Value and proximal operators of penalties

Illustrate the value and proximal operators of some sparse penalties.

# Author: Mathurin Massias <mathurin.massias@gmail.com>

import numpy as np
import matplotlib.pyplot as plt

from skglm.penalties import WeightedL1, L1, L1_plus_L2, MCPenalty, SCAD, L0_5, L2_3


penalties = [
    WeightedL1(alpha=1, weights=np.array([2.])),
    L1(alpha=1),
    L1_plus_L2(alpha=1, l1_ratio=0.7),
    MCPenalty(alpha=1, gamma=3.),
    SCAD(alpha=1, gamma=3.),
    L0_5(alpha=1),
    L2_3(alpha=1),
]


x_range = np.linspace(-4, 4, num=300)

fig, axarr = plt.subplots(1, 2, figsize=(8, 3), constrained_layout=True)

for pen in penalties:
    axarr[0].plot(x_range,
                  [pen.value(np.array([x])) for x in x_range],
                  label=pen.__class__.__name__)
    axarr[1].plot(x_range,
                  [pen.prox_1d(x, 1, 0) for x in x_range],
                  label=pen.__class__.__name__)

axarr[0].legend()
axarr[0].set_title("Penalty value")
axarr[1].set_title("Proximal operator of penalty")
plt.show(block=False)