Reproducing Random Numbers in Matlab and Python / NumPy

TLDR:

• rand: works the same in Matlab and Python / NumPy
• randn: use randn2.m and randn2.py provided in this repository to create the same samples in Matlab and Python

Uniform Distribution (rand)

Current versions of Matlab and NumPy use the same random number generator. Thus, it is easy to create the same samples from a uniform distribution.

Matlab:

rng(22); % seed
samples = rand(1, 5);
disp(samples);
% Output: 0.2085    0.4817    0.4205    0.8592    0.1712

Python / NumPy:

import numpy as np
np.random.seed(22)
samples = np.random.rand(5)
print(samples)
# Output: [ 0.20846054  0.48168106  0.42053804  0.859182    0.17116155 ]

Standard Normal Distribution (randn)

Unfortunately, Matlab and NumPy use different transformations to create samples from the standard normal distribution. Thus, we need our own implementation that uses the same transformation in both Matlab and Python / NumPy. For example, we can use inverse transform sampling.

Matlab:

rng(22); % seed
samples = rand(1, 5);
% transform from uniform to standard normal distribution using inverse cdf
samples = sqrt(2) * erfinv(2 * samples - 1);
disp(samples);
% Output: -0.8118   -0.0459   -0.2005    1.0767   -0.9496

Python / NumPy:

import numpy as np
from scipy.special import erfinv
np.random.seed(22)
samples = np.random.rand(5)
# transform from uniform to standard normal distribution using inverse cdf
samples = np.sqrt(2) * erfinv(2 * samples - 1)
print(samples)
# Output: [-0.81177443 -0.04593492 -0.20051725  1.07665147 -0.94958511]

For convenience, this repository provides two files, randn2.m and randn2.py, which can be used as a drop-in replacement for randn.

Matlab:

rng(22); % seed
samples = randn2(1, 5);
disp(samples);
% Output: -0.8118   -0.0459   -0.2005    1.0767   -0.9496

Python / NumPy:

import numpy as np
np.random.seed(22)
samples = np.random.randn2(5)
print(samples)
# Output: [-0.81177443 -0.04593492 -0.20051725  1.07665147 -0.94958511]

---

Compare this to the standard implementations of randn, which yield different results in Matlab and Python / NumPy.

Matlab:

rng(22); % seed
samples = randn(1, 5);
disp(samples);
% Output: -1.1193   -0.0729   -0.2847    1.5111   -1.5112

Python / NumPy:

import numpy as np
np.random.seed(22)
samples = np.random.randn(5)
print(samples)
# Output: [-0.09194992 -1.46335065  1.08179168 -0.23932517 -0.49112914]