/*
Program: Gauss Elimination Method
All array indexes are assumed to start from 1
*/
#include<iostream>
#include<iomanip>
#include<math.h>
#include<stdlib.h>
#define SIZE 10
using namespace std;
int main()
{
float a[SIZE][SIZE], x[SIZE], ratio;
int i,j,k,n;
/* Setting precision and writing floating point values in fixed-point notation. */
cout<< setprecision(3)<< fixed;
/* Inputs */
/* 1. Reading number of unknowns */
cout<<"Enter number of unknowns: ";
cin>>n;
/* 2. Reading Augmented Matrix */
cout<<"Enter Coefficients of Augmented Matrix: "<< endl;
for(i=1;i<=n;i++)
{
for(j=1;j<=n+1;j++)
{
cout<<"a["<< i<<"]"<< j<<"]= ";
cin>>a[i][j];
}
}
/* Applying Gauss Elimination */
for(i=1;i<=n-1;i++)
{
if(a[i][i] == 0.0)
{
cout<<"Mathematical Error!";
exit(0);
}
for(j=i+1;j<=n;j++)
{
ratio = a[j][i]/a[i][i];
for(k=1;k<=n+1;k++)
{
a[j][k] = a[j][k] - ratio*a[i][k];
}
}
}
/* Obtaining Solution by Back Substitution Method */
x[n] = a[n][n+1]/a[n][n];
for(i=n-1;i>=1;i--)
{
x[i] = a[i][n+1];
for(j=i+1;j<=n;j++)
{
x[i] = x[i] - a[i][j]*x[j];
}
x[i] = x[i]/a[i][i];
}
/* Displaying Solution */
cout<< endl<<"Solution: "<< endl;
for(i=1;i<=n;i++)
{
cout<<"x["<< i<<"] = "<< x[i]<< endl;
}
return(0);
}
