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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include("Engine.jl")
using SparseArrays
using AbstractAlgebra
using PolynomialRoots
# initialize the partial gram matrix for a sphere inscribed in a regular
# tetrahedron
J = Int64[]
K = Int64[]
values = BigFloat[]
for j in 1:8
for k in 1:8
filled = false
if j == k
push!(values, 1)
filled = true
elseif (j == 1 || k == 1)
push!(values, 0)
filled = true
elseif (j == 2 || k == 2)
push!(values, -1)
filled = true
end
if filled
push!(J, j)
push!(K, k)
end
end
end
append!(J, [6, 4, 6, 5, 7, 5, 7, 3, 8, 3, 8, 4])
append!(K, [4, 6, 5, 6, 5, 7, 3, 7, 3, 8, 4, 8])
append!(values, fill(-1, 12))
gram = sparse(J, K, values)
# set initial guess (random)
## Random.seed!(58271) # stuck; step size collapses on step 48
## Random.seed!(58272) # good convergence
## Random.seed!(58273) # stuck; step size collapses on step 18
## Random.seed!(58274) # stuck
## Random.seed!(58275) #
## guess = Engine.rand_on_shell(fill(BigFloat(-1), 8))
# set initial guess
guess = hcat(
Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
Engine.sphere(BigFloat[0, 0, 0], BigFloat(1//2)),
Engine.plane(BigFloat[1, 0, 0], BigFloat(1)),
Engine.plane(BigFloat[cos(2pi/3), sin(2pi/3), 0], BigFloat(1)),
Engine.plane(BigFloat[cos(-2pi/3), sin(-2pi/3), 0], BigFloat(1)),
Engine.sphere(BigFloat[-1, 0, 0], BigFloat(1//5)),
Engine.sphere(BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//5)),
Engine.sphere(BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//5))
)
# complete the gram matrix using gradient descent
L, history = Engine.realize_gram(gram, guess, max_descent_steps = 200)
completed_gram = L'*Engine.Q*L
println("Completed Gram matrix:\n")
display(completed_gram)
println("\nSteps: ", size(history.stepsize, 1))
println("Loss: ", history.scaled_loss[end], "\n")