# common.py

import numpy as np
from Bar import Bar

def fdm_heat_extraction(t_0, t_1, dx, bar:'Bar', order=2):
    '''Get the heat conduction at the point t_1 using Taylor series'''
    if order == 1:
        return -1 * bar.k * bar.area * (t_1 - t_0) / dx
    elif order == 2:
        return -1 * bar.k * bar.area * (((t_1 - t_0) / dx) + (bar.alpha**2 * dx * t_1 / 2))

def fem_heat_extraction(t_0, t_1, dx, bar:'Bar'):
    '''Get the heat conduction at the point t_1 using FEM equation'''
    term_1 = (-1/dx + bar.alpha**2*dx/6) * t_0
    term_2 = (1/dx + 2*bar.alpha**2*dx/6) * t_1
    return -1 * bar.k * bar.area * (term_1 + term_2)

def calc_error(exact, q_1):
    return np.abs((exact - q_1) / exact)

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

def calc_extrapolated(q1, q2, q3):
    '''Calcs the Richardson Extrapolation value based on 3 different meshes.
    Assumes that q3 is 2x finer than q2 is 2x finer than q1'''
    numerator = q1*q3 - q2**2
    denominator = q1 + q3 - 2*q2
    return numerator / denominator