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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
Conversation 9 Commits 133 Files Changed 20 +33 -13
1 changed files with 33 additions and 13 deletions
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46
engine-proto/gram-test/sphere-in-tetrahedron.jl
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@ -8,16 +8,32 @@ using Random
J = Int64[]
K = Int64[]
values = BigFloat[]
for j in 1:5
for k in 1:5
push!(J, j)
push!(K, k)
if j == k
for j in 1:6
for k in 1:6
filled = false
if j == 6
if k <= 4
push!(values, 0)
filled = true
end
elseif k == 6
if j <= 4
push!(values, 0)
filled = true
end
elseif j == k
push!(values, 1)
filled = true
elseif (j <= 4 && k <= 4)
push!(values, -1/BigFloat(3))
filled = true
else
push!(values, -1)
filled = true
end
if filled
push!(J, j)
push!(K, k)
end
end
end
@ -25,19 +41,23 @@ gram = sparse(J, K, values)
# set initial guess
Random.seed!(99230)
guess = sqrt(1/BigFloat(3)) * BigFloat[
1 1 -1 -1 0
1 -1 1 -1 0
1 -1 -1 1 0
1 1 1 1 -2
1 1 1 1 1
] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5))
guess = hcat(
sqrt(1/BigFloat(3)) * BigFloat[
1 1 -1 -1 0
1 -1 1 -1 0
1 -1 -1 1 0
1 1 1 1 -2
1 1 1 1 1
] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
BigFloat[0, 0, 0, 1, 1]
)
frozen = [CartesianIndex(j, 6) for j in 1:5]
# complete the gram matrix
#=
L, history = Engine.realize_gram_newton(gram, guess)
=#
L, success, history = Engine.realize_gram(gram, guess)
L, success, history = Engine.realize_gram(gram, guess, frozen)
completed_gram = L'*Engine.Q*L
println("Completed Gram matrix:\n")
display(completed_gram)