Gauss-Seidel method to compute 3 systems of linear equations - c++

Question

My assignment to develop a program to compute 3 systems of linear equations: the program must allow the user to input the coefficients and constants, number of iterations and level of acceptable error. I can't seem to include both the number of iterations and level of error as parameters to stop the loop and show the final values of the variables. Here's what I have so far:
#include <iostream>
#include <windows.h>
using namespace std;
int main()
{
cout<<"Welcome. This is Problem 1. "<<endl;
cout<<"computing systems of three linear equations through gauss-seidel method"<<endl;
float coefEqxn1[3];
for (int x=0; x<3;)
{
for ( int eq1=1; eq1<=3; eq1++)
{
cout<<"Please enter Coefficient " <<eq1<< " of equation 1 : ";
cin>>coefEqxn1[x];
x++;
}
}
float coefEqxn2[3];
for (int x=0; x<3;)
{
for ( int eq2=1; eq2<=3; eq2++)
{
cout<<"Please enter Coefficient " <<eq2<<" of equation 2 :" ;
cin>>coefEqxn2[x];
x++;
}
}
float coefEqxn3[3];
for (int x=0; x<3;)
{
for ( int eq3=1; eq3<=3; eq3++)
{
cout<<"Please enter Coefficient "<<eq3<<" of equation 3 :";
cin>>coefEqxn3[x];
x++;
}
}
float constants[3];
for (int y=0; y<3;)
{
for (int con=1; con<=3; con++)
{
cout<<"Please enter the contant of equation "<<con<<" : ";
cin>>constants[y];
y++;
}
}
cout<<"Calculating through Cramer's Rule..."<<endl;
int iteration=0;
cout<<"enter # iteration"<<endl;
cin>>iteration;
int stopC=0;
cout<<"enter level of error"<<endl;
cin>>stopC;
float matrixArray[3][4];
{
for ( int y=0; y<3;)
{
for (int x=0; x<=3;x++)
matrixArray[0][y]=coefEqxn1[y];
y++;
}
matrixArray[0][3]=constants[0];
for ( int y=0; y<3;)
{
for (int x=0; x<=3;x++)
matrixArray[1][y]=coefEqxn2[y];
y++;
}
matrixArray[1][3]=constants[1];
for ( int y=0; y<3;)
{
for (int x=0; x<=3;x++)
matrixArray[2][y]=coefEqxn3[y];
y++;
}
matrixArray[2][3]=constants[2];
}
for(int a=0; a<3; a++)
{
for(int b=0; b<=3; b++)
cout<<"matrixArray["<<a<<"]["<<b<<"]: "<<matrixArray[a][b]<<endl;
}
float valueOfX[100], valueOfY[100], valueOfZ[100];
for( int i=1; i<iteration; )
{
valueOfX[0]=0, valueOfY[0]=0, valueOfZ[0]=0;
valueOfX[i]=(matrixArray[0][3]-(matrixArray[0][2]*valueOfZ[i-1]+matrixArray[0][1]*valueOfY[i-1]))/matrixArray[0][0];
valueOfY[i]=(matrixArray[1][3]-(matrixArray[1][2]*valueOfZ[i-1]+matrixArray[1][0]*valueOfX[i]))/matrixArray[1][1];
valueOfZ[i]=(matrixArray[2][3]-(matrixArray[2][1]*valueOfY[i]+matrixArray[2][0]*valueOfX[i]))/matrixArray[2][2];
float reX=0, reY=0, reZ=0;
reX=((valueOfX[i+1]-valueOfX[i])/valueOfX[i+1])*100;
reY=((valueOfY[i+1]-valueOfY[i])/valueOfY[i+1])*100;
reX=((valueOfZ[i+1]-valueOfZ[i])/valueOfZ[i+1])*100;
if (reX<=inputErrorLevel)
break;
if (reY<=inputErrorLevel)
break;
if (reZ<=inputErrorLevel)
break;
cout<<"reX = "<<reX<<endl;
cout<<"reY = "<<reY<<endl;
cout<<"reY = "<<reX<<endl;
i++;
}
cout<<"x = "<<valueOfX[iteration-1]<<endl;
cout<<"y = "<<valueOfY[iteration-1]<<endl;
cout<<"z = "<<valueOfZ[iteration-1]<<endl;
}

Answer 1

Based on what you want you should have something like
double inputErrorLevel; //Read from user input
// The for loop guarantees that the loop will run at max iteration times.
// Noticed I changed it to start from zero otherwise it will only run
// iteration -1 times
for( int i=0; i<iteration; ++i )
{
//Do heavy computation stuff.
double currentErrorLevel = ComputeErrorAtCurrentIteration();
if ( currentErrorLevel < inputErrorLevel )
break; // break will ensure more iterations are not done
// if error level is acceptable
}
Typical programming practice is to to
for ( int i = 0 ; i < 5; ++i )
{
}
instead of
for ( int i = 0 ; i < 5; )
{
++i;
}

Answer 2

This looks like a typo?
reX=((valueOfZ[i+1]-valueOfZ[i])/valueOfZ[i+1])*100;
Shouldn't that be:
reZ=((valueOfZ[i+1]-valueOfZ[i])/valueOfZ[i+1])*100;
Same here:
cout<<"reY = "<<reX<<endl;
But to answer your question this should be using i to index the results not iteration. iteration variable is going to always be constant so it will always give that result regardless of error.
Like:
cout<<"x = "<<valueOfX[i-1]<<endl;
cout<<"y = "<<valueOfY[i-1]<<endl;
cout<<"z = "<<valueOfZ[i-1]<<endl;