fig_decode_error.py

# decode angle error with N and kappa

import numpy as np
import os
import matplotlib.pyplot as plt
from matplotlib.font_manager import FontProperties


def encode_angle(phi, theta, kappa):
    return np.exp(kappa * np.cos(phi - theta)) / np.exp(kappa)

def decode_angle(F, theta):
    complex_sum = np.sum(F * np.exp(1j * theta))
    return np.angle(complex_sum)

def angle_error_simulation(phi, kappas, N_list):
    """
    Simulate angle error for a range of discrete point numbers N.
    """
    errors = {}
    for kappa in kappas:
        error = []
        for N in N_list:
            pref_theta = np.linspace(0, 2 * np.pi, N, endpoint=False)
            hat_phi = decode_angle(encode_angle(phi, pref_theta, kappa), pref_theta)
            angle_error = np.abs(hat_phi - phi) % np.pi  # Relative to phi
            error.append(angle_error)
        errors[kappa] = np.array(error)
    return errors

if __name__ == "__main__":
    # folder
    project_folder = os.path.dirname(os.path.abspath(__file__))
    data_folder = os.path.join(project_folder, 'data', 'method')
    if not os.path.exists(data_folder):
        os.makedirs(data_folder)

    # Define extended ranges of kappa and phi
    kappa_values = [0.000005, 0.1, 0.5, 1, 2, 4, 10, 50, 100]  # Example kappa values to test concentration effects
    phi_values = 7*np.pi/1000 # Different phi values
    N_list = np.linspace(2, 82, 41)  # Range of discrete point numbers
    N_list = N_list.astype(int)
    errors = angle_error_simulation(phi_values, kappa_values, N_list)

    # Plot results for each combination of kappa and phi
    plt.figure(figsize=(10, 8))
    fontsize = 18
    font = FontProperties()
    font.set_size(fontsize)
    font.set_weight('bold')

    for i, (key, error) in enumerate(errors.items()):
        color_value = plt.cm.viridis(i / len(kappa_values))
        plt.plot(N_list, np.rad2deg(error), marker='o', color=color_value, label=f'$\kappa$ = {key}')
    plt.xlabel('Number of Neuron ($N$)', fontsize=fontsize, fontweight='bold')
    plt.ylabel('Encoded Angle Error (degree)', fontsize=fontsize, fontweight='bold')
    plt.xticks(fontsize=fontsize-1, fontweight='bold')
    plt.yticks(fontsize=fontsize-1, fontweight='bold')
    plt.grid(alpha=0.2)
    plt.legend(loc='upper right', prop=font)

    # save
    fts = {'.png', '.eps'}
    for ft in fts:
        filename = 'angle_error_vs_N' + ft
        plt.savefig(os.path.join(data_folder, filename), dpi=600)
    print('figure saved')