Merge pull request #27 from kalmarek/enh/simplify_wlmetric

simplify wlmetric_ball

Project.toml

@@ -1,20 +1,19 @@
 name = "Groups"
 uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
 authors = ["Marek Kaluba <[email protected]>"]
-version = "0.7.5"
+version = "0.7.6"
 
 [deps]
-Folds = "41a02a25-b8f0-4f67-bc48-60067656b558"
 GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
 KnuthBendix = "c2604015-7b3d-4a30-8a26-9074551ec60a"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 PermutationGroups = "8bc5a954-2dfc-11e9-10e6-cd969bffa420"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
-Folds = "0.2.7"
 GroupsCore = "0.4"
 KnuthBendix = "0.4"
 OrderedCollections = "1"

src/Groups.jl

@@ -1,12 +1,9 @@
 module Groups
 
-import Folds
 import Logging
 
 using GroupsCore
-import GroupsCore.Random
-
-import OrderedCollections: OrderedSet
+import Random
 
 import KnuthBendix
 import KnuthBendix: AbstractWord, Alphabet, Word

src/autgroups.jl

@@ -4,7 +4,7 @@ function KnuthBendix.Alphabet(S::AbstractVector{<:GSymbol})
     return Alphabet(S, inversions)
 end
 
-struct AutomorphismGroup{G<:Group,T,RW,S} <: AbstractFPGroup
+mutable struct AutomorphismGroup{G<:Group,T,RW,S} <: AbstractFPGroup
     group::G
     gens::Vector{T}
     rw::RW

src/hashing.jl

@@ -1,6 +1,6 @@
 ## Hashing
 
-equality_data(g::AbstractFPGroupElement) = (normalform!(g); word(g))
+equality_data(g::AbstractFPGroupElement) = word(g)
 
 bitget(h::UInt, n::Int) = Bool((h & (1 << n)) >> n)
 bitclear(h::UInt, n::Int) = h & ~(1 << n)

src/iteration.jl

@@ -1,3 +1,5 @@
+import OrderedCollections: OrderedSet
+
 mutable struct FPGroupIter{S,T,GEl}
     seen::S
     seen_iter_state::T

src/types.jl

@@ -144,7 +144,18 @@ end
 
 function Base.:(*)(g::GEl, h::GEl) where {GEl<:AbstractFPGroupElement}
     @boundscheck @assert parent(g) === parent(h)
-    return GEl(word(g) * word(h), parent(g))
+    A = alphabet(parent(g))
+    k = 0
+    while k + 1 ≤ min(length(word(g)), length(word(h)))
+        if inv(word(g)[end-k], A) == word(h)[k+1]
+            k += 1
+        else
+            break
+        end
+    end
+    w = @view(word(g)[1:end-k]) * @view(word(h)[k+1:end])
+    res = GEl(w, parent(g))
+    return res
 end
 
 function GroupsCore.isfiniteorder(g::AbstractFPGroupElement)

src/wl_ball.jl

@@ -1,6 +1,6 @@
 """
     wlmetric_ball(S::AbstractVector{<:GroupElem}
-        [, center=one(first(S)); radius=2, op=*, threading=true])
+        [, center=one(first(S)); radius=2, op=*])
 Compute metric ball as a list of elements of non-decreasing length, given the
 word-length metric on the group generated by `S`. The ball is centered at `center`
 (by default: the identity element). `radius` and `op` keywords specify the
@@ -11,57 +11,27 @@ function wlmetric_ball(
     center::T = one(first(S));
     radius = 2,
     op = *,
-    threading = true,
 ) where {T}
-    threading && return wlmetric_ball_thr(S, center; radius = radius, op = op)
-    return wlmetric_ball_serial(S, center; radius = radius, op = op)
-end
-
-function wlmetric_ball_serial(
-    S::AbstractVector{T},
-    center::T = one(first(S));
-    radius = 2,
-    op = *,
-) where {T}
-    @assert radius >= 1
-    old = union!(OrderedSet([center]), [center * s for s in S])
-    sizes = [1, length(old)]
-    for _ in 2:radius
-        new = collect(
-            op(o, s) for o in @view(old.dict.keys[sizes[end-1]:end]) for s in S
-        )
-        union!(old, new)
-        push!(sizes, length(old))
-    end
-    return old.dict.keys, sizes[2:end]
-end
-
-function wlmetric_ball_thr(
-    S::AbstractVector{T},
-    center::T = one(first(S));
-    radius = 2,
-    op = *,
-) where {T}
-    @assert radius >= 1
-    old = union!([center], [center * s for s in S])
-    return _wlmetric_ball(S, old, radius, op, Folds.collect, Folds.unique)
-end
-
-function _wlmetric_ball(S, old, radius, op, collect, unique)
-    sizes = [1, length(old)]
-    for _ in 2:radius
-        old = let old = old, S = S
-            new = collect(
-                (g = op(o, s);
-                normalform!(g);
-                hash(g);
-                g) for o in @view(old[sizes[end-1]:end]) for s in S
-            )
-
-            append!(old, new)
-            unique(old)
+    ball = [center]
+    sizes = [1]
+    if radius ≤ 0
+        return ball, sizes[2:end]
+    else
+        ball = union!(ball, [center * s for s in S])
+        push!(sizes, length(ball))
+        if radius == 1
+            return ball, sizes[2:end]
+        else
+            for _ in 2:radius
+                new = collect(
+                    op(o, s) for o in @view(ball[sizes[end-1]:end]) for s in S
+                )
+                append!(ball, new)
+                unique!(ball)
+                push!(sizes, length(ball))
+            end
         end
-        push!(sizes, length(old))
+        return ball, sizes[2:end]
     end
-    return old, sizes[2:end]
+    # return wlmetric_ball_serial(S, center; radius = radius, op = op)
 end

test/benchmarks.jl

@@ -5,14 +5,18 @@ using Groups
 
 function wl_ball(F; radius::Integer)
     g, state = iterate(F)
-    while length(word(g)) <= radius
+    sizes = Int[]
+    while length(sizes) ≤ radius
         res = iterate(F, state)
         isnothing(res) && break
         g, state = res
+        if length(word(g)) > length(sizes)
+            push!(sizes, length(state.seen) - 1)
+        end
     end
     elts = collect(state.seen)
-    elts = resize!(elts, length(elts)-1)
-    return elts
+    resize!(elts, sizes[end] - 1)
+    return elts, sizes[2:end]
 end
 
 @testset "Benchmarks" begin
@@ -25,21 +29,16 @@ end
         let G = FN
             S = unique([gens(G); inv.(gens(G))])
 
-            sizes1 = last(Groups.wlmetric_ball(S, radius=R, threading=false))
-            sizes2 = last(Groups.wlmetric_ball(S, radius=R, threading=true))
-
-            l = length(wl_ball(G, radius=R))
+            sizes1 = last(Groups.wlmetric_ball(S; radius = R))
+            sizes2 = last(wl_ball(G; radius = R))
 
             @test sizes1 == sizes2
-            @test last(sizes1) == l
 
-            @info "Ball of radius $R in $(parent(first(S)))" sizes=sizes1
+            @info "Ball of radius $R in $(parent(first(S)))" sizes = sizes1
             @info "serial"
-            @time Groups.wlmetric_ball(S, radius=R, threading=false)
-            @info "threaded"
-            @time Groups.wlmetric_ball(S, radius=R, threading=true)
+            @time Groups.wlmetric_ball(S, radius = R)
             @info "iteration"
-            @time wl_ball(G, radius=R)
+            @time wl_ball(G, radius = R)
         end
     end
 
@@ -51,21 +50,16 @@ end
         let G = SAutFN
             S = unique([gens(G); inv.(gens(G))])
 
-            sizes1 = last(Groups.wlmetric_ball(S, radius=R, threading=false))
-            sizes2 = last(Groups.wlmetric_ball(S, radius=R, threading=true))
-
-            l = length(wl_ball(G, radius=R))
+            sizes1 = last(Groups.wlmetric_ball(S; radius = R))
+            sizes2 = last(wl_ball(G; radius = R))
 
             @test sizes1 == sizes2
-            @test last(sizes1) == l
 
-            @info "Ball of radius $R in $(parent(first(S)))" sizes=sizes1
+            @info "Ball of radius $R in $(parent(first(S)))" sizes = sizes1
             @info "serial"
-            @time Groups.wlmetric_ball(S, radius=R, threading=false)
-            @info "threaded"
-            @time Groups.wlmetric_ball(S, radius=R, threading=true)
+            @time Groups.wlmetric_ball(S, radius = R)
             @info "iteration"
-            @time wl_ball(G, radius=R)
+            @time wl_ball(G, radius = R)
         end
     end
 end

test/matrix_groups.jl

@@ -22,8 +22,6 @@ using Groups.MatrixGroups
         S = unique([S; inv.(S)])
         _, sizes = Groups.wlmetric_ball(S; radius = 4)
         @test sizes == [7, 33, 141, 561]
-        _, sizes = Groups.wlmetric_ball_serial(S; radius = 4)
-        @test sizes == [7, 33, 141, 561]
 
         Logging.with_logger(Logging.NullLogger()) do
             @testset "GroupsCore conformance" begin
@@ -35,9 +33,9 @@ using Groups.MatrixGroups
             end
         end
 
-        x = w * inv(w) * r
+        x = w * inv(SL3Z(word(w)[end:end])) * r
 
-        @test length(word(x)) == 5
+        @test length(word(x)) == length(word(r))
         @test size(x) == (3, 3)
         @test eltype(x) == Int8
 
@@ -65,10 +63,10 @@ using Groups.MatrixGroups
             end
         end
 
-        x = gens(Sp6, 1)
-        x *= inv(x) * gens(Sp6, 2)
+        x = gens(Sp6, 1) * gens(Sp6, 2)^2
+        x *= inv(gens(Sp6, 2)^2) * gens(Sp6, 3)
 
-        @test length(word(x)) == 3
+        @test length(word(x)) == 2
         @test size(x) == (6, 6)
         @test eltype(x) == Int8
 
@@ -80,7 +78,7 @@ using Groups.MatrixGroups
         @test contains(sprint(show, MIME"text/plain"(), x), "∈ Sp{6,Int8}")
         @test sprint(print, x) isa String
 
-        @test length(word(x)) == 1
+        @test length(word(x)) == 2
 
         for g in gens(Sp6)
             @test MatrixGroups.issymplectic(MatrixGroups.matrix(g))
@@ -101,10 +99,10 @@ using Groups.MatrixGroups
             end
         end
 
-        x = gens(G, 1)
-        x *= inv(x) * gens(G, 2)
+        x = gens(G, 1) * gens(G, 2)^3
+        x *= gens(G, 2)^-3
 
-        @test length(word(x)) == 3
+        @test length(word(x)) == 1
         @test size(x) == (6, 6)
         @test eltype(x) == Int16