package edu.princeton.cs.algs4.ch60;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* 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 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/