I'm running a bit of code whose purpose is to take a list/array of floats and an associated list/array of the same length acting as an "error" and shuffle the first list around according to a Gaussian distribution.
This is a MWE of the code:
import random
import numpy as np
def random_data(N, a, b):
# Generate some random data.
return np.random.uniform(a, b, N).tolist()
# Obtain values for x.
x = random_data(100, 0., 1.)
# Obtain error/sigma values for x.
x_sigma = random_data(100, 0., 0.2)
# Generate new x values shuffling each float around a
# Gaussian distribution with a given sigma.
x_gauss = random.gauss(np.array(x), np.array(x_sigma))
print x-x_gauss
What I find is that the result of doing x-x_gauss is a list of floats that is always either positive or negative. This means the random.gauss call is always assigning either a larger new value for each float in x or a smaller one for all values in x.
I would expect the random.gauss call to shuffle the floats in x around its values both to the right and to the left, since this is a random process.
Why is this not happening? Am I understanding something wrong about the process?
This is the definition of random.gauss:
def gauss(self, mu, sigma):
random = self.random
z = self.gauss_next
self.gauss_next = None
if z is None:
x2pi = random() * TWOPI
g2rad = _sqrt(-2.0 * _log(1.0 - random()))
z = _cos(x2pi) * g2rad
self.gauss_next = _sin(x2pi) * g2rad
return mu + z*sigma
Notice that is is generating one value for z, and returning mu + z*sigma. Since mu and sigma are numpy arrays, this calculation is being done element-wise. Since sigma is positive, the shift z*sigma is either always positive or negative, depending on the sign of z
If you are using NumPy, unless there is a specific reason to do otherwise, I would use the np.random module to generate these values. It would be quicker than using a Python loop with calls to random.gauss:
import numpy as np
N = 100
x = np.random.uniform(0., 1., size=N)
x_sigma = np.random.uniform(0., 0.2, size=N)
z = np.random.normal(0, 1, size=N)
x_gauss = x + z*x_sigma
print x-x_gauss
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