STHB - 3 months ago 12

C++ Question

I'm making a function for doing the Jacobian Method. My problem is that my iterations are supposed to let the x vector elements converge to 1s, however instead of 1s the x vector elements in my functions just become 'nan's ?

`void Jacobi(int n, double (* A)[20], double * b, double * x)`

{

double sum[20];

double xnext[20];

cout << "sum" << endl;

for (int i = 0 ; i < 20 ; i++)

{

sum[i]=0;

cout << sum[i]<<endl;

}

cout << endl;

cout << endl;

cout << "xnext" << endl;

for (int i = 0 ; i < 20 ; i++)

{

xnext[i]=0;

cout << xnext[i]<< endl;

}

//iterations loop

for (int iter = 0 ; iter < n ; iter++)

{

for (int i = 0; i < 20 ; i++)

{

sum[i] = 0;

for (int j = 0 ; j < 20 ; j++)

{

if (i != j)

sum[i] = sum[i] + (A[i][j] * x[j]) ;

}

xnext[i] = (1/A[i][i])*(b[i]-sum[i]);

}

cout << endl;

cout << "xnext "<< iter <<endl;

for(int i= 0; i < 20 ; i++)

{

x[i]=xnext[i];

cout << x[i]<< endl;

}

}

cout << endl;

cout << "New x vector" << endl;

for (int i = 0 ; i < 20 ; i++)

{

cout << x[i] << endl;

}

return;

}

Answer

It is almost right, but there are some problems.

The matrix A is not initialized correctly. The main diagonal is filled in with 2.0. However, the code that fills the next closest diagonals with -1.0 goes out of bounds when i is 19. Furthermore, none of the other elements of A are initialized. This leads to the following changes:

```
// initialize everything to zero
memset(A[0], 0, 20*20*sizeof(double));
// set elements for main three diagonals
for (int i = 0 ; i< 19; ++i)
{
A[i][i] = 2.0;
A[i][i+1] = -1.0;
A[i+1][i] = -1.0;
}
// set last element
A[19][19] = 2.0;
```

The next change is to the Jacobi method itself. `xnext[i] = (1.0/A[i][i])*(b[i] - sum[i]);`

is the correct formula for the next x. However, the next line replaces `xnext`

with the delta between the iterates. After increasing the number of iterations to 600, the resulting vector ended up being pretty close to what Octave came up for a solution.