dyna3/engine-proto/gram-test/circles-in-triangle.jl

include("Engine.jl")

using SparseArrays
using Random

# initialize the partial gram matrix for a sphere inscribed in a regular
# tetrahedron
J = Int64[]
K = Int64[]
values = BigFloat[]
for j in 1:9
  for k in 1:9
    filled = false
    if j == 9
      if k <= 5 && k != 2
        push!(values, 0)
        filled = true
      end
    elseif k == 9
      if j <= 5 && j != 2
        push!(values, 0)
        filled = true
      end
    elseif 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))
#= make construction rigid
append!(J, [3, 4, 4, 5])
append!(K, [4, 3, 5, 4])
append!(values, fill(-0.5, 4))
=#
gram = sparse(J, K, values)

# set initial guess
Random.seed!(58271)
guess = hcat(
  Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
  Engine.sphere(BigFloat[0, 0, 0], BigFloat(1//2)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.plane(-BigFloat[1, 0, 0], BigFloat(-1)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.plane(-BigFloat[cos(2pi/3), sin(2pi/3), 0], BigFloat(-1)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.plane(-BigFloat[cos(-2pi/3), sin(-2pi/3), 0], BigFloat(-1)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.sphere(BigFloat[-1, 0, 0], BigFloat(1//5)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.sphere(BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//5)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  Engine.sphere(BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//5)) + 0.1*Engine.rand_on_shell([BigFloat(-1)]),
  BigFloat[0, 0, 0, 0, 1]
)
frozen = [CartesianIndex(j, 9) for j in 1:5]

# complete the gram matrix using Newton's method with backtracking
L, success, history = Engine.realize_gram(gram, guess, frozen)
completed_gram = L'*Engine.Q*L
println("Completed Gram matrix:\n")
display(completed_gram)
if success
  println("\nTarget accuracy achieved!")
else
  println("\nFailed to reach target accuracy")
end
println("Steps: ", size(history.scaled_loss, 1))
println("Loss: ", history.scaled_loss[end], "\n")