package algs91; // section 9.9
import stdlib.*;
/* ***********************************************************************
 *  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 Error("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]);
		}

	}

}