import numpy as np import matplotlib.pyplot as plt import scipy

import tempfile import os import imageio

1. generate random samples from

def plot_bridge(samples=None, n=1000, dist=scipy.stats.norm, dist_name="normal", low=-3, high=+3):

   fig, axes = plt.subplot_mosaic("ABB", figsize=(20, 6))    ax1 = axes["A"]    ax2 = axes["B"] 

   if samples is None:        samples = dist.rvs(size=n)    else:        n = len(samples)    x = sorted(samples)    y = dist.cdf(x)    ref_x = np.linspace(low,high, 1000)    ref_y = dist.cdf(ref_x) 

   # calculate empirical cdf    ecdf = np.arange(n) / len(samples)    # plot cdf of standard normal distribution and empirical cdf of samples    ax1.plot(ref_x, ref_y, label='Standard CDF')    ax1.plot(x, ecdf, label='Empirical CDF')    ax1.set_title()    ax1.set_xlim(low,high)    ax1.legend()    ax1.set_ylim(0,1)    ax2.plot([0.0] + dist.cdf(x)                        .tolist() + [1.0],              [0.0] + (np.sqrt(n) * (ecdf - dist.cdf(x))).tolist() + [0.0])    ax2.set_title('centered, scaled, and re-timed')    ax2.set_ylim(-0.9, 0.9)    fig.suptitle(f"{dist_name}, with n = {n}")    return fig 

def interpolate_counts(counts, frames_per_step):

   interpolated_counts = [counts[0]]    for i in range(1,len(counts)):        interval = (counts[i] - counts[i-1]) // i        interpolated_counts += list(range(counts[i-1], counts[i], interval))    return interpolated_counts + [counts[-1]] 

with tempfile.TemporaryDirectory() as temp_dir:

   dist = scipy.stats.norm    dist_name = "normal"    low, high = -3.5, +3.5     

   n_steps = 16    frames_per_step = 10    sample_counts = interpolate_counts([2**n for n in range(n_steps)], frames_per_step)    n_frames = len(sample_counts)-1    samples = dist.rvs(size=sample_counts[0]).tolist()        for i in range(n_frames):        samples += dist.rvs(size=sample_counts[i+1]-sample_counts[i]).tolist()        fig = plot_bridge(samples, dist=dist, dist_name=dist_name, low=low,high=high)        filename = os.path.join(temp_dir, f"plot_{i:03d}.png")        fig.savefig(filename)        plt.close(fig) 

   # Compile images into GIF    fps = 12    images = []    for i in range(n_frames):        filename = os.path.join(temp_dir, f"plot_{i:03d}.png")        images.append(imageio.imread(filename))    imageio.mimsave(f"{dist_name} Donsker theorem.gif", images, duration=1/fps)