68 lines
1.9 KiB
Julia
68 lines
1.9 KiB
Julia
"""
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wlmetric_ball(S::AbstractVector{<:GroupElem}
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[, center=one(first(S)); radius=2, op=*, threading=true])
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Compute metric ball as a list of elements of non-decreasing length, given the
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word-length metric on the group generated by `S`. The ball is centered at `center`
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(by default: the identity element). `radius` and `op` keywords specify the
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radius and multiplication operation to be used.
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"""
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function wlmetric_ball(
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S::AbstractVector{T},
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center::T = one(first(S));
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radius = 2,
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op = *,
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threading = true,
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) where {T}
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threading && return wlmetric_ball_thr(S, center; radius = radius, op = op)
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return wlmetric_ball_serial(S, center; radius = radius, op = op)
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end
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function wlmetric_ball_serial(
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S::AbstractVector{T},
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center::T = one(first(S));
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radius = 2,
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op = *,
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) where {T}
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@assert radius >= 1
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old = union!(OrderedSet([center]), [center * s for s in S])
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sizes = [1, length(old)]
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for _ in 2:radius
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new = collect(
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op(o, s) for o in @view(old.dict.keys[sizes[end-1]:end]) for s in S
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)
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union!(old, new)
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push!(sizes, length(old))
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end
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return old.dict.keys, sizes[2:end]
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end
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function wlmetric_ball_thr(
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S::AbstractVector{T},
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center::T = one(first(S));
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radius = 2,
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op = *,
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) where {T}
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@assert radius >= 1
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old = union!([center], [center * s for s in S])
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return _wlmetric_ball(S, old, radius, op, Folds.collect, Folds.unique)
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end
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function _wlmetric_ball(S, old, radius, op, collect, unique)
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sizes = [1, length(old)]
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for _ in 2:radius
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old = let old = old, S = S
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new = collect(
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(g = op(o, s);
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normalform!(g);
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hash(g);
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g) for o in @view(old[sizes[end-1]:end]) for s in S
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)
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append!(old, new)
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unique(old)
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end
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push!(sizes, length(old))
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end
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return old, sizes[2:end]
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end
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