log_compare.py

#!/usr/bin/env python3.7

from typing import Callable

import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from functools import partial


def ext_log_barrier_quadra_2(t, z):
    if z <= - 1 / t**2:
        return - np.log(-z) / t
    else:
        return t * z**2 + - np.log(-1 / t**2) / t - 1 / t**3


def ext_log_barrier_quadra(t, z):
    if z <= - 1 / t:
        return - np.log(-z) / t
    else:
        return t * z**2 - np.log(1/t) / t - 1 / t


def ext_log_barrier(t, z):
    if z <= - 1 / t**2:
        return - np.log(-z) / t
    else:
        return t * z + -np.log(1 / (t**2)) / t + 1 / t


def log_barrier(t, z):
    if z <= - 1 / t**2:
        return - np.log(-z) / t
    else:
        return t * z + -np.log(1 / (t**2)) / t + 1 / t


def quadratic(z):
    return np.maximum(z, 0) ** 2


def relu(z):
    return np.maximum(z, 0)


if __name__ == "__main__":
    v_penalty: Callable = np.vectorize(quadratic)
    v_relu: Callable = np.vectorize(relu)

    matplotlib.rc('font', **{'size': 12})
    matplotlib.rc('text', usetex=True)

    xs: np.ndarray = np.linspace(-2, 2, 2000, dtype=np.float32)
    plt.plot(xs, v_penalty(xs), label='$f$ = Quadratic')
    plt.plot(xs, v_relu(xs), label='$f$ = ReLU')
    for t in []:
        v_barrier = np.vectorize(partial(ext_log_barrier, t))
        plt.plot(xs, v_barrier(xs), label=f'Extended Log-barrier (t={t})')
    plt.plot([0, 0], [0, 100], linewidth=1, color='gray', linestyle='--')
    plt.plot([-100, 0], [0, 0], linewidth=1, color='gray', linestyle='--')
    plt.xlabel('$z$')
    plt.ylabel('$f(z)$', rotation=0)
    plt.ylim(-1, 5)
    plt.xlim(-2, 2)
    plt.legend(loc='upper left')
    plt.show()