50 lines
1.1 KiB
Julia
50 lines
1.1 KiB
Julia
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using LowRankModels
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using LinearAlgebra
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using SparseArrays
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# testing Gram matrix recovery using the LowRankModels package
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# initialize the partial gram matrix for an arrangement of seven spheres in
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# which spheres 1 through 5 are mutually tangent, and spheres 3 through 7 are
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# also mutually tangent
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I = Int64[]
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J = Int64[]
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values = Float64[]
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for i in 1:7
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for j in 1:7
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if (i <= 5 && j <= 5) || (i >= 3 && j >= 3)
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push!(I, i)
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push!(J, j)
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push!(values, i == j ? 1 : -1)
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end
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end
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end
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gram = sparse(I, J, values)
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# in this initial guess, the mutual tangency condition is satisfied for spheres
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# 1 through 5
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X₀ = sqrt(0.5) * [
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1 0 1 1 1;
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1 0 1 -1 -1;
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1 0 -1 1 -1;
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1 0 -1 -1 1;
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2 -sqrt(6) 0 0 0;
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0.2 0.3 -0.1 -0.2 0.1;
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0.1 -0.2 0.3 0.4 -0.1
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]'
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Y₀ = diagm([-1, 1, 1, 1, 1]) * X₀
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# search parameters
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search_params = ProxGradParams(
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1.0;
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max_iter = 100,
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inner_iter = 1,
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abs_tol = 1e-16,
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rel_tol = 1e-9,
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min_stepsize = 0.01
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)
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# complete gram matrix
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model = GLRM(gram, QuadLoss(), ZeroReg(), ZeroReg(), 5, X = X₀, Y = Y₀)
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X, Y, history = fit!(model, search_params)
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