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Investigate why witness sets aren't reproducible 

All the random number generators seems to be seeded, so why aren't the results
reproducible?
This commit is contained in:
Aaron Fenyes 2024-02-15 14:17:03 -08:00
parent 291d5c8ff6
commit a6da6f9925
2 changed files with 21 additions and 18 deletions
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15
engine-proto/Engine.Numerical.jl
View File

@ -1,5 +1,6 @@
module Numerical
using Random: default_rng
using LinearAlgebra
using AbstractAlgebra
using HomotopyContinuation:
@ -28,16 +29,18 @@ end
# --- sampling ---
function real_samples(F::AbstractSystem, dim)
function real_samples(F::AbstractSystem, dim; rng = default_rng())
# choose a random real hyperplane of codimension `dim` by intersecting
# hyperplanes whose normal vectors are uniformly distributed over the unit
# sphere
# [to do] guard against the unlikely event that one of the normals is zero
normals = transpose(hcat(
(normalize(randn(nvariables(F))) for _ in 1:dim)...
))
cut = LinearSubspace(normals, fill(0., dim))
filter(isreal, results(witness_set(F, cut)))
##normals = transpose(hcat(
## (normalize(randn(rng, nvariables(F))) for _ in 1:dim)...
##))
##cut = LinearSubspace(normals, fill(0., dim))
##filter(isreal, results(witness_set(F, cut, seed = 0x8af341df)))
##filter(isreal, results(witness_set(F, seed = 0x8af341df)))
results(witness_set(F, seed = 0x8af341df))
end
AbstractAlgebra.evaluate(pt::Point, vals::Vector{<:RingElement}) =

24
engine-proto/Engine.jl
View File

@ -59,13 +59,13 @@ tangencies = [
ctx_tan_sph = Engine.Construction{CoeffType}(elements = Set(spheres), relations = Set(tangencies))
ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
##small_eqns_tan_sph = eqns_tan_sph
small_eqns_tan_sph = [
eqns_tan_sph;
spheres[2].coords - [1, 0, 0, 0, 1];
spheres[3].coords - [1, 0, 0, 0, -1];
]
small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph)
freedom = Engine.dimension(small_ideal_tan_sph)
##small_eqns_tan_sph = [
## eqns_tan_sph;
## spheres[2].coords - [1, 0, 0, 0, 1];
## spheres[3].coords - [1, 0, 0, 0, -1];
##]
##small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph)
freedom = Engine.dimension(ideal_tan_sph)
println("Three mutually tangent spheres, with two fixed: $freedom degrees of freedom")
##points = [Engine.Point{CoeffType}() for _ in 1:3]
@ -83,17 +83,17 @@ println("Three mutually tangent spheres, with two fixed: $freedom degrees of fre
# --- test rational cut ---
coordring = base_ring(small_ideal_tan_sph)
coordring = base_ring(ideal_tan_sph)
vbls = Variable.(symbols(coordring))
# test a random witness set
system = CompiledSystem(System(small_eqns_tan_sph, variables = vbls))
system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
norm2 = vec -> real(dot(conj.(vec), vec))
Random.seed!(6071)
n_planes = 36
rng = MersenneTwister(6701)
n_planes = 6
samples = []
for _ in 1:n_planes
real_solns = solution.(Engine.Numerical.real_samples(system, freedom))
real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))
for soln in real_solns
if all(norm2(soln - samp) > 1e-4*length(gens(coordring)) for samp in samples)
push!(samples, soln)