Start tetrahedron radius ratio example

Add the vertices of the tetrahedron to the `sphere-in-tetrahedron`
example.
This commit is contained in:
Aaron Fenyes 2024-07-17 17:33:32 -07:00
parent 4728959ae0
commit ea640f4861

View File

@ -0,0 +1,87 @@
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 1:10
for k in 1:10
filled = false
if j == 10
if k <= 4
push!(values, 0)
filled = true
end
elseif k == 10
if j <= 4
push!(values, 0)
filled = true
end
elseif j == k
push!(values, j <= 5 ? 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 k <= 9 && k - j != 5
push!(values, 0)
filled = true
end
elseif k <= 4
if j == 5
push!(values, 1)
filled = true
elseif j <= 9 && j - k != 5
push!(values, 0)
filled = true
end
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
1 -1 1 -1 0
1 -1 -1 1 0
0 0 0 0 1.5
1 1 1 1 0.5
] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
Engine.point([-1, -1, -1]),
Engine.point([ 1, -1, -1]),
Engine.point([-1, 1, -1]),
Engine.point([ 1, -1, 1]),
BigFloat[0, 0, 0, 0, 1]
)
frozen = vcat(
[CartesianIndex(4, k) for k in 6:9],
[CartesianIndex(j, 10) for j in 1:5]
)
# complete the gram matrix
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")