105 lines
2.8 KiB
Julia
105 lines
2.8 KiB
Julia
include("Engine.jl")
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using SparseArrays
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# --- construct the nucleus spheres ---
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println("--- Nucleus spheres ---\n")
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# initialize the partial gram matrix for the circumscribing and nucleus spheres
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J = Int64[]
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K = Int64[]
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values = BigFloat[]
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for n in 1:3
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push!(J, n)
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push!(K, n)
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push!(values, 1)
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if n > 1
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append!(J, [1, n])
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append!(K, [n, 1])
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append!(values, [1, 1])
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end
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end
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gram_nuc = sparse(J, K, values)
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# make an initial guess
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guess_nuc = hcat(
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Engine.sphere(BigFloat[0, 0, 0], BigFloat(15)),
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Engine.sphere(BigFloat[0, 0, -10], BigFloat(5)),
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Engine.sphere(BigFloat[0, 0, 11], BigFloat(3)),
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)
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frozen_nuc = [CartesianIndex(4, k) for k in 1:3]
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# complete the gram matrix using Newton's method with backtracking
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L_nuc, success_nuc, history_nuc = Engine.realize_gram(gram_nuc, guess_nuc, frozen_nuc)
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completed_gram_nuc = L_nuc'*Engine.Q*L_nuc
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println("Completed Gram matrix:\n")
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display(completed_gram_nuc)
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if success_nuc
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println("\nTarget accuracy achieved!")
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else
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println("\nFailed to reach target accuracy")
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end
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println("Steps: ", size(history_nuc.scaled_loss, 1))
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println("Loss: ", history_nuc.scaled_loss[end], "\n")
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# --- construct the chain of spheres ---
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# initialize the partial gram matrix for the chain of spheres
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J = Int64[]
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K = Int64[]
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values = BigFloat[]
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for a in 4:9
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push!(J, a)
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push!(K, a)
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push!(values, 1)
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# each chain sphere is internally tangent to the circumscribing sphere
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append!(J, [a, 1])
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append!(K, [1, a])
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append!(values, [1, 1])
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# each chain sphere is externally tangent to the nucleus spheres
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for n in 2:3
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append!(J, [a, n])
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append!(K, [n, a])
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append!(values, [-1, -1])
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end
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# each chain sphere is externally tangent to the next sphere in the chain
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#=
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a_next = 4 + mod(a-3, 6)
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append!(J, [a, a_next])
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append!(K, [a_next, a])
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append!(values, [-1, -1])
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=#
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end
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gram_chain = sparse(J, K, values)
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if success_nuc
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println("--- Chain spheres ---\n")
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# make an initial guess, with the circumscribing and nucleus spheres included
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# as frozen elements
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guess_chain = hcat(
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L_nuc,
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(
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Engine.sphere(10*BigFloat[cos(k*π/3), sin(k*π/3), 0], BigFloat(2.5))
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for k in 1:6
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)...
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)
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frozen_chain = [CartesianIndex(j, k) for k in 1:3 for j in 1:5]
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# complete the gram matrix using Newton's method with backtracking
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L_chain, success_chain, history_chain = Engine.realize_gram(gram_chain, guess_chain, frozen_chain)
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completed_gram_chain = L_chain'*Engine.Q*L_chain
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println("Completed Gram matrix:\n")
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display(completed_gram_chain)
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if success_chain
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println("\nTarget accuracy achieved!")
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else
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println("\nFailed to reach target accuracy")
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end
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println("Steps: ", size(history_chain.scaled_loss, 1))
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println("Loss: ", history_chain.scaled_loss[end], "\n")
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end |