import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
plt.style.use("ggplot")
from matplotlib import colors, cm

import os
import pandas as pd
from tensorflow import keras

# plt.rcParams controls the appearance of your plots globally,
# affecting all subsequent plots created in your session.
plt.rcParams["axes.grid"] = False
plt.rcParams.update({'font.size': 20})
plt.rcParams.update({'figure.figsize': (12,9)})
plt.rcParams['lines.markersize'] = 8

# Generate data points with gaussian smearing
data = np.random.uniform(size=100)
labels = 5.*data*data*data + 1 + np.random.normal(loc=0.0, scale=0.1, size=100)
# show plot
plt.scatter(data, labels, label="data")
plt.legend()
plt.show()

# define chi2 like cost function
def cost(params):
    W, b = params
    return np.mean((labels - (W*data*data*data + b))**2)

# call minimizer
# provides a collection of optimization algorithms for finding the minimum o
# maximum of a given function. 
from scipy.optimize import minimize
res = minimize(cost, [1., 1.])
# returns an OptimizeResult object
# x :the solution (minimum) of the optimization problem, represented as an
# array.
# Results of the minimization
W, b = res.x
print ('function value at the minimum and fitted parameters',res.fun,'  ',W,'  ',b)

points = np.linspace(0, 1, 100)
prediction = W*points*points*points + b

# plot fit model
plt.scatter(data, labels, label="data")
plt.plot(points, prediction, label="model", color="green")
plt.legend()
plt.show()