42 lines
935 B
Julia
42 lines
935 B
Julia
include("Engine.jl")
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using SparseArrays
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using Random
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# initialize the partial gram matrix for a sphere inscribed in a regular
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# tetrahedron
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J = Int64[]
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K = Int64[]
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values = BigFloat[]
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for j in 1:5
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for k in 1:5
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push!(J, j)
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push!(K, k)
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if j == k
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push!(values, 1)
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elseif (j <= 4 && k <= 4)
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push!(values, -1/BigFloat(3))
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else
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push!(values, -1)
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end
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end
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end
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gram = sparse(J, K, values)
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# set initial guess
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Random.seed!(99230)
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guess = sqrt(1/BigFloat(3)) * BigFloat[
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1 1 -1 -1 0
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1 -1 1 -1 0
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1 -1 -1 1 0
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1 1 1 1 -2
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1 1 1 1 1
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] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5))
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# complete the gram matrix using Newton's method
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L, history = Engine.realize_gram_newton(gram, guess)
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completed_gram = L'*Engine.Q*L
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println("Completed Gram matrix:\n")
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display(completed_gram)
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println("\nSteps: ", size(history.scaled_loss, 1))
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println("Loss: ", history.scaled_loss[end], "\n") |