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33e9f46 | 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 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 | import unittest
import itertools
import numpy as np
import sympy as s
from src.continuation import *
class AlgebraTests(unittest.TestCase):
def test_wedge_pairing(self):
a=s.Matrix([[1,2,3]]);b=s.Matrix([[2,-1,4]])
x=s.Matrix([[2,3,1]]);y=s.Matrix([[-1,4,2]])
self.assertEqual((wedge(a,b)*wedge(x,y).T)[0],
(a*x.T)[0]*(b*y.T)[0]-(a*y.T)[0]*(b*x.T)[0])
def test_compound_composition(self):
A=s.Matrix([[1,2,0],[2,1,3],[1,0,1]])
B=s.Matrix([[1,0,2],[0,2,1],[3,1,1]])
self.assertEqual(compound2(A*B),compound2(A)*compound2(B))
def test_compound_row_transport(self):
A=s.Matrix([[1,2,0],[2,1,3],[1,0,1]])
a=s.Matrix([[2,1,4]]);b=s.Matrix([[3,0,2]])
self.assertEqual(wedge(a*A,b*A),wedge(a,b)*compound2(A))
def test_bad_wedge(self):
with self.assertRaises(ValueError):wedge(s.ones(2,1),s.ones(1,2))
def test_empty_library(self):
with self.assertRaises(ValueError):compile_exterior([],[])
def test_nonpositive_rejected(self):
with self.assertRaises(ValueError):compile_exterior([s.eye(3)],[s.ones(1,3)])
def test_constant_output_empty_signature(self):
T=s.ones(3)/3
c=compile_exterior([T],[s.ones(1,3)])
self.assertEqual(c.R.rows,0);self.assertTrue(c.verify())
def test_hadamard(self):
for n in [4,8,16,32]:
H=hadamard_exact(n);self.assertEqual(H*H.T,n*s.eye(n))
def test_bad_family_size(self):
with self.assertRaises(ValueError):separation_family(6)
def test_bad_perturbation(self):
with self.assertRaises(ValueError):separation_family(4,s.Rational(1,8))
class FamilyTests(unittest.TestCase):
def test_positive_instrument(self):
for n in [4,8,16]:
m=separation_family(n)
self.assertTrue(min(m.A)>0 and min(m.B)>0)
self.assertEqual(s.ones(1,n)*(m.A+m.B),s.ones(1,n))
def test_branch_mass_floor(self):
for n in [4,8,16]:
m=separation_family(n)
for T in [m.A,m.B]:
self.assertGreaterEqual(min(s.ones(1,n)*T),s.Rational(3,8))
def test_affine_full_exact(self):
for n in [4,8]:
m=separation_family(n)
W=affine_closure([m.A,m.B],m.F[[0,1],:])
self.assertEqual(W.rows,n)
def test_exterior_two_dimensional(self):
for n in [4,8]:
m=separation_family(n);c=compile_exterior([m.A,m.B],[m.F[1,:]])
self.assertEqual(c.R.rows,2);self.assertEqual(c.depth,1)
def test_exact_nonlinear_updates(self):
m=separation_family(8)
x=s.Matrix(range(1,9))/36
for label,T in enumerate([m.A,m.B]):
self.assertEqual(m.signature(normalize(T,x)),m.compact_step(m.signature(x),label))
def test_all_words_six(self):
m=separation_family(4);x=s.Matrix([1,2,3,4])/10
for word in itertools.product(range(2),repeat=6):
y=x;z=m.signature(x)
for a in word:
y=normalize([m.A,m.B][a],y);z=m.compact_step(z,a)
self.assertEqual(z,m.signature(y))
def test_fiber_noninjective(self):
m=separation_family(8);nu=s.ones(8,1)/8
x=nu+m.F[4,:].T/s.Integer(64)
self.assertNotEqual(x,nu);self.assertEqual(m.signature(x),m.signature(nu))
def test_local_rank_two(self):
m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]])
self.assertEqual(jacobian_rank(c,s.ones(4,1)/4),2)
def test_lp_representative_update(self):
m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]])
x=s.Matrix([1,2,3,4])/10
z=list(c.signature_exact(x))
for a,T in enumerate([m.A,m.B]):
np.testing.assert_allclose(c.update_float(z,a),
np.array(c.signature_exact(normalize(T,x)),dtype=float).ravel(),atol=1e-10)
def test_invalid_signature_dimension(self):
m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]])
with self.assertRaises(ValueError): c.fiber_matrix([1,2,3])
def test_invalid_state(self):
m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]])
with self.assertRaises(ValueError): c.signature_exact(s.ones(4,1))
class RewriteTests(unittest.TestCase):
def test_rank_one_and_equal_spectra(self):
for n in [4,8,16]:
a=separation_family(n);b=separation_family(n,s.Rational(1,10000))
self.assertEqual((b.B-a.B).rank(),1)
self.assertEqual(a.LB.charpoly().as_expr(),b.LB.charpoly().as_expr())
self.assertEqual((a.LA+a.LB).charpoly().as_expr(),(b.LA+b.LB).charpoly().as_expr())
self.assertEqual(s.ones(1,n)*a.B,s.ones(1,n)*b.B)
def test_uniform_stationary(self):
for n in [4,8,16]:
m=separation_family(n,s.Rational(1,10000));nu=s.ones(n,1)/n
self.assertEqual((m.A+m.B)*nu,nu)
def test_reconstruction_inversion(self):
for n in [4,8,16]:
m=separation_family(n,s.Rational(1,1000));x=s.Matrix(range(1,n+1))/(n*(n+1)//2)
y=x;ys=[]
for _ in range(n-3):
y=normalize(m.B,y);ys.append((m.F[1,:]*y)[0])
got=reconstruct_hidden_from_B_readouts(n,ys,m.delta)
self.assertEqual(got,(m.F*x)[3:,:])
def test_rewrite_distinguishes_old_memory(self):
n=8;m=separation_family(n,s.Rational(1,1000));nu=s.ones(n,1)/n
x=nu+m.F[3,:].T/(4*n); y=nu-m.F[3,:].T/(4*n)
self.assertEqual(m.signature(x),m.signature(y))
self.assertNotEqual((m.F[1,:]*normalize(m.B,x))[0],(m.F[1,:]*normalize(m.B,y))[0])
def test_new_local_rank_full(self):
m=separation_family(4,s.Rational(1,1000))
c=compile_exterior([m.A,m.B],[m.F[1,:]])
self.assertEqual(jacobian_rank(c,s.ones(4,1)/4),3)
def test_perturbation_output_bound(self):
m=separation_family(8,s.Rational(1,1000))
for j in range(8):
x=s.eye(8)[:,j];v=(m.F[1,:]*normalize(m.B,x))[0]
self.assertLessEqual(abs(v),8*m.delta/3)
def test_span_admission_not_necessary(self):
n=3;e=s.ones(1,n);R=s.Matrix.vstack(*[wedge(s.eye(n)[j,:],e) for j in [0,1]])
T=s.Matrix([[3,2,1],[1,4,2],[2,1,5]])/20
self.assertEqual(R.rows,2)
self.assertGreater(s.Matrix.vstack(R,R*compound2(T)).rank(),R.rows)
# Full simplex memory makes any positive update possible regardless of this failure.
self.assertEqual(s.Matrix.vstack(e,s.eye(n)[0,:],s.eye(n)[1,:]).rank(),n)
def test_vertex_promotion_failure(self):
t=s.symbols('t',real=True)
d=1/(1+t)-3/(2+t)+s.Rational(13,25)
self.assertEqual(d.subs(t,0),s.Rational(1,50));self.assertEqual(d.subs(t,1),s.Rational(1,50))
self.assertLess(float(d.subs(t,(s.sqrt(3)-1)/2)),0)
def test_certificate_tamper(self):
m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]])
c.transports[0][0,0]+=1
self.assertFalse(c.verify())
class SnapshotTests(unittest.TestCase):
def test_factor_two_sharp(self):
for r in [1,2,3,4]:
c=factor_two_fixture(r);n=2*r+1
self.assertEqual(jacobian_rank(c,s.ones(n,1)/n),r)
self.assertEqual(snapshot_space(c).rows-1,2*r)
def test_family_snapshot_three(self):
for n in [4,8]:
m=separation_family(n);c=compile_exterior([m.A,m.B],[m.F[1,:]])
self.assertEqual(snapshot_space(c).rows-1,3)
def test_denominator_validation(self):
with self.assertRaises(ValueError):
compile_ratios([s.ones(3)/3],[Ratio(s.Matrix([[1,0,0]]),s.Matrix([[0,1,1]]),())])
def test_snapshot_initializes_compact(self):
m=separation_family(8);x=s.Matrix(range(1,9))/36;z=m.F*x
self.assertEqual(m.signature(x),s.Matrix([z[1],z[2]/(1+m.tau*z[3])]))
class CertificateIntegrityTests(unittest.TestCase):
def cert(self):
m=separation_family(4)
return compile_exterior([m.A,m.B],[m.F[1,:]])
def test_provenance_tampering_rejected(self):
c=self.cert();r=c.ratios[1]
c.ratios[1]=Ratio(r.numerator,r.denominator,(1,))
self.assertFalse(c.verify())
def test_missing_seed_coverage_rejected(self):
c=self.cert()
extra=Ratio(s.eye(4)[0,:],s.ones(1,4),())
c.seeds=c.seeds+(extra,)
self.assertFalse(c.verify())
def test_transport_truncation_rejected(self):
c=self.cert();c.transports.pop()
self.assertFalse(c.verify())
def test_denominator_tampering_rejected(self):
c=self.cert();r=c.ratios[0]
c.ratios[0]=Ratio(r.numerator,-r.denominator,r.word)
self.assertFalse(c.verify())
def test_seed_word_rejected(self):
with self.assertRaises(ValueError):
compile_ratios([s.ones(3)/3],[Ratio(s.Matrix([[1,0,0]]),s.ones(1,3),(0,))])
def test_mode_aware_same_evidence_control(self):
m=separation_family(8);x=s.Matrix(range(1,9))/36
for word in itertools.product([0,1],repeat=5):
y=x;initial=m.F*x
# The ordinary controller starts from three affine scalars, then
# retains one sufficient scalar plus a mode after the first label.
stored=(initial[1],initial[2],initial[3]);mode="initial"
for label in word:
if label==1:
mode="reset";stored=s.Integer(0);pred=s.Integer(0)
else:
if mode=="initial":
v=stored[1]/(1+m.tau*stored[2])
elif mode=="reset":
v=s.Integer(0)
else:
v=stored
pred=m.gamma*v;stored=m.kappa*v;mode="one-scalar"
y=normalize([m.A,m.B][label],y)
self.assertEqual(pred,(m.F[1,:]*y)[0])
if __name__=='__main__': unittest.main()
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