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Engine prototype #13

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glen merged 133 commits from engine-proto into main 2024-10-21 03:18:48 +00:00
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engine-proto/gram-test/irisawa-hexlet_bad.jl
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include("Engine.jl")
using SparseArrays
# --- construct the nucleus spheres ---
println("--- Nucleus spheres ---\n")
# initialize the partial gram matrix for the circumscribing and nucleus spheres
J = Int64[]
K = Int64[]
values = BigFloat[]
for n in 1:3
push!(J, n)
push!(K, n)
push!(values, 1)
if n > 1
append!(J, [1, n])
append!(K, [n, 1])
append!(values, [1, 1])
end
end
gram_nuc = sparse(J, K, values)
# make an initial guess
guess_nuc = hcat(
Engine.sphere(BigFloat[0, 0, 0], BigFloat(15)),
Engine.sphere(BigFloat[0, 0, -10], BigFloat(5)),
Engine.sphere(BigFloat[0, 0, 11], BigFloat(3)),
)
frozen_nuc = [CartesianIndex(4, k) for k in 1:3]
# complete the gram matrix using Newton's method with backtracking
L_nuc, success_nuc, history_nuc = Engine.realize_gram(gram_nuc, guess_nuc, frozen_nuc)
completed_gram_nuc = L_nuc'*Engine.Q*L_nuc
println("Completed Gram matrix:\n")
display(completed_gram_nuc)
if success_nuc
println("\nTarget accuracy achieved!")
else
println("\nFailed to reach target accuracy")
end
println("Steps: ", size(history_nuc.scaled_loss, 1))
println("Loss: ", history_nuc.scaled_loss[end], "\n")
# --- construct the chain of spheres ---
# initialize the partial gram matrix for the chain of spheres
J = Int64[]
K = Int64[]
values = BigFloat[]
for a in 4:9
push!(J, a)
push!(K, a)
push!(values, 1)
# each chain sphere is internally tangent to the circumscribing sphere
append!(J, [a, 1])
append!(K, [1, a])
append!(values, [1, 1])
# each chain sphere is externally tangent to the nucleus spheres
for n in 2:3
append!(J, [a, n])
append!(K, [n, a])
append!(values, [-1, -1])
end
# each chain sphere is externally tangent to the next sphere in the chain
#=
a_next = 4 + mod(a-3, 6)
append!(J, [a, a_next])
append!(K, [a_next, a])
append!(values, [-1, -1])
=#
end
gram_chain = sparse(J, K, values)
if success_nuc
println("--- Chain spheres ---\n")
# make an initial guess, with the circumscribing and nucleus spheres included
# as frozen elements
guess_chain = hcat(
L_nuc,
(
Engine.sphere(10*BigFloat[cos(k*π/3), sin(k*π/3), 0], BigFloat(2.5))
for k in 1:6
)...
)
frozen_chain = [CartesianIndex(j, k) for k in 1:3 for j in 1:5]
# complete the gram matrix using Newton's method with backtracking
L_chain, success_chain, history_chain = Engine.realize_gram(gram_chain, guess_chain, frozen_chain)
completed_gram_chain = L_chain'*Engine.Q*L_chain
println("Completed Gram matrix:\n")
display(completed_gram_chain)
if success_chain
println("\nTarget accuracy achieved!")
else
println("\nFailed to reach target accuracy")
end
println("Steps: ", size(history_chain.scaled_loss, 1))
println("Loss: ", history_chain.scaled_loss[end], "\n")
end