70 lines
1.8 KiB
Julia
70 lines
1.8 KiB
Julia
###############################################################################
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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, S::Vector{REl}, T::Type=Float64) where {REl<:AbstractAlgebra.ModuleElem}
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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 Laplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.ModuleElem
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R = parent(first(S))
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return Laplacian(S, one(R), radius)
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end
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function Laplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.GroupElem
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G = parent(first(S))
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return Laplacian(S, G(), radius)
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end
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function Laplacian(S, Id, radius)
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@info "Generating metric ball of radius" radius=2radius
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@time E_R, sizes = Groups.generate_balls(S, Id, radius=2radius)
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@info "Generated balls:" sizes
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@info "Creating product matrix..."
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rdict = GroupRings.reverse_dict(E_R)
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@time pm = GroupRings.create_pm(E_R, rdict, sizes[radius]; twisted=true)
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RG = GroupRing(parent(Id), E_R, rdict, 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 saveGRElem(fname::String, g::GroupRingElem)
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RG = parent(g)
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JLD.save(fname, "coeffs", g.coeffs, "pm", RG.pm, "G", RG.group)
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end
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function loadGRElem(fname::String, RG::GroupRing)
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coeffs = load(fname, "coeffs")
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return GroupRingElem(coeffs, RG)
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end
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function loadGRElem(fname::String, G::Group)
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pm = load(fname, "pm")
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RG = GroupRing(G, pm)
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return loadGRElem(fname, RG)
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end
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function loadGRElem(fname::String)
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pm, G = load(fname, "pm", "G")
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RG = GroupRing(G, pm)
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return loadGRElem(fname, RG)
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end
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