from matplotlib import pyplot as plt
import numpy as np

def f(x):
    return x**2

"""calculate normal at x"""
def get_normal(f, x):
    dx = 0.05
    dy = f(x+dx)-f(x)
    length = (dx**2+dy**2)**0.5
    return dy/length,-dx/length

"""generate size # of points in range lower to upper"""
def generate_points(f, lower, upper, size):
    xs = lower + (upper-lower) * np.random.sample(size)
    return xs, [f(x) for x in xs]

"""
apply noise on the x,y points (both are lists).
size denotes the intensity of noise, should be trialed
f is the function, needed for calculating the normal
"""
def apply_noise(f, x, y, size):
    xs = []
    ys = []
    for point in zip(x,y):
        dx, dy = get_normal(f, point[0])
        xs.append(point[0]+dx*size*np.random.randn(1))
        ys.append(point[1]+dy*size*np.random.randn(1))
    return xs, ys

if __name__=='__main__':
    x, y = generate_points(f, 0, 1, 100) # generate points
    plt.scatter(x, y, color='b') # plot in blue
    x, y = apply_noise(f, x, y, 0.08) # apply noises
    plt.scatter(x, y, color='r') # plot in red