import scipy.stats
import numpy as np
import pandas as pd

x = list(range(-10, 11))
y = [0, 2, 2, 2, 2, 3, 3, 6, 7, 4, 7, 6, 6, 9, 4, 5, 5, 10, 11, 12, 14]
x_, y_ = np.array(x), np.array(y)
x__, y__ = pd.Series(x_), pd.Series(y_)

n = len(x)
mean_x, mean_y = sum(x) / n, sum(y) / n
cov_xy = (sum((x[k] - mean_x) * (y[k] - mean_y) for k in range(n))/ (n - 1))

var_x = sum((item - mean_x)**2 for item in x) / (n - 1)
var_y = sum((item - mean_y)**2 for item in y) / (n - 1)
std_x, std_y = var_x ** 0.5, var_y ** 0.5
r = cov_xy / (std_x * std_y)
print("correlation coefficient using pure python: ",r)

######################### scipy.stats.pearsonr() #####################
r= scipy.stats.pearsonr(x_, y_)
print("correlation coefficient using scipy.stats: ",r)

######################## numpy.corrcoef() ################
corr_matrix = np.corrcoef(x_, y_)
print("correlation coefficient matrix using numpy.corrcoef: \n",corr_matrix)

r = corr_matrix[0, 1]
print("correlation coefficient using numpy.corrcoef: ",r)

r = corr_matrix[1, 0]
print("correlation coefficient using numpy.corrcoef: ",r)

#################### using pandas Series #####################
print("correlation coefficient using pandas series objects: ",x__.corr(y__))

print("correlation coefficient using pandas series objects: ",y__.corr(x__))