Datasets:
Formats:
csv
Languages:
English
Size:
100K - 1M
Tags:
research-artifact
synthetic-data
mathematical-proofs
system-identification
inverse-problems
nonlinear-dynamics
License:
| #!/usr/bin/env python3 | |
| """Scientific figure from saved data and explicitly labeled analytic geometry.""" | |
| from pathlib import Path | |
| import csv | |
| import numpy as np | |
| import matplotlib | |
| matplotlib.use("Agg") | |
| import matplotlib.pyplot as plt | |
| ROOT=Path(__file__).resolve().parents[1] | |
| with (ROOT/"data/nonlinear/distance_grid_queries.csv").open() as f: | |
| grid=list(csv.DictReader(f)) | |
| with (ROOT/"results/nonlinear_drift_summary.csv").open() as f: | |
| drift=list(csv.DictReader(f)) | |
| plt.rcParams.update({"font.size":10,"axes.spines.top":False,"axes.spines.right":False, | |
| "axes.titlesize":11,"figure.dpi":160,"pdf.fonttype":42}) | |
| fig,axs=plt.subplots(2,2,figsize=(10.2,7.8),layout="constrained") | |
| blue,red,orange="#216785","#B64842","#C07819" | |
| t=np.linspace(0,2*np.pi,501) | |
| ax=axs[0,0] | |
| ax.fill(np.cos(t),np.sin(t),color=blue,alpha=.15,label="Disk: all interior points") | |
| ax.plot(np.cos(t),np.sin(t),color=red,lw=2,label="Circle: boundary only") | |
| ax.scatter([0],[0],s=30,color=blue) | |
| ax.set(aspect="equal",xlabel="Output 1",ylabel="Output 2", | |
| title="A Identical linear supports, different sets") | |
| ax.legend(loc="upper right",fontsize=8) | |
| ax=axs[0,1];r=np.linspace(0,1.5,401) | |
| ax.plot(r,(r-1)**2,color=red,label="Circle") | |
| ax.plot(r,np.maximum(r-1,0)**2,color=blue,label="Disk") | |
| ax.plot(r,np.maximum.reduce([np.sqrt(.02)-r,r-1,np.zeros_like(r)])**2, | |
| "--",color=orange,label="Annulus, hole radius 0.141") | |
| ax.set(xlabel="Target distance from center",ylabel="Minimum squared mismatch", | |
| title="B Quadratic probes reveal missing points") | |
| ax.legend(fontsize=8) | |
| ax=axs[1,0] | |
| sel=[x for x in grid if x["shape"]=="circle" and float(x["delta"])==.001 and x["selected"]=="1"] | |
| ax.scatter([float(x["u"]) for x in sel],[float(x["v"]) for x in sel],s=2,color=blue,alpha=.5,label="Recovered grid points") | |
| ax.plot(np.cos(t),np.sin(t),color=red,lw=1,label="True circle") | |
| ax.set(aspect="equal",xlabel="Output 1",ylabel="Output 2", | |
| title="C Finite grid with loss noise bound 0.001") | |
| ax.legend(loc="upper right",fontsize=8) | |
| ax=axs[1,1] | |
| rows=sorted([x for x in drift if x["kind"]=="drift" and float(x["delta"])==.0001 | |
| and float(x["timing_bound"])==.00001],key=lambda x:float(x["h"])) | |
| h=[float(x["h"]) for x in rows] | |
| ax.loglog(h,[float(x["drift_error_max"]) for x in rows],"o-",color=blue,label="Largest observed drift error") | |
| ax.loglog(h,[float(x["drift_bound"]) for x in rows],"s--",color=orange,label="Certified upper bound") | |
| ax.set(xlabel="Finite difference step h",ylabel="Euclidean drift error", | |
| title="D Noise and time resolution tradeoff") | |
| ax.grid(True,which="both",alpha=.16);ax.legend(fontsize=8) | |
| fig.savefig(ROOT/"figures/05_nonlinear_geometry.pdf") | |
| fig.savefig(ROOT/"figures/05_nonlinear_geometry.png") | |
| plt.close(fig) | |
| print("Saved nonlinear geometry figure.") | |