Jacobi Iteration in numerical methods

Question

In the following code I implemented Jacobi iteration. My code right now runs through $25$ iterations. If I wanted to change it to just run through one iteration how would I do that? Would I need to change my jacobi function?

from pprint import pprint
from numpy import array, zeros, diag, diagflat, dot

def jacobi(A,b,N=25,x=None):
    """Solves the equation Ax=b via the Jacobi iterative method."""
    # Create an initial guess if needed                                                                                                                                                            
    if x is None:
        x = zeros(len(A[0]))

    # Create a vector of the diagonal elements of A                                                                                                                                                
    # and subtract them from A                                                                                                                                                                     
    D = diag(A)
    R = A - diagflat(D)

    # Iterate for N times                                                                                                                                                                          
    for i in range(N):
        x = (b - dot(R,x)) / D
    return x

A = array([[2.0,1.0],[5.0,7.0]])
b = array([11.0,13.0])
guess = array([1.0,1.0])

sol = jacobi(A,b,N=25,x=guess)

print ("A:")
pprint(A)

print ("b:")
pprint(b)

print ("x:")
pprint(sol)

Answer 1

Nothing, just call the function jacobi with a different argument

sol = jacobi(A, b, N = 1, x = guess)

This should give you

A:
array([[2., 1.],
       [5., 7.]])
b:
array([11., 13.])
x:
array([5.        , 1.14285714])