"""
How we might sample from a log-uniform distribution
https://stats.stackexchange.com/questions/155552/what-does-log-uniformly-distribution-mean

Only run one of these three cases at a time, otherwise the plots update each
other. Run with these versions:

matplotlib      3.2.1
numpy           1.18.3
"""
import numpy as np
import matplotlib.pyplot as plt
np.set_printoptions(suppress=True, linewidth=200, edgeitems=10)
low = 0.01
high = 0.7
size = 10000
nb_bins = 50

if False:
    data = np.random.uniform(low=low, high=high, size=size)
    count, bins, ignored = plt.hist(data, bins=nb_bins, align='mid')
    plt.title('Uniform({}, {})'.format(low, high))
    plt.xlabel('Epsilon')
    plt.savefig('distr_uniform.png')

if False:
    data = np.random.uniform(low=np.log(low), high=np.log(high), size=size)
    count, bins, ignored = plt.hist(data, bins=nb_bins, align='mid')
    plt.title('Uniform(log({}), log({})'.format(low, high))
    plt.xlabel('Epsilon')
    plt.savefig('distr_uniform_log.png')

# Number of classes are the number of intervals.
nb_classes = 5 + 1

if True:
    data = np.random.uniform(low=np.log(low), high=np.log(high), size=size)
    discretized = np.linspace(np.log(low), np.log(high), num=nb_classes)
    data = np.exp(data)
    count, bins, ignored = plt.hist(data, bins=nb_bins, align='mid')
    plt.title('exp( Uniform(log({}), log({}) )'.format(low, high))
    plt.xlabel('Epsilon')
    plt.savefig('distr_uniform_log_true.png')

    # Now let's add dicretized ranges.
    print('Discretized bounds (len {}) for epsilons:\nLog: {}\nNormal: {}'.format(
            len(discretized), discretized, np.exp(discretized)))
    for idx,item in enumerate(discretized):
        plt.axvline(x=np.exp(item), color='black')
        if idx < len(discretized) - 1:
            start = np.exp(discretized[idx])
            end = np.exp(discretized[idx+1])
            count = np.sum( (start <= data) & (data < end) )
            print('{:.3f} <= x < {:.3f} count: {}'.format(start, end, count))
    plt.savefig('distr_uniform_log_true_bounds.png')