import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

class RandomNumberGenerator:
    def __init__(self, num):
        self.num = num

    def uniform_sample(self, lb=0, ub=1):
        return np.random.uniform(low=lb, high=ub, size=self.num)

    def normal_sample(self, mu=0, sigma=1):
        return np.random.normal(loc=mu, scale=sigma, size=self.num)

    def laplace_dist(self, mu, b, method='inverse', const=5):

        def inverse(x, mu, b):
            return mu - b*np.sign(x-0.5)*np.log(1-2*abs(x-0.5))

        def target(x, mu, b):
            return 1/(2*b)*np.exp(-abs(x-mu)/b)

        def proposal_normal(x, mu=0, sigma=1):
            return 1/(np.sqrt(2*np.pi)*sigma)*np.exp(-0.5*(x-mu)**2/sigma**2)

        if method is 'inverse':
            u = self.uniform_sample(lb=0, ub=1)
            sample = inverse(u, mu, b)
            return sample

        elif method is 'reject':
            x = self.normal_sample(mu, b)
            gx = proposal_normal(x, 0, 1)
            U = self.uniform_sample(lb=0, ub=const*gx)
            fx = target(x, mu, b)
            sample = x[fx >= U]
            return sample

if __name__ == '__main__':
    rng = RandomNumberGenerator(num=1000000)

    try_list = [[0, 1, 0.1], [0, 2, 0.1], [0, 4, 0.1], [-5, 4, 0.1], [0, 4, 0.5]]
    for item in try_list:
        mu, b, const = item[0], item[1], item[2]
        sample = rng.laplace_dist(mu, b, method='reject', const=const)

        sns.distplot(sample)

    k = ['μ = ' + str(item[0]) + ', b = ' + str(item[1]) + ', const = ' + str(item[2]) for item in try_list]
    plt.legend(k, fontsize=20)
    plt.title('Random Number Generator', fontsize=20)
    plt.show()