| """Checks the new polynomial-jet implementation and local rank diagnostics. |
| |
| Finite rank tests are not a proof/certificate of a projection's global injectivity. |
| The universal projection and CAD existence claims rely on manuscript proofs. |
| """ |
| from pathlib import Path |
| import json,time |
| import numpy as np |
| import sympy as sp |
| from exact_inverse import layer_product,moments |
| from jet_compression import jets_from_layers,draw_projection,complex_step_jacobian |
|
|
| ROOT=Path(__file__).resolve().parents[1] |
| rng=np.random.default_rng(260926);start=time.time() |
| max_jet_error=0.;cases=0 |
| for r in [1,2,3,4]: |
| for repeat in range(5): |
| cs=[sp.Rational(int(rng.integers(2,7)),2) for _ in range(r)] |
| ts=[sp.Rational(int(rng.integers(1,5)),8) for _ in range(r)] |
| H=layer_product(list(zip(cs,ts)));N=2**r |
| fm=moments(H[0][0],2*N);gm=moments(H[0][1],2*N) |
| exact=[] |
| for j in range(1,N):exact.extend([(-1)**j*fm[2*j],(-1)**j*gm[2*j+1]/(2*j+1)]) |
| exact=np.array([float(x) for x in exact]) |
| num=jets_from_layers([float(c*c) for c in cs],[float(t) for t in ts]) |
| err=float(np.max(np.abs(num-exact)/(1+np.abs(exact)))) |
| max_jet_error=max(max_jet_error,err);cases+=1 |
| assert err<1e-10 |
| ranks=[] |
| for r in [2,3]: |
| for resource in [False,True]: |
| P=draw_projection(r,known_resource=resource) |
| smallest=1e100;max_condition=0.;count=0 |
| for repeat in range(30): |
| qs=rng.uniform(.6,4.,r) |
| ts=rng.uniform(.4,1.3,r);ts/=ts.sum() |
| Q=float(qs@ts) |
| if resource: |
| x=np.r_[qs[:-1],ts[:-1]] |
| def f(z): |
| q1=z[:r-1];t1=z[r-1:];last=1-t1.sum() |
| qq=np.r_[q1,(Q-q1@t1)/last];tt=np.r_[t1,last] |
| return P@jets_from_layers(qq,tt,r) |
| else: |
| x=np.r_[qs,ts[:-1]] |
| def f(z): |
| qq=z[:r];t1=z[r:];tt=np.r_[t1,1-t1.sum()] |
| return P@jets_from_layers(qq,tt,r) |
| J=complex_step_jacobian(f,x) |
| sv=np.linalg.svd(J,compute_uv=False) |
| smallest=min(smallest,float(sv[-1]));max_condition=max(max_condition,float(sv[0]/sv[-1])) |
| assert sv[-1]>1e-12*max(1.,sv[0]) |
| count+=1 |
| ranks.append({'layers':r,'known_resource':resource,'outputs':P.shape[0], |
| 'parameter_dimension':len(x),'samples':count, |
| 'minimum_observed_singular_value':smallest, |
| 'maximum_observed_condition_number':max_condition}) |
| report={'seed':260926,'polynomial_jet_vs_exact_exponential_cases':cases, |
| 'max_relative_jet_error':max_jet_error,'rank_diagnostics':ranks, |
| 'global_CAD_projection_search_executed':False, |
| 'projection_global_injectivity_certified_by_these_tests':False, |
| 'all_assertions_passed':True,'elapsed_seconds':time.time()-start} |
| (ROOT/'results'/'verification_inverse_v2.json').write_text(json.dumps(report,indent=2)+'\n') |
| print(json.dumps(report,indent=2)) |
|
|
