// 迭代法解線性方程組.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include "iostream.h"
#include "iomanip.h"


int main(int argc, char* argv[])
{
	cout << "  ****************************************" << endl;
    cout << "  **                                    **" << endl;
	cout << "  **         迭代法解線性方程組         **" << endl;
    cout << "  **                                    **" << endl;
	cout << "  ****************************************" << endl << endl;

	double B[4][5]={9,15,3,-2,7,7,2,1,-2,4,1,3,2,13,0,-2,-2,11,5,-1};	//增廣矩陣
	int i,j,k,m;

	//消元過程
	for (i=0;i<2;i++)
	{
		double a;
		a=B[i][i];			
		for (j=i;j<4;j++)
			B[i][j]=B[i][j]/a;
		for (k=i+1;k<3;k++)
		{
			double b;
			b=B[k][i];
			if (b==0)
				continue;
			else
			{
				for (m=i;m<4;m++)
					B[k][m]=B[k][m]-b*B[i][m];
			}
			
		}
	}
	cout << "化簡后的右上三角矩陣為：" << endl;
	for (i=0;i<3;i++)
	{
		cout.setf(ios::left);
		for (j=0;j<4;j++)
			cout << setw(12) << B[i][j];
		cout << endl;
	}
	cout << endl;

	//回代過程
	double X[3];	//方程組的解x1,x2,x3
	for (i=2;i>=0;i--)
	{
		for (j=i+1;j<3;j++)
			B[i][3]=B[i][3]-B[i][j]*X[j];
		X[i]=B[i][3]/B[i][i];
	}
	cout <<  "所求方程組的解為：";
	for (i=0;i<=3;i++)
		cout << "x" << i+1 << "=" << X[i] << ", ";
	cout << endl;
	
	return 0;
}