How to sample from a log-uniform distribution.

log_unif_example.py

"""
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')

(July 26) Now log(0.01) to log(0.7) with discretized bins.

Here is a plot which also has nb_classes=5+1 (because nb_classes is really the number of vertical ticks).

For classes, I get:

0.010 <= x < 0.023 count: 1998
0.023 <= x < 0.055 count: 1968
0.055 <= x < 0.128 count: 2020
0.128 <= x < 0.299 count: 2021
0.299 <= x < 0.700 count: 1993

If it's nb_classes=10+1) then we get:

0.010 <= x < 0.015 count: 991
0.015 <= x < 0.023 count: 1034
0.023 <= x < 0.036 count: 1043
0.036 <= x < 0.055 count: 968
0.055 <= x < 0.084 count: 983
0.084 <= x < 0.128 count: 1020
0.128 <= x < 0.196 count: 1051
0.196 <= x < 0.299 count: 1022
0.299 <= x < 0.458 count: 961
0.458 <= x < 0.700 count: 927