Inroduction

import matplotlib.pyplot as plt
import numpy as np
import torch 
import pandas as pd
# Retina mode
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

first_4_chars = "appl"

probs = np.zeros(27) # 26 letters + space (EOS)

# Store i to s
itos = list("abcdefghijklmnopqrstuvwxyz ")

# stoi 
stoi = {char: i for i, char in enumerate(itos)}

# Fill in the probabilities
probs[stoi["a"]] = 0.1
probs[stoi["e"]] = 0.3
probs[stoi["i"]] = 0.2
probs[stoi["o"]] = 0.1
probs[stoi["u"]] = 0.05
probs[stoi[" "]] = 0.05

probability_distribution = torch.distributions.Categorical(torch.tensor(probs))

sample = probability_distribution.sample()
print(f"Sampled character: {itos[sample]}")

Sampled character: a

samples_numpy = np.random.uniform(0, 1, 1000)
print(samples_numpy[:10])
plt.hist(samples_numpy)

[0.18872185 0.29419573 0.05307716 0.4139927  0.80335078 0.64528118
 0.4575413  0.76490687 0.53933945 0.3135855 ]

(array([100.,  86., 105.,  99., 102.,  90., 105., 106., 104., 103.]),
 array([0.00367548, 0.10305437, 0.20243325, 0.30181214, 0.40119103,
        0.50056992, 0.59994881, 0.6993277 , 0.79870659, 0.89808548,
        0.99746437]),
 <BarContainer object of 10 artists>)

class SimplePRNG:
    def __init__(self, seed=42):
        # Initialize the generator with a seed
        self.modulus = 2**31 - 1  # Large prime modulus
        self.multiplier = 1664525
        self.increment = 1013904223
        self.state = seed

    def uniform(self, low=0.0, high=1.0, size=None):
        # Generate random numbers in the range [low, high)
        if size is None:
            size = 1  # Default to a single number if size is None
        if isinstance(size, int):
            size = (size,)  # Convert size to tuple

        # Generate random numbers
        random_numbers = np.empty(size)
        for idx in np.ndindex(size):
            self.state = (self.multiplier * self.state + self.increment) % self.modulus
            random_numbers[idx] = low + (high - low) * (self.state / self.modulus)

        return random_numbers 

# Example usage:
prng = SimplePRNG(seed=12345)
print(prng.uniform(0, 1, 50))  

[0.04080538 0.04087837 0.54709049 0.26713204 0.42986223 0.90642683
 0.59240588 0.8643601  0.45993872 0.96243078 0.56511522 0.88322526
 0.98992417 0.00597593 0.55550726 0.19979239 0.90062773 0.84657695
 0.96436855 0.03375009 0.34428985 0.54191328 0.67693687 0.81460587
 0.30590164 0.39907677 0.73545432 0.56768856 0.26844794 0.78549411
 0.06020346 0.63806449 0.76347271 0.89276656 0.72407304 0.15397659
 0.35789549 0.46641842 0.58988864 0.86842092 0.80445417 0.54725703
 0.48183308 0.68513887 0.24797944 0.44857785 0.52156459 0.77294949
 0.22528635 0.23579403]

samples_our_prng = prng.uniform(0, 1, 1000)

plt.hist(samples_our_prng)

(array([ 96.,  94., 101.,  98.,  92.,  97., 107., 129.,  81., 105.]),
 array([0.00156537, 0.10117911, 0.20079286, 0.30040661, 0.40002035,
        0.4996341 , 0.59924785, 0.69886159, 0.79847534, 0.89808909,
        0.99770283]),
 <BarContainer object of 10 artists>)