76 lines
1.9 KiB
Julia
76 lines
1.9 KiB
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 1:6
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for k in 1:6
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filled = false
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if j == 6
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if k <= 4
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push!(values, 0)
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filled = true
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end
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elseif k == 6
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if j <= 4
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push!(values, 0)
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filled = true
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end
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elseif j == k
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push!(values, 1)
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filled = true
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elseif j <= 4 && k <= 4
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push!(values, -1/BigFloat(3))
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filled = true
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else
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push!(values, -1)
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filled = true
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end
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if filled
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push!(J, j)
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push!(K, k)
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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 = hcat(
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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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0 0 0 0 1.5
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1 1 1 1 -0.5
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] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
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BigFloat[0, 0, 0, 0, 1]
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)
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frozen = [CartesianIndex(j, 6) for j in 1:5]
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# complete the gram matrix using Newton's method with backtracking
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L, success, history = Engine.realize_gram(gram, guess, frozen)
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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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if success
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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.scaled_loss, 1))
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println("Loss: ", history.scaled_loss[end], "\n")
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# test an alternate technique for finding the projected base step from the
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# unprojected Hessian
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L_alt, success_alt, history_alt = Engine.realize_gram_alt_proj(gram, guess, frozen)
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completed_gram_alt = L_alt'*Engine.Q*L_alt
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println("\nDifference in result using alternate projection:\n")
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display(completed_gram_alt - completed_gram)
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println("\nDifference in steps: ", size(history_alt.scaled_loss, 1) - size(history.scaled_loss, 1))
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println("Difference in loss: ", history_alt.scaled_loss[end] - history.scaled_loss[end], "\n") |