"""
Exercise 5.18 from "A primer on..." fit a polynomial
to the data read from file in Ex. 5.16, using
the NumPy functions polyfit and poly1d.
"""

import matplotlib.pyplot as plt
import numpy as np

#import the function we wrote in exercise 5.16:
from read_density_data import read_density_file

#a)
def fit(x, y, deg):
    for d in deg:
        coeff = np.polyfit(x, y, d)
        p = np.poly1d(coeff)

        y_fitted = p(x)
        plt.plot(x,y_fitted,label=f'deg={d}')
    plt.plot(x, y,'ro', label='data')
    plt.legend()
    plt.show()


#b)
if __name__ == '__main__':
    temp, dens = read_density_file('density_water.txt')
    fit(temp, dens, [1,2])

    """
    Terminal> python fit_density_data.py 
    (output is a plot)
    """