Implementing Gauss Seidel iterative method on C++ - c++

Question

I am trying to implement the Gauss seidel Iterative method in C++. i have a very messy code because i am still learning. for some reason my while loop seems to run without implementing the loop at all. I cannot get do while to work either.
The test matrix im using is
number of equations=2
x[0][0]=4
x[0][1]=2
x[1][0]=1
x[1][1]=3
b[0][0]=1
b[1][0]=-1
accuracy=0.2
the loop should continue until K has become less than accuracy.
The results should be;
x1=0.4583
x2= 0.4681
(i printed the F matrix just to make sure that part was working correct)
k=0.136
iterations performed=2
Again sorry for the messy code, like i said i am still learning.
Also i've tested the maths on separate codes and it works perfectly.
int main()
{
int n,i,j,p=0,l=0;
cout<<"Enter number of Equations = ";
cin>>n;
double a[n][n],b[n-1][1],F[n-1][1],x[n-1][1],T[n-1][1],e,k,B,C;
cout<<"[a].[x]=[b]"<<endl;
cout<<"Enter Matrix a:"<<endl;
for(i=0;i<n;i++)
for(j=0;j<n;j++)
{
cout<<"a["<<i<<","<<j<<"] = ";
cin>>a[i][j];
}
cout<<"Enter Matrix b:"<<endl;
for(j=0;j<n;j++)
{
cout<<"b[0,"<<j<<"] = ";
cin>>b[0][j];
}
cout<<"Enter the Accuracy = ";
cin>>e;
for (i=0;i<n;i++){
T[i][0]=0;
}
for(i=0;i<n;i++){
x[i][0]=0;
}
for(i=0;i<n;i++){
F[i][0]=0;
}
while (k>=e){
C=0;
p=p+1;
k=0;
for(i=0;i<n;i++){
B=0;
T[i][0]=(b[i][0]/a[i][i]);
C=a[i][i];
for (j = 0; j < n; j++) {
if (j!=i)
B=B+(a[i][j])*(x[j][0]);
}
x[i][0]=T[i][0]-(B/C);
}
cout<<x[0][0]<<endl;
cout<<x[1][0]<<endl;
for(i=0;i<n;i++)
{
for(j=0;j<n;j++){
F[i][0]=F[i][0]+(a[i][j]*x[j][0]);
}
}
for(i=0;i<n;i++){
F[i][0]=(F[i][0]-b[i][0]);
}
for(i=0;i<n;i++){
k=k+((F[i][0])*F[i][0]);
}
k=sqrt(k);
}
for (i=0;i<n;i++){
cout<<"x"<<i+1<<"="<<x[i][0]<<endl;}
cout<<"number of iterations used: "<<p<<endl;
for (i=0;i<n;i++){
cout<<"F"<<i+1<<"="<<F[i][0]<<endl;}
cout<<"k="<<k<<endl;
return 0;
}
Edit: i tried giving k an initial value and that goes infinitely and the pro gram crashes.
Heres are a run down.
The 3 important Matrixes are a,x and b.
ax=b
each row is changed into an equation and solved for x(i) with initial value for all the position in matrix x to be 0.
after completing this for all values in matrix x the accuracy "k" is checked by function: ax-b=matrix F, All values of F are then squared, added and under root to get k which is checked against e.
the results are:
x1=0
x2=0
number of iterations used: 0
F1=0
F2=0
k=2.96439e-323

Answer 1

First please note that the method you implement is the Jacobi iterative method, not Gauss-Seidel method.
There were several issues in your code:
k was not initialized: it must me set to a large value before the while loop, and set to 0 prior the calculation inside this loop
Some vectors were not initialized at the good size: n-1 instead of n
The F[.] vector should be reset to 0 at each iteration, not only at the start of the program
Moreover, I made some other modifications
I replaced variable length arrays (not C++) by std::vector
I replace [n][1] arrays by [n] vectors
I tried to avoid some i, j global variables
Here is a working code:
#include <iostream>
#include <cmath>
#include <vector>
using std::cin, std::cout;
int main() {
int n, p = 0;
cout << "Enter number of equations = ";
cin >> n;
double e , k, C;
std::vector<double> b(n), F(n, 0), x(n, 0), T(n, 0);
std::vector<std::vector<double>> a(n, std::vector<double> (n));
cout << "[a].[x]=[b]" << "\n";
cout << "Enter Matrix a:" << "\n";
for (int i = 0;i < n; i++) {
for(int j = 0; j < n; j++) {
cout << "a[" << i << ","<< j << "] = ";
cin >> a[i][j];
}
}
cout << "Enter Vector b:" << "\n";
for(int j = 0; j < n; j++)
{
cout << "b[" << j << "] = ";
cin >> b[j];
}
cout << "Enter the Accuracy = ";
cin >> e;
k = 1e10;
while (k >= e){
p = p + 1;
for (int i = 0; i < n; i++) {
double B = 0;
T[i] = b[i]/a[i][i];
C = a[i][i];
for (int j = 0; j < n; j++) {
if (j!=i)
B += a[i][j] * x[j];
}
x[i] = T[i]-B/C;
}
cout << x[0] << "\n";
cout << x[1] << "\n";
for (int i = 0; i < n; i++)
{
F[i] = 0.0;
for (int j = 0; j < n; j++){
F[i] = F[i] + a[i][j]*x[j];
}
}
for (int i = 0; i < n; i++){
F[i] = F[i]-b[i];
}
k = 0.0;
for (int i = 0;i < n;i++) {
k += F[i] * F[i];
}
k = std::sqrt(k);
}
cout << "Solution :\n";
for (int i = 0; i < n; i++){
cout << "x" << i << "=" << x[i] << "\n";
}
cout << "number of iterations used: " << p <<"\n";
for (int i = 0; i< n; i++){
cout <<"F" << i << "=" << F[i] << "\n";
}
cout << "Final error = " << k << "\n";
return 0;
}