59 lines
1.7 KiB
Julia
59 lines
1.7 KiB
Julia
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###############################################################################
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#
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# Laplacians
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#
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###############################################################################
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function spLaplacian(RG::GroupRing, S, T::Type=Float64)
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result = RG(T)
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result[RG.group()] = T(length(S))
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for s in S
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result[s] -= one(T)
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end
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return result
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end
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function spLaplacian(RG::GroupRing{R}, S, T::Type=Float64) where {R<:Ring}
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result = RG(T)
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result[one(RG.group)] = T(length(S))
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for s in S
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result[s] -= one(T)
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end
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return result
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end
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function computeLaplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.RingElem
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R = parent(first(S))
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return computeLaplacian(S, one(R), radius)
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end
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function computeLaplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.GroupElem
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G = parent(first(S))
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return computeLaplacian(S, G(), radius)
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end
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function computeLaplacian(S, Id, radius)
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info("Generating metric ball of radius $radius...")
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@time E_R, sizes = Groups.generate_balls(S, Id, radius=2radius)
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info("Generated balls of sizes $sizes.")
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info("Creating product matrix...")
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@time pm = GroupRings.create_pm(E_R, GroupRings.reverse_dict(E_R), sizes[radius]; twisted=true)
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RG = GroupRing(parent(Id), E_R, pm)
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Δ = spLaplacian(RG, S)
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return Δ
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end
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function loadLaplacian(name::String, G::Group)
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if exists(filename(name, :Δ)) && exists(filename(name, :pm))
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info("Loading precomputed Δ...")
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RG = GroupRing(G, load(filename(name, :pm), "pm"))
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Δ = GroupRingElem(load(filename(name, :Δ), "Δ")[:, 1], RG)
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else
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throw("You need to precompute $(filename(name, :pm)) and $(filename(name, :Δ)) to load it!")
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end
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return Δ
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end
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