import numpy as np
import matplotlib.pyplot as plt

# number of points
num_points = 300

# For the sample data
# Input
x = []
# Output
y = []

# Answer values
x_ans = [i * 0.01 for i in range(-200, 200)]
W_ans = 0.1

# Generate normal random values for input and output
for i in range(num_points):
    _x = np.random.normal(0.0, 0.55)
    _y = W_ans * _x + np.random.normal(0.0, 0.03)

    x.append(_x)
    y.append(_y)

# Draw input, output and answer line
plt.plot(x, y, "ro")
plt.plot(x_ans, [W_ans * _x for _x in x_ans], label="W=0.1")
plt.xlabel("X")
plt.ylabel("Y")
plt.legend()
plt.title("y = 0.1 * x")
plt.show()

# For the Mean Square Error
# Weight from 0 to 0.2
W = [i * 0.001 for i in range(0, 200)]
# Cost
cost = []

for w in W:
    # hypothesis = W * x
    hypo = [w * _x for _x in x]
    diffSqrt = 0

    for i in range(num_points):
        _hypo = hypo[i]
        _y = y[i]

        # sum((W * x - y)^2)
        diffSqrt = diffSqrt + (_hypo - _y)**2

    # 1 / m * sum(W * x - y)^2
    cost.append(1 / (len(W)) * diffSqrt)

# Draw cost function
plt.plot(W, cost)
plt.title("Cost Function")
plt.xlabel("W")
plt.ylabel("Cost(W)")
plt.show()