File size: 3,033 Bytes
9755170 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | """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))
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