| """Exact theorem illustrations; no simulated or empirical values are plotted.""" |
| from pathlib import Path |
| from math import comb |
| import numpy as np |
| import matplotlib |
| matplotlib.use('Agg') |
| import matplotlib.pyplot as plt |
|
|
| plt.rcParams.update({'font.family':'DejaVu Sans', 'font.size':11, |
| 'axes.spines.top':False, 'axes.spines.right':False, |
| 'axes.labelcolor':'#182832', 'text.color':'#182832'}) |
| fig, axes = plt.subplots(1, 2, figsize=(9.4, 3.75), layout='constrained') |
| n, rank, lam, mu = 8, 3, 1., .15 |
| widths = np.arange(n+1) |
| pointwise = np.array([lam]*rank+[mu]*(n-rank)+[0.]) |
| global_error = np.array([lam]*n+[0.]) |
| axes[0].plot(widths, global_error, 's-', color='#A44865', lw=2, ms=5, label='Continuous global family') |
| axes[0].plot(widths, pointwise, 'o-', color='#156D72', lw=2, ms=5, label='Pointwise factors') |
| axes[0].set(xlabel='Fixed complex output coordinates, m', ylabel='Optimal worst-case energy error', |
| title='(a) n = 8, r = 3, λ = 1, μ = 0.15', xticks=[0,2,3,4,6,8], ylim=(-.04,1.15)) |
| axes[0].legend(fontsize=9, loc='center', bbox_to_anchor=(.5,.6), frameon=False) |
| axes[0].grid(axis='y', alpha=.2) |
| ranks = np.arange(1,n) |
| minimal = ranks*(n-ranks)+1 |
| coordinate = [comb(n,int(r)) for r in ranks] |
| axes[1].plot(ranks, coordinate, 'o-', color='#A44865', lw=2, ms=5, label='Coordinate atlas') |
| axes[1].plot(ranks, minimal, 's-', color='#156D72', lw=2, ms=5, label='Minimum fixed-reference atlas') |
| axes[1].set(xlabel='Subspace rank, r', ylabel='Number of fixed reference frames', |
| title='(b) Exact atlas counts for n = 8', xticks=ranks, ylim=(0,80)) |
| axes[1].legend(fontsize=9, loc='upper left', frameon=False) |
| axes[1].grid(axis='y',alpha=.2) |
| fig.savefig(Path(__file__).with_name('FIGURE_01.png'),dpi=300,facecolor='white') |
| plt.close(fig) |
|
|
