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add GroupRing cache and basis manipulation
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@ -13,84 +13,6 @@ import Base: convert, show, hash, ==, +, -, *, ^, //, /, length, getindex, setin
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export GroupRing, GroupRingElem, complete!, create_pm, star, aug, supp
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function reverse_dict(::Type{I}, iter) where I<:Integer
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length(iter) > typemax(I) && error("Can not produce reverse dict: $(length(iter)) is too large for $T")
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return Dict{eltype(iter), I}(x => i for (i,x) in enumerate(iter))
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end
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reverse_dict(iter) = reverse_dict(Int, iter)
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function create_pm(basis::Vector{T}, basis_dict::Dict{T, Int},
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limit::Int=length(basis); twisted::Bool=false, check=true) where {T<:GroupElem}
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product_matrix = zeros(Int, (limit,limit))
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Threads.@threads for i in 1:limit
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x = basis[i]
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if twisted
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x = inv(x)
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end
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for j in 1:limit
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product_matrix[i,j] = basis_dict[x*basis[j]]
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end
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end
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check && check_pm(product_matrix, basis, twisted)
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return product_matrix
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end
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create_pm(b::Vector{T}) where {T<:GroupElem} = create_pm(b, reverse_dict(b))
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function check_pm(product_matrix, basis, twisted=false)
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idx = findfirst(product_matrix' .== 0)
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if idx != nothing
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@warn("Product is not supported on basis")
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i,j = Tuple(idx)
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x = basis[i]
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if twisted
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x = inv(x)
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end
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throw(KeyError(x*basis[j]))
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end
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return true
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end
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function complete!(RG::GroupRing)
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isdefined(RG, :basis) || throw(ArgumentError("Provide basis for completion first!"))
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if !isdefined(RG, :pm)
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initializepm!(RG, fill=false)
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return RG
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end
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warning = false
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for idx in findall(RG.pm .== 0)
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i,j = Tuple(idx)
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g = RG.basis[i]*RG.basis[j]
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if haskey(RG.basis_dict, g)
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RG.pm[i,j] = RG.basis_dict[g]
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else
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if !warning
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warning = true
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end
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end
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end
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warning && @warn("Some products were not supported on basis")
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return RG
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end
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function initializepm!(RG::GroupRing; fill::Bool=false)
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isdefined(RG, :basis) || throw("For baseless Group Rings You need to provide pm.")
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isdefined(RG, :pm) && return RG
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if fill
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RG.pm = try
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create_pm(RG.basis, RG.basis_dict)
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catch err
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isa(err, KeyError) && throw("Product is not supported on basis, $err.")
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throw(err)
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end
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else
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RG.pm = zeros(Int, length(RG.basis), length(RG.basis))
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end
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return RG
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end
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end # of module GroupRings
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96
src/types.jl
96
src/types.jl
@ -159,3 +159,99 @@ function AbstractAlgebra.change_base_ring(X::GroupRingElem, R::Ring)
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end
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end
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###############################################################################
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#
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# Cache Manipulation
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#
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###############################################################################
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hasbasis(RG::GroupRing) = isdefined(RG, :basis)
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cachesmultiplication(RG::GroupRing) = isdefined(RG, :pm)
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reverse_dict(iter) = reverse_dict(Int32, iter)
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function reverse_dict(::Type{I}, iter) where I<:Integer
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length(iter) > typemax(I) && error("Can not produce reverse dict: $(length(iter)) is too large for $I")
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return Dict{eltype(iter), I}(x => i for (i,x) in enumerate(iter))
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end
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setcache!(RG::GroupRing, pm::Matrix{<:Integer}) = (RG.pm = pm; return RG)
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function complete!(RG::GroupRing,
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indX=1:size(RG.pm, 1),
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indY=1:size(RG.pm, 2);
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twisted::Bool=false)
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@assert hasbasis(RG)
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# preallocate elements:
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res = RG.group()
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x = RG.group()
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i_old = 0
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for (i,j) in Iterators.ProductIterator((indX, indY))
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if iszero(RG.pm[i,j])
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if i == i_old
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x = ifelse(twisted, inv(RG[i]), RG[i])
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i_old = i
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end
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RG.pm[i,j] = RG[AbstractAlgebra.mul!(res, x, RG[j])]
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end
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end
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return RG
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end
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function complete!(RG::GroupRing, limit::Integer; twisted::Bool=false, check::Bool=true)
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hasbasis(RG) || throw(ArgumentError("Provide basis for completion first!"))
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if !cachesmultiplication(RG)
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setcache!(RG, create_pm(RG.basis, RG.basis_dict, limit, twisted=twisted, check=false))
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# we check correctness below
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else
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complete!(RG, 1:limit, 1:limit; twisted=twisted)
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end
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check && @assert check_pm(RG.pm, RG.basis; twisted=twisted)
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return RG
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end
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function create_pm(basis::AbstractVector{T}, basis_dict::Dict{T, <:Integer},
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limit::Integer=length(basis); twisted::Bool=false, check::Bool=true) where T
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product_matrix = zeros(Int32, limit, limit)
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Threads.@threads for i in 1:size(product_matrix, 1)
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x = ifelse(twisted, inv(basis[i]), basis[i])
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for j in 1:size(product_matrix, 2)
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product_matrix[i,j] = basis_dict[x*basis[j]]
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end
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end
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# exceptions in threaded code are not critical so we need to
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check && @assert check_pm(product_matrix, basis, twisted=twisted)
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return product_matrix
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end
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function check_pm(pm::Matrix{<:Integer}, basis::Vector; twisted::Bool=false)
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idx = (0,0)
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for i in 1:size(pm, 1), j in 1:size(pm,2)
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# @info "" i j
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if iszero(pm[i,j])
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idx = (i,j)
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break
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end
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end
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if idx == (0,0)
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return true
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else
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i,j = Tuple(idx)
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x = ifelse(twisted, inv(basis[i]), basis[i])
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@error "Product x*y is not supported on basis:" x y=basis[j]
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throw(KeyError(x*basis[j]))
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end
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end
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