mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 15:25:29 +01:00
kalmarek
76b8fed6b1
* MatSpaces are no longer Rings, they are modules (that's a hack, I know) * DirectProduct → DirectPower * full → GroupRings.dense * constructors of GroupRings require explicit basis
70 lines
1.9 KiB
Julia
70 lines
1.9 KiB
Julia
###############################################################################
|
|
#
|
|
# Laplacians
|
|
#
|
|
###############################################################################
|
|
|
|
function spLaplacian(RG::GroupRing, S, T::Type=Float64)
|
|
result = RG(T)
|
|
result[RG.group()] = T(length(S))
|
|
for s in S
|
|
result[s] -= one(T)
|
|
end
|
|
return result
|
|
end
|
|
|
|
function spLaplacian(RG::GroupRing, S::Vector{REl}, T::Type=Float64) where {REl<:AbstractAlgebra.ModuleElem}
|
|
result = RG(T)
|
|
result[one(RG.group)] = T(length(S))
|
|
for s in S
|
|
result[s] -= one(T)
|
|
end
|
|
return result
|
|
end
|
|
|
|
function Laplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.ModuleElem
|
|
R = parent(first(S))
|
|
return Laplacian(S, one(R), radius)
|
|
end
|
|
|
|
function Laplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.GroupElem
|
|
G = parent(first(S))
|
|
return Laplacian(S, G(), radius)
|
|
end
|
|
|
|
function Laplacian(S, Id, radius)
|
|
@info("Generating metric ball of radius $(2radius)...")
|
|
@time E_R, sizes = Groups.generate_balls(S, Id, radius=2radius)
|
|
@info("Generated balls of sizes $sizes.")
|
|
|
|
@info("Creating product matrix...")
|
|
rdict = GroupRings.reverse_dict(E_R)
|
|
@time pm = GroupRings.create_pm(E_R, rdict, sizes[radius]; twisted=true)
|
|
|
|
RG = GroupRing(parent(Id), E_R, rdict, pm)
|
|
Δ = spLaplacian(RG, S)
|
|
return Δ
|
|
end
|
|
|
|
function saveGRElem(fname::String, g::GroupRingElem)
|
|
RG = parent(g)
|
|
JLD.save(fname, "coeffs", g.coeffs, "pm", RG.pm, "G", RG.group)
|
|
end
|
|
|
|
function loadGRElem(fname::String, RG::GroupRing)
|
|
coeffs = load(fname, "coeffs")
|
|
return GroupRingElem(coeffs, RG)
|
|
end
|
|
|
|
function loadGRElem(fname::String, G::Group)
|
|
pm = load(fname, "pm")
|
|
RG = GroupRing(G, pm)
|
|
return loadGRElem(fname, RG)
|
|
end
|
|
|
|
function loadGRElem(fname::String)
|
|
pm, G = load(fname, "pm", "G")
|
|
RG = GroupRing(G, pm)
|
|
return loadGRElem(fname, RG)
|
|
end
|