// GaussianElimination.java
// David Kosbie, 15-111/AB, Spring 2007

/*
Standard disclaimer:  As usual with sample code designed in
class to demonstrate specific issues, the style may not be perfect
(it is especially lacking comments and some top-down design, and as we've
not yet reviewed classes, it's lacking those, too!), and there may
even be a bug or two lurking in the code!

To understand the algorithm used here, please see the class notes
from today's lecture (31-Jan-2007).  They contain a detailed explanation.

*/

import java.util.*;

public class GaussianElimination {

	// This is the problem we solved in class
	private static double[][] problem1 = {
		// x = 1, y = 2, z = 3
		{ 1,  2, 3, 14 },  // 1x + 2y + 3z = 14
		{ 1, -1, 1,  2 },  // 1x - 1y + 1z = 2
		{ 4, -2, 1,  3 }   // 4x - 2y + 1z = 3
	};

	// This is the problem solved in the lecture notes
	private static double[][] problem2 = {
		// x = 1, y = 2, z = 3
		{ 2,  3, -4, -4 },  // 2x + 3y - 4z = -4
		{ 1, -2,  1,  0 },  // 1x - 2y + 1z =  0
		{-1,  1,  2,  7 }   // -1x + 1y + 2z = 7
	};
	
	public static void solve(double[][] c, int row) {
		int rows = c.length;
		int cols = rows + 1;
		// 1. set c[row][row] equal to 1
		double factor = c[row][row];
		for (int col=0; col<cols; col++)
			c[row][col] /= factor;
		
		// 2. set c[row][row2] equal to 0
		for (int row2=0; row2<rows; row2++)
			if (row2 != row) {
				factor = -c[row2][row];
				for (int col=0; col<cols; col++)
					c[row2][col] += factor * c[row][col];
			}
	}
	
	public static void solve(double[][] c) {
		int rows = c.length;
		for (int row=0; row<rows; row++)
			solve(c,row);
	}
	
	public static void print(double[][] c) {
		int rows = c.length;
		int cols = rows + 1;
		for (int row=0; row<rows; row++) {
			for (int col=0; col<cols; col++)
				System.out.printf("%5.1f ",c[row][col]);
			System.out.println();
		}
		System.out.println();
	}
	
	public static void printSolution(double[][] c) {
		int rows = c.length, cols = rows + 1;
		char variable = (char)((rows > 3) ? ('z' - (rows-1)) : 'x');
		System.out.println("Solution:\n");
		for (int row=0; row<rows; row++)
			System.out.printf("  %c = %1.1f\n",(char)variable++,c[row][cols-1]);
		System.out.println();
	}

	public static void doProblem(double[][] problem, String description) {
		System.out.printf("******* %s ********\n",description);
		System.out.println("Original Equations:");
		print(problem);
		solve(problem);
		System.out.println("Solved (reduced row echelon form):");
		print(problem);
		printSolution(problem);
	}

	public static void main(String[] args) {
		doProblem(problem1,"Problem 1 (from class)");
		doProblem(problem2,"Problem 2 (from lecture notes)");
	}
}