dyna3/engine-proto/gram-test/tetrahedron-radius-ratio.jl

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include("Engine.jl")
using LinearAlgebra
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 1:11
for k in 1:11
filled = false
if j == 11
if k <= 4
push!(values, 0)
filled = true
end
elseif k == 11
if j <= 4
push!(values, 0)
filled = true
end
elseif j == k
push!(values, j <= 6 ? 1 : 0)
filled = true
elseif j <= 4
if k <= 4
push!(values, -1/BigFloat(3))
filled = true
elseif k == 5
push!(values, -1)
filled = true
elseif 7 <= k <= 10 && k - j != 6
push!(values, 0)
filled = true
end
elseif k <= 4
if j == 5
push!(values, -1)
filled = true
elseif 7 <= j <= 10 && j - k != 6
push!(values, 0)
filled = true
end
elseif j == 6 && 7 <= k <= 10 || k == 6 && 7 <= j <= 10
push!(values, 0)
filled = true
end
if filled
push!(J, j)
push!(K, k)
end
end
end
gram = sparse(J, K, values)
# set initial guess
Random.seed!(99230)
guess = hcat(
sqrt(1/BigFloat(3)) * BigFloat[
1 1 -1 -1 0 0
1 -1 1 -1 0 0
1 -1 -1 1 0 0
0 0 0 0 1.5 0.5
1 1 1 1 -0.5 -1.5
] + 0.0*Engine.rand_on_shell(fill(BigFloat(-1), 6)),
Engine.point([-0.5, -0.5, -0.5] + 0.3*randn(3)),
Engine.point([-0.5, 0.5, 0.5] + 0.3*randn(3)),
Engine.point([ 0.5, -0.5, 0.5] + 0.3*randn(3)),
Engine.point([ 0.5, 0.5, -0.5] + 0.3*randn(3)),
BigFloat[0, 0, 0, 0, 1]
)
frozen = vcat(
[CartesianIndex(4, k) for k in 7:10],
[CartesianIndex(j, 11) for j in 1:5]
)
2024-07-18 07:50:48 +00:00
# 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])
if success
infty = BigFloat[0, 0, 0, 0, 1]
radius_ratio = dot(infty, Engine.Q * L[:,5]) / dot(infty, Engine.Q * L[:,6])
println("\nCircumradius / inradius: ", radius_ratio)
end