add reworked FPGroups_GAP.jl

src/FPGroups_GAP.jl

@@ -0,0 +1,178 @@
+using JLD
+using DelimitedFiles
+
+abstract type WordReduction end
+struct KnuthBendix <: WordReduction end
+struct AutomaticStructure <: WordReduction end
+
+const GAP_EXECUTABLE = get(ENV, "GAP_EXECUTABLE", "gap")
+
+const PRODUCT_MATRIX_FUNCTIONS = """
+MetricBalls := function(rws, halfradius)
+    local l, basis, sizes, i;
+    l := EnumerateReducedWords(rws, 0, halfradius);;
+    SortBy(l, Length);
+    sizes := [1..halfradius];
+    Apply(sizes, i -> Number(l, w -> Length(w) <= i));
+    return [l, sizes];
+end;;
+
+ProductMatrix := function(rws, basis, len)
+    local result, dict, g, tmpList, t;
+    result := [];
+    dict := NewDictionary(basis[1], true);
+    t := Runtime();
+    for g in [1..Length(basis)] do;
+        AddDictionary(dict, basis[g], g);
+    od;
+    Print("Creating dictionary: \t\t", StringTime(Runtime()-t), "\\n");
+    for g in basis{[1..len]} do;
+        tmpList := List(Inverse(g)*basis{[1..len]}, w->ReducedForm(rws, w));
+        #t := Runtime();
+        tmpList := List(tmpList, x -> LookupDictionary(dict, x));
+        #Print(Runtime()-t, "\\n");
+        Assert(1, ForAll(tmpList, x -> x <> fail));
+        Add(result, tmpList);
+    od;
+    return result;
+end;;
+
+SaveCSV := function(fname, pm)
+   local file, i, j, k;
+   file := OutputTextFile(fname, false);;
+   for i in pm do;
+      k := 1;
+      for j in i do;
+         if k < Length(i) then
+            AppendTo(file, j, ", ");
+         else
+            AppendTo(file, j, "\\n");
+         fi;
+         k := k+1;
+      od;
+   od;
+   CloseStream(file);
+end;;
+"""
+
+function product_matrix_GAP_code(reduction::Type{<:WordReduction},
+    G::FPGroup, dir, halfradius; maxeqns=100_000, infolevel=2)
+    code = """
+LogTo("$(dir)/GAP.log");
+RequirePackage("kbmag");
+SetInfoLevel(InfoRWS, $infolevel);
+
+$PRODUCT_MATRIX_FUNCTIONS
+$(GAP_code(G))
+
+# G:= SimplifiedFpGroup(G);
+rws := KBMAGRewritingSystem(G);
+# ResetRewritingSystem(rws);
+O:=OptionsRecordOfKBMAGRewritingSystem(rws);;
+O.maxeqns := $maxeqns;
+O.maxstates := 1000*$maxeqns;
+#O.maxstoredlen := [100,100];
+
+before := Runtimes();;
+$reduction(rws);
+after := Runtimes();;
+delta := after.user_time_children - before.user_time_children;;
+Print("$reduction time: \t", StringTime(delta), "\\n");
+
+t := Runtime();
+res := MetricBalls(rws,$(2halfradius));;
+Print("Metric-Balls generation: \t", StringTime(Runtime()-t), "\\n");
+B := res[1];; sizes := res[2];;
+Print("Sizes of generated Balls: \t", sizes, "\\n");
+
+t := Runtime();
+pm := ProductMatrix(rws, B, sizes[$halfradius]);;
+Print("Computing ProductMatrix: \t", StringTime(Runtime()-t), "\\n");
+
+S := EnumerateReducedWords(rws, 1, 1);
+S := List(S, s -> Position(B,s));
+
+SaveCSV("$(dir)/pm.csv", pm);
+SaveCSV("$(dir)/S.csv", [S]);
+SaveCSV("$(dir)/sizes.csv", [sizes]);
+SaveCSV("$(dir)/B_$(2halfradius).csv", [B]);
+
+Print("DONE!\\n");
+
+quit;""";
+    return code
+end
+
+function GAP_code(G::FPGroup)
+    S = gens(G);
+    rels = [k*inv(v) for (k,v) in G.rels]
+    F = "FreeGroup("*join(["\"$v\"" for v in S], ", ") *");"
+    m = match(r".*(\[.*\])$", string(rels))
+    rels_gap = replace(m.captures[1], " "=>"\n")
+
+    gap_code = """
+    F := $F;
+    AssignGeneratorVariables(F);;
+    relations := $rels_gap;;
+    G := F/relations;
+    """
+    return gap_code
+end
+
+function GAP_execute(gap_code, dir)
+    isdir(dir) || mkpath(dir)
+    GAP_file = joinpath(dir, "GAP_code.g")
+    @info "Writing GAP code to $GAP_file"
+
+    open(GAP_file, "w") do io
+        write(io, gap_code)
+    end
+    run(pipeline(`cat $(GAP_file)`, `$GAP_EXECUTABLE -q`))
+end
+
+function prepare_pm_delta_csv(reduction::Type{<:WordReduction},
+    G::FPGroup, name::AbstractString, halfradius::Integer; kwargs...)
+
+    @info "Preparing multiplication table using GAP (via kbmag)"
+    gap_code = product_matrix_GAP_code(reduction, G, name, halfradius; kwargs...)
+    return GAP_execute(gap_code, name)
+end
+
+function prepare_pm_delta(reduction::Type{<:WordReduction},
+    G::FPGroup, name::AbstractString, halfradius::Integer; kwargs...)
+    pm_fname = joinpath(name, "pm.csv")
+    S_fname = joinpath(name, "S.csv")
+    sizes_fname = joinpath(name, "sizes.csv")
+    delta_fname = joinpath(name, "delta.jld")
+
+    csv_files_exist = isfile(pm_fname) && isfile(S_fname) && isfile(sizes_fname)
+
+    if !csv_files_exist
+        @info "Creating csv files"
+        prepare_pm_delta_csv(reduction, G, name, halfradius; kwargs...)
+    elseif isfile(sizes_fname)
+        sizes = readdlm(sizes_fname, ',')[1,:]
+        if 2halfradius > length(sizes)
+            prepare_pm_delta_csv(reduction, G, name, halfradius; kwargs...)
+        end
+    end
+
+    @assert isfile(pm_fname) && isfile(S_fname) && isfile(sizes_fname)
+
+    @info "Reading csv files"
+    pm = Int.(readdlm(pm_fname, ','))
+    S = Int.(readdlm(S_fname, ',')[1,:])
+    sizes = Int.(readdlm(sizes_fname, ',')[1,:])
+
+    Δ = spzeros(Int, sizes[2halfradius])
+    Δ[S] .= -1
+    Δ[1] = length(S)
+
+    pm = pm[1:sizes[halfradius], 1:sizes[halfradius]]
+    @info "Writing delta.jld for radius $(2halfradius)"
+    save(joinpath(name, "delta.jld"), "coeffs", Δ, "pm", pm)
+end
+
+function prepare_pm_delta(G::FPGroup, dir, halfradius; kwargs...)
+    return prepare_pm_delta(KnuthBendix, G, dir, halfradius; kwargs... )
+end