If/break test for convergence triggering too early in python

Question

I'm trying to use an if statement to check when the approximated values converge, but it keeps returning that it converges after 2 iterations, which it shouldn't since removing the if-break statement and setting it to 1000 iterations gets very different values.

def Jacobi2D(U,xrange,yrange,order):
    Up=sym.zeros(len(xrange),len(yrange))
    for k in range(1,order):
        if k>=2 and U==Up:
            print('Approximation converges after',k,'iterations')
            break
        Up=U #Save the U of the previous iteration for use in the formula
        for i in range(1,len(xrange)-1):
            for j in range(1,len(yrange)-1):
                U[i,j]=Up[i,j]+(1/4)*(Up[i+1,j]+Up[i-1,j]+Up[i,j+1]+Up[i,j-1]-4*Up[i,j])
                continue
            continue
        continue
    return U

The function takes U as a matrix with dimensions (len(xrange),len(yrange)) and 'order' is how many iterations you want the approximation to go through. Does anyone know why the condition is being triggered before redefining Up=U? Any help would be appreciated, thank you!

Just FYI, you don't need a [`continue`](https://docs.python.org/3/reference/simple_stmts.html#continue) statement at the end of every `for` loop. — MattDMo, Oct 26 '20 at 18:54

Jace · Answer 1 · 2020-10-26T19:39:55.217

0

Your condition will break when k >= 2 and when U == Up. On the second iteration, k = 2 and you set Up = U, so U == Up. Therefore, your loop will always break on the second iteration as it satisfies the conditions.

I might suggest a different condition for convergence: track the difference between the previous approximation and this iteration's approximations. Once the difference is smaller than some target precision (say epsilon = 0.0000001), break and return.

EDIT: The problem has to do with the Up = U pointing both variables to the same object so that changes in either object change the other object as well. You can resolve this by replacing Up = U with Up = U.copy().

edited Oct 26 '20 at 19:39

answered Oct 26 '20 at 18:52

Jace

177
6

But I redefine U in the 2 for loops within the k loop, so why is it not waiting to redefine Up till after the if statement? – Scott Oct 26 '20 at 19:28
Maybe it has to do with the `==` here? I just ran a test comparing a `Up` of all zeros to a `U` of all 1s with `U == Up` and it is returning `true`. – Jace Oct 26 '20 at 19:36
Nevermind. It has to do with references to the same object. Your `U` is pointing to the same object as your `Up`, so editing `U` edits `Up` as well. You should use `Up = U.copy()`. Editing my answer to reflect that. – Jace Oct 26 '20 at 19:38

If/break test for convergence triggering too early in python

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