# 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))
    elif order == 4:
        return -1 * bar.k * bar.area * ((144*t_1 - 144*t_0 + 72*dx**2*bar.alpha**2*t_1 + 6*dx**4*bar.alpha**4*t_1) / (144 * dx + 24*dx**3 * bar.alpha**2))

def fem_heat_extraction(t_0, t_1, dx, bar:'Bar', order=2):
    '''Get the heat conduction at the point t_1 using FEM equation'''
    if order == 2:
        # term_1 = (-1/dx + bar.alpha**2*dx/6) * t_0
        # term_2 = (1/dx + 2*bar.alpha**2*dx/6) * t_1
        term_1 = (t_1 - t_0) / dx
        term_2  = bar.alpha**2 * dx * t_1 / 2
        return -1 * bar.k * bar.area * (term_1 + term_2)
    elif order == 4:
        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 heat_extraction(t_0, t_1, dx, bar:'Bar', order=2, method="FDM"):
    if method == "FDM":
        return fdm_heat_extraction(t_0, t_1, dx, bar, order)
    elif method == "FEM":
        return fdm_heat_extraction(t_0, t_1, dx, bar, order)

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, tolerance=1e-10):
    '''Calculate Richardson extrapolation, returns NaN if denominator is too small.'''
    numerator = q1 * q3 - q2**2
    denominator = q1 + q3 - 2 * q2
    if abs(denominator) < tolerance:
        return float('NaN')  # Return NaN if denominator is close to zero
    return numerator / denominator