Task 2 - root_simple unable to find root for tanh(x)

[WildJimmy]

I'm having some issues with task 2. I can't get root_simple to find the roots of tanh(x) when given a positive initial guess. It will always exceed the maximum number of steps. However, for negative guesses it is fine. Any ideas on how to resolve this without changing the algorithm? I'm a little confused because tan and tanh have roughly the same behavior around x = 0 and I do not have this issue with finding the roots of tan

[tirthbha]

@WildJimmy Which method have you adopted to find the roots?

[WildJimmy]

I'm using methods from the rootfinding.py file, specifically here I'm referring to root_simple

def root_simple(f, x, dx, accuracy=1.0e-6, max_steps=1000, root_debug=False):
    """Return root of f(x) given guess x and step dx with specified accuracy.
    Step must be in direction of root: dx must have same sign as (root - x).
    """
    f0 = f(x)
    fx = f0
    step = 0
    iterations = []
    if root_debug:        
        root_print_header("Simple Search with Step Halving", accuracy)
        root_print_step(step, x, dx, f0)
        iterations.append([x,f0])
    while abs(dx) > abs(accuracy) and f0 != 0.0:
        x += dx
        fx = f(x)
        if f0 * fx < 0.0:   # stepped past root
            x -= dx         # step back
            dx /= 2.0       # use smaller step
        step += 1
        if step > max_steps:
            root_max_steps("root_simple", max_steps)
        if root_debug:
            root_print_step(step, x, dx, fx)
            iterations.append([x,fx])
    return x,np.array(iterations)

[tirthbha]

@WildJimmy In my opinion, the tanh function's behavior near x = 0 is indeed similar to tan, but the critical difference is in their asymptotic behavior for large positive and negative x, which impacts the effectiveness of the root_simple method.

[WildJimmy]

I'm not sure. I have to do some better debugging, but since all root simple checks is the function's distance from 0 I don't understand what's appreciably different about tan and tanh, given that the guess is reasonably close to 0... Unless using it for tan has been finding the root NOT at x = 0, but at pi or something... I should check that

[tirthbha]

@WildJimmy I used Bisection and Newton-Raphson methods to get roots, they worked.

[tirthbha]

@WildJimmy Have you sorted out the issue with the root_simple method?

[LinxuanHu]

did you fidured it out?

[s4il3sh]

tanh(x) has only one root that is zero.