78 lines
2.1 KiB
Julia
78 lines
2.1 KiB
Julia
using IntervalArithmetic
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IntervalArithmetic.setrounding(Interval, :tight)
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IntervalArithmetic.setformat(sigfigs=12)
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function fma_SOS_thr!(result::AbstractVector{T}, pm::AbstractMatrix{<:Integer},
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Q::AbstractMatrix{T}, acc_matrix=zeros(T, size(pm)...)) where T
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s1, s2 = size(pm)
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@inbounds for k in 1:s2
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let k=k, s1=s1, s2=s2, Q=Q, acc_matrix=acc_matrix
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Threads.@threads for j in 1:s2
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for i in 1:s1
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@inbounds acc_matrix[i,j] = muladd(Q[i, k], Q[j, k], acc_matrix[i,j])
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end
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end
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end
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end
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@inbounds for j in 1:s2
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for i in 1:s1
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result[pm[i,j]] += acc_matrix[i,j]
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end
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end
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return result
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end
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function compute_SOS(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix)
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result = zeros(eltype(Q), maximum(pm));
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return fma_SOS_thr!(result, pm, Q)
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end
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function compute_SOS(RG::GroupRing, Q::AbstractMatrix{<:Real})
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result = compute_SOS(RG.pm, Q)
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return GroupRingElem(result, RG)
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end
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function compute_SOS_square(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix{<:Real})
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result = zeros(eltype(Q), maximum(pm));
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for i in 1:size(Q,2)
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GroupRings.fmac!(result, view(Q,:,i), view(Q,:,i), pm)
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end
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return result
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end
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function compute_SOS_square(RG::GroupRing, Q::AbstractMatrix{<:Real})
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return GroupRingElem(compute_SOS_square(RG.pm, Q), RG)
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end
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function augIdproj(Q::AbstractMatrix{T}) where {T<:Real}
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result = zeros(size(Q))
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l = size(Q, 2)
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Threads.@threads for j in 1:l
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col = sum(view(Q, :,j))/l
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for i in 1:size(Q, 1)
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result[i,j] = Q[i,j] - col
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end
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end
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return result
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end
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function augIdproj(::Type{Interval}, Q::AbstractMatrix{T}) where {T<:Real}
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result = zeros(Interval{T}, size(Q))
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l = size(Q, 2)
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Threads.@threads for j in 1:l
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col = sum(view(Q, :,j))/l
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for i in 1:size(Q, 1)
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result[i,j] = @interval(Q[i,j] - col)
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end
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end
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check = all([zero(T) in sum(view(result, :, i)) for i in 1:size(result, 2)])
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return result, check
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end
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