d0340c0b65
The balance between the light cone basis vectors was wrong, throwing the point's coordinates off by a factor of two.
96 lines
2.3 KiB
Julia
96 lines
2.3 KiB
Julia
include("Engine.jl")
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using LinearAlgebra
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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 1:11
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for k in 1:11
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filled = false
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if j == 11
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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 == 11
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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, j <= 6 ? 1 : 0)
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filled = true
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elseif j <= 4
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if k <= 4
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push!(values, -1/BigFloat(3))
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filled = true
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elseif k == 5
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push!(values, -1)
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filled = true
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elseif 7 <= k <= 10 && k - j != 6
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push!(values, 0)
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filled = true
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end
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elseif k <= 4
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if j == 5
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push!(values, -1)
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filled = true
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elseif 7 <= j <= 10 && j - k != 6
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push!(values, 0)
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filled = true
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end
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elseif j == 6 && 7 <= k <= 10 || k == 6 && 7 <= j <= 10
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push!(values, 0)
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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 0
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1 -1 1 -1 0 0
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1 -1 -1 1 0 0
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0 0 0 0 1.5 0.5
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1 1 1 1 -0.5 -1.5
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] + 0.0*Engine.rand_on_shell(fill(BigFloat(-1), 6)),
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Engine.point([-0.5, -0.5, -0.5] + 0.3*randn(3)),
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Engine.point([-0.5, 0.5, 0.5] + 0.3*randn(3)),
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Engine.point([ 0.5, -0.5, 0.5] + 0.3*randn(3)),
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Engine.point([ 0.5, 0.5, -0.5] + 0.3*randn(3)),
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BigFloat[0, 0, 0, 0, 1]
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)
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frozen = vcat(
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[CartesianIndex(4, k) for k in 7:10],
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[CartesianIndex(j, 11) for j in 1:5]
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)
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# complete the gram matrix
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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])
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if success
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infty = BigFloat[0, 0, 0, 0, 1]
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radius_ratio = dot(infty, Engine.Q * L[:,5]) / dot(infty, Engine.Q * L[:,6])
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println("\nCircumradius / inradius: ", radius_ratio)
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end |