How do I generate Log Uniform Distribution in Python?

From http://ecolego.facilia.se/ecolego/show/Log-Uniform%20Distribution:

In a loguniform distribution, the logtransformed random variable is assumed to be uniformly distributed.

Thus

logU(a, b) ~ exp(U(log(a), log(b))

Thus, we could create a log-uniform distribution using numpy:

def loguniform(low=0, high=1, size=None):    return np.exp(np.random.uniform(low, high, size))

If you want to choose a different base, we could define a new function as follows:

def lognuniform(low=0, high=1, size=None, base=np.e):    return np.power(base, np.random.uniform(low, high, size))

EDIT: @joaoFaria's answer is also correct.

def loguniform(low=0, high=1, size=None):    return scipy.stats.reciprocal(np.exp(low), np.exp(high)).rvs(size)

SciPy v1.4 includes a loguniform random variable: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.loguniform.html

Here's how to use it:

from scipy.stats import loguniformrvs = loguniform.rvs(1e-2, 1e0, size=1000)

This will create random variables evenly spaced between 0.01 and 1. That best shown by visualizing the log-scaled histogram:

This "log-scaling" works regardless of base; loguniform.rvs(2**-2, 2**0, size=1000) also produces log-uniform random variables. More details are in loguniform's documentation.

I believe the scipy.stats.reciprocal is the distribution you want.
From the documentation:

The probability density function for reciprocal is:

f(x, a, b) = \frac{1}{x \log(b/a)}

for a <= x <= b and a, b > 0

reciprocal takes a and b as shape parameters.