src/run_experiments.py

"""Reproduce deterministic research figures and raw tables (not hardware data)."""
from pathlib import Path
import sys,json,csv
import numpy as np
from scipy.linalg import eigh
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from aelyrion import MirrorState,chain,density_optimum,coherence_witness,complete_frame,polynomial_graph

ROOT=Path(__file__).resolve().parents[1]
OUT=ROOT/'results';FIG=ROOT/'figures'
OUT.mkdir(exist_ok=True);FIG.mkdir(exist_ok=True)

def save(name):
    plt.tight_layout()
    plt.savefig(FIG/(name+'.pdf'),bbox_inches='tight')
    plt.savefig(FIG/(name+'.png'),dpi=170,bbox_inches='tight')
    plt.close()

def table(name,header,rows):
    with open(OUT/(name+'.csv'),'w',newline='') as f:
        w=csv.writer(f);w.writerow(header);w.writerows(rows)

n=20;b=chain(n);rho,lam=density_optimum(b,float(n));j=np.arange(1,n+1)
plt.figure(figsize=(6.7,3.6));plt.plot(j,rho,'o-',label='Globally optimal density');plt.plot(j,np.ones(n),'--',label='Uniform density')
plt.xlabel('Residual index j');plt.ylabel('Density (budget = 20)');plt.legend();save('density_profile')
table('density_profile',['j','optimal_density','uniform_density'],zip(j,rho,np.ones(n)))

rows=[]
for n in range(2,101):
    b=chain(n);rr,ll=density_optimum(b,float(n));un=eigh(b.T@b,eigvals_only=True)[0]
    rows.append((n,ll,un,ll/un))
rows=np.array(rows)
plt.figure(figsize=(6.7,3.6));plt.loglog(rows[:,0],rows[:,1],label='Best allocation, exact');plt.loglog(rows[:,0],rows[:,2],'--',label='Uniform allocation')
plt.xlabel('Number of hidden modes');plt.ylabel('Slowest relaxation rate');plt.legend();save('chain_scaling')
table('chain_scaling',['n','optimal_rate','uniform_rate','rate_ratio'],rows)

q=2.;b=np.array([[1.,0],[-q,1.]])
rhos=[1.,.1,.01,.001,0.];s=np.logspace(-7,1,240)
plt.figure(figsize=(6.7,3.6));cusp=[]
for r in rhos:
    st=MirrorState(b,[[1],[0]],np.diag([1.,r]),[[1.]])
    vals=[float(((st.response(z)-st.S)/z)[0,0].real) for z in s]
    plt.semilogx(s,vals,label=f'rho = {r:g}')
    cusp.extend((r,z,y) for z,y in zip(s,vals))
plt.xlabel('Positive Laplace parameter s');plt.ylabel('(Y(s) - S) / s');plt.legend();save('rank_cusp')
table('rank_cusp',['rho','s','normalized_boundary_departure'],cusp)

hierarchy=[]
for r in range(2,8):
    f=complete_frame(r);n=len(f);o=coherence_witness(f,1.)
    val=np.trace(o['C']@o['X']).real
    hierarchy.append((r,n,int(np.linalg.matrix_rank(o['X'],tol=1e-8)),val,1/val))
plt.figure(figsize=(6.7,3.6));plt.plot([x[1] for x in hierarchy],[x[2] for x in hierarchy],'o-')
plt.xlabel('Ambient hidden modes n = 2r^2 - r');plt.ylabel('Unique optimal certificate rank r');save('coherence_hierarchy')
table('coherence_hierarchy',['r','n','verified_rank','dual_optimum','rate_for_budget_one'],hierarchy)

n=12;b=chain(n);rho,lam=density_optimum(b,n);e=np.eye(n)[:,:1]
t=np.linspace(0,350,220);init=np.zeros(n)
su=MirrorState(b,e,np.eye(n),[[1]]);so=MirrorState(b,e,np.diag(rho),[[1]])
# Use the respective worst-mode initial error, so the plotted decay is exact rate decay.
plt.figure(figsize=(6.7,3.6));lu=eigh(su.A,eigvals_only=True)[0]
plt.semilogy(t,np.exp(-lu*t),label='Uniform: worst-mode error');plt.semilogy(t,np.exp(-lam*t),label='Optimal: worst-mode error')
plt.xlabel('Dimensionless time');plt.ylabel('Normalized worst-mode error');plt.legend();save('relaxation')
table('relaxation',['time','uniform_worst_error','optimal_worst_error'],zip(t,np.exp(-lu*t),np.exp(-lam*t)))

rho0=1.;T=2.;t=np.linspace(0,T,200);rr=rho0*(1-t/T)**2
integral=rho0*T/3*(1-(1-t/T)**3);z=np.exp(-integral)
plt.figure(figsize=(6.7,3.6));plt.plot(t,rr,label='Collapsing density');plt.plot(t,z,label='Remaining residual amplitude')
plt.xlabel('Time');plt.ylabel('Normalized value');plt.legend();save('collapse_freeze')
table('collapse_freeze',['time','density','residual'],zip(t,rr,z))

terms=[(2,(0,0,1)),(-3,(1,2)),(1,()),(.5,(2,2,2))]
b,e,f=polynomial_graph(terms,[.5,1/3,.25]);value=(f@np.linalg.solve(b,e))[0,0]
summary={'seed_policy':'All plotted data are deterministic; randomized tests fix seed per test.',
 'polynomial_value':float(value.real),'polynomial_exact':'355/384','polynomial_modes':len(b),
 'chain_20_optimal_rate':float(6*20/(20*21*41)),
 'chain_20_uniform_rate':float(eigh(chain(20).T@chain(20),eigvals_only=True)[0]),
 'chain_100_rate_ratio':float(rows[-1,3]),
 'cusp_positive_density_slope':5.,'cusp_zero_density_slope':1.,
 'collapse_final_residual':float(z[-1]),'physical_measurements':0,'pytest_cases':90}
(OUT/'experiment_summary.json').write_text(json.dumps(summary,indent=2))
print(json.dumps(summary,indent=2))