Function bisection

solutions.py:6–52

Calculate the root of an equation by the Bisection method. Args: f (function): equation f(x). a (float): lower limit. b (float): upper limit. toler (float): tolerance (stopping criterion). iter_max (int): maximum number of iterations (stopping criterion).

(f, a, b, toler, iter_max)

def bisection(f, a, b, toler, iter_max):
    """Calculate the root of an equation by the Bisection method.

    Args:
        f (function): equation f(x).
        a (float): lower limit.
        b (float): upper limit.
        toler (float): tolerance (stopping criterion).
        iter_max (int): maximum number of iterations (stopping criterion).

    Returns:
        root (float): root value.
        iter (int): number of iterations used by the method.
        converged (boolean): flag to indicate if the root was found.
    """
    fa = f(a)
    fb = f(b)

    if fa * fb > 0:
        raise ValueError("The function does not change signal at \
              the ends of the given interval.")

    delta_x = math.fabs(b - a) / 2

    x = 0
    converged = False
    for i in range(0, iter_max + 1):
        x = (a + b) / 2
        fx = f(x)

        print(f"i = {i:03d},\tx = {x:+.4f},\t", end="")
        print(f"fx = {fx:+.4f},\tdx = {delta_x:+.4f}")

        if delta_x <= toler and math.fabs(fx) <= toler:
            converged = True
            break

        if fa * fx > 0:
            a = x
            fa = fx
        else:
            b = x

        delta_x = delta_x / 2

    root = x
    return root, i, converged


def secant(f, a, b, toler, iter_max):