Datasets:
Formats:
csv
Languages:
English
Size:
< 1K
Tags:
mathematics
homogenization
spectral-theory
variational-methods
matrix-analysis
scientific-computing
| #!/usr/bin/env python3 | |
| """Rebuild both final-release figures from the recorded datasets.""" | |
| from pathlib import Path | |
| import json | |
| import subprocess | |
| import sys | |
| import numpy as np | |
| import matplotlib | |
| matplotlib.use('Agg') | |
| import matplotlib.pyplot as plt | |
| ROOT=Path(__file__).resolve().parents[1] | |
| subprocess.run([sys.executable,str(ROOT/'code/make_supporting_figures.py')],check=True) | |
| c=json.loads((ROOT/'results/critical.json').read_text()) | |
| nx=json.loads((ROOT/'results/nexus_uniform.json').read_text()) | |
| plt.rcParams.update({'font.family':'DejaVu Sans','font.size':9, | |
| 'axes.spines.top':False,'axes.spines.right':False}) | |
| fig,axes=plt.subplots(3,1,figsize=(6.3,7.3),constrained_layout=True) | |
| taus=np.logspace(-1,5,400) | |
| for j,color in [(1,'#136d87'),(2,'#67499c')]: | |
| axes[0].semilogx(taus,taus/(taus+(2*np.pi*j)**2),color=color,label=f'Frequency j={j}') | |
| axes[0].set_xlabel(r'Critical ratio $\tau=\rho/n^2$') | |
| axes[0].set_ylabel(r'$D_{\tau,jj}$');axes[0].set_title('Exact critical frequency filter') | |
| axes[0].legend(fontsize=8) | |
| for case,color in zip([q for q in c['cases'] if q['kind']=='mixed'],['#136d87','#67499c','#9b425a','#7c7f34']): | |
| axes[1].loglog([r['n'] for r in case['rows']], | |
| [r['relative_error_to_effective_response'] for r in case['rows']], | |
| 'o-',ms=4,color=color,label=r'$\tau='+str(int(case['tau']))+'$') | |
| axes[1].set_xlabel(r'Spatial frequency $n$');axes[1].set_ylabel('Relative response error') | |
| axes[1].set_title('Full mixed-matrix model approaches the critical law') | |
| axes[1].legend(fontsize=8,ncol=2) | |
| for strength,label,color in [(0.,'No added port','#136d87'),(1e8,r'$\lambda=10^8$','#67499c'),('infinity','Hard constraint','#9b425a')]: | |
| rows=[r for r in nx['rows'] if r['kind']=='balanced' and r['strength']==strength and 'check' not in r] | |
| axes[2].semilogx([r['epsilon'] for r in rows],[r['scaled_capacity'] for r in rows], | |
| 'o-',ms=4,color=color,label=label) | |
| axes[2].axhline(3,color='#17243c',ls='--',lw=1) | |
| axes[2].invert_xaxis();axes[2].set_xlabel(r'Twist strength $\varepsilon$') | |
| axes[2].set_ylabel(r'$\kappa/\varepsilon$');axes[2].set_title('Balanced ports share one leading capacity') | |
| axes[2].legend(fontsize=8,ncol=3) | |
| for ax in axes:ax.grid(alpha=.15) | |
| out=ROOT/'figures';out.mkdir(exist_ok=True) | |
| fig.savefig(out/'critical_results.pdf');fig.savefig(out/'critical_results.png',dpi=180) | |
| print(out/'critical_results.pdf') | |