# common.py

import numpy as np


k = 0.5                 # W / (cm K)
area = np.pi / 100      # cm^2


def taylor_extraction(t_0, t_1, dx, a=0, order=1):
    if order == 1:
        return -1 * k * area * (t_1 - t_0) / dx
    elif order == 2:
        return -1 * k * area * (((t_1 - t_0) / dx) + (a**2 * dx * t_1 / 2))
    
def calc_error(q_exact, q_1):
    return np.abs((q_exact - q_1) / q_exact)

def calc_beta(q_exact, q_1, q_2, dx_1, dx_2):
    return np.log(np.abs((q_exact - q_1)/(q_exact - q_2))) / np.log(dx_1 / dx_2)