <= EPSILON) {
throw new ArithmeticException("Matrix is singular or nearly singular");
}

// pivot within A and b
for (int i = p + 1; i < n; i++) {
double alpha = A[i][p] / A[p][p];
b[i] -= alpha * b[p];
for (int j = p; j < n; j++) {
A[i][j] -= alpha * A[p][j];
}
}
}

// back substitution
double[] x = new double[n];
for (int i = n - 1; i >= 0; i--) {
double sum = 0.0;
for (int j = i + 1; j < n; j++) {
sum += A[i][j] * x[j];
}
x[i] = (b[i] - sum) / A[i][i];
}
return x;
}

// sample client
public static void main(String[] args) {
int n = 3;
double[][] A = {
{ 0, 1,  1 },
{ 2, 4, -2 },
{ 0, 3, 15 }
};
double[] b = { 4, 2, 36 };
double[] x = lsolve(A, b);

// print results
for (int i = 0; i < n; i++) {
StdOut.println(x[i]);
}

}

}
```

Copyright © 2000–2017, Robert Sedgewick and Kevin Wayne.
Last updated: Fri Oct 20 14:12:12 EDT 2017.