"""

lectureNote/chapters/chapt04/codes/try_except3.py

try-except example, written by Prof. Dongwook Lee for AM 129/209.

Modified by Ian May, FA2021

"""

import numpy as np

def fdf(x):
    f  = x  + np.exp(x) + 10/(1 + x**2) - 5
    df = 1.0 + np.exp(x) - 20*x/(1 + x**2)**2
    return f,df

def root_finder(func, x0, thresh, MaxIter=100):
    # Put initial guess in list to store history
    x = [x0]
    # Query function at initial guess
    f,df = func(x0)
    res = [abs(f)]
    for i in range(0,MaxIter):
        # Raise error if slope is very flat
        if (abs(df)<1.e-5):
            raise ArithmeticError
        # Newton's iteration
        x.append(x[-1] - f/df)
        # Query function at new guess
        f,df = func(x[-1])
        # Update residual
        res.append(abs(f))
        print(x[-1],f,df)
        # Check for convergence
        if (res[-1] < thresh):
            break
    
    # If final residual is too big we stagnated
    if (res[-1] > thresh):
        raise ArithmeticError

    # Return sequence of guesses and residuals
    return x,res


if __name__ == '__main__':
    # take an initial value as an input from users
    x0 = float(input("Please enter an initial search value: "))
    # take a threshold value as an input from users
    threshold = float(input("Please enter a threshold value: "))
    # Call Newton's method
    try:
        x, res = root_finder(fdf,x0,threshold)
    except ArithmeticError:
        print("Newton's method failed for that initial guess")
    else:
        print("Newton's method converged in %d iterations" % len(x))
        for v,r in zip(x,res):
            print(v, r)