From 4cfad002de7cc7edbbde7b383793b917f57b660a Mon Sep 17 00:00:00 2001
From: Caroline Rogers <carolinerogers@ufl.edu>
Date: Fri, 28 Oct 2022 12:17:20 -0400
Subject: [PATCH] ENH: Layouts generated by majoriztion algorithm

---
 experiments/layout/Project.toml         |   4 +
 experiments/layout/src/Majorization.jl  | 187 ++++++++++++++++++++++++
 experiments/layout/src/Setup.jl         |  68 +++++++++
 experiments/layout/src/Visualization.jl | 153 +++++++++++++++++++
 experiments/layout/src/layout.jl        |   5 +
 5 files changed, 417 insertions(+)
 create mode 100644 experiments/layout/Project.toml
 create mode 100644 experiments/layout/src/Majorization.jl
 create mode 100644 experiments/layout/src/Setup.jl
 create mode 100644 experiments/layout/src/Visualization.jl
 create mode 100644 experiments/layout/src/layout.jl

diff --git a/experiments/layout/Project.toml b/experiments/layout/Project.toml
new file mode 100644
index 000000000..b2e802954
--- /dev/null
+++ b/experiments/layout/Project.toml
@@ -0,0 +1,4 @@
+name = "layout"
+uuid = "8dadf337-1fa2-4dfe-88ac-366e9b2dd86c"
+authors = ["Caroline Rogers <carolinerogers@ufl.edu>"]
+version = "0.1.0"
diff --git a/experiments/layout/src/Majorization.jl b/experiments/layout/src/Majorization.jl
new file mode 100644
index 000000000..a4b295519
--- /dev/null
+++ b/experiments/layout/src/Majorization.jl
@@ -0,0 +1,187 @@
+using Catlab
+import Graphs as grs
+import Catlab.Graphs as cat_grs 
+import Catlab.Graphics: Graphviz
+using Catlab.Graphics, Catlab.CategoricalAlgebra, Catlab.Graphics.GraphvizGraphs
+using LinearAlgebra
+using ..Visualization
+using NLsolve
+using Random
+
+# TO ADD: ideal path vs shortest path
+# look into figuring out how to specify rotation (think square) 
+# need right angles for squares and one right angle for triangle
+
+# graph generators - Owen
+
+
+#======= file I/O to get positions =======#
+
+#=
+function get_positions(g)
+    to_graphviz(prog="dot", g)
+end
+=#
+
+#======= create weighted laplacian =======#
+function weighted_laplacian(g, num_vert)
+    # calculate shortest distance
+    weighted_lap = - grs.floyd_warshall_shortest_paths(g).dists
+    the_sum = sum(weighted_lap)
+
+    # check for i = j
+    n = num_vert
+    for i in 1:n
+        for j in 1:n
+            if(weighted_lap[i,j] == 0)
+                weighted_lap[i,j] = the_sum
+            end
+        end
+    end
+    
+    return weighted_lap
+end
+
+#current pos is vector of positions (x,y)
+
+#======= create X(t) laplacian =======#
+function x_laplacian(g, current_pos, num_vert)
+    n = num_vert
+    x_lap = zeros(n,n)
+    # might want to change floyd warshall to something else - meant to be the IDEAL path
+    dist = grs.floyd_warshall_shortest_paths(g).dists
+
+    for i in 1:n
+        current = current_pos[i]
+        
+        if(i == n) 
+            neighbor = current_pos[i-1]
+        else
+            neighbor = current_pos[i+1]
+        end
+
+        for j in 1:n
+            if(i != j)
+                # node i is located at Xi
+                # confused on the x,y of positions --- FIX THIS
+                x_lap[i,j] = -1 * dist[i,j] * inv(norm(current - neighbor))
+            end
+        end
+    end
+
+    the_sum = sum(x_lap)
+
+    #find zeros
+    for i in n
+        for j in n
+            if(x_lap[i,j] == 0)
+                x_lap[i,j] = -1 * the_sum
+            end
+        end
+    end
+
+    return x_lap
+end
+
+#current_pos is vector of positions (x,y)
+
+#======= create stress function =======#
+function stress_function(graph, current_pos, num_vert)
+    stress = []
+
+    # constant, calculate once
+    w_lap = weighted_laplacian(graph, num_vert)
+    n = num_vert
+
+    # recomputed at every iteration (bc it includes position)
+    x_lap = x_laplacian(graph, current_pos, num_vert)
+
+    #equation
+    (x, y) -> (inv(weighted_lap[i,j]) * x_lap[i,j] * x)
+    new_pos = 0;
+
+    for i in 1:n
+        current = current_pos[i]
+        for j in 1:n
+
+            function f!(F, x)
+                F[1] = (inv(w_lap[i,j]) * x_lap[i,j] * x[1])
+                F[2] = (inv(w_lap[i,j]) * x_lap[i,j] * x[2])
+            end
+            new_pos = nlsolve(f!, current)
+        end
+        push!(stress, new_pos.zero)
+    end
+
+    return stress
+end
+
+# current_pos is vector of positions (vector of vectors?)
+
+#======= calculate for all nodes =======#
+function stress_majorization(original_pos, old_graph, num_vert)
+    n = num_vert
+    new_positions = Vector{String}()
+
+    #end when [stress(X(t)) - stress(X(t+1))] / stress(X(t)) < 10^-4
+
+    #gives a vector of NL solve results
+    original_stress = stress_function(old_graph, original_pos, n)
+
+    new_graph = old_graph
+    new_pos = original_pos
+    current_stress = original_stress
+
+    # FIX ME!!!!! while loop broken
+    #while((original_stress[n][1] - current_stress[n][1]) / original_stress[n][1] < 10^(-4))
+    #for i in 1:2
+       
+    empty!(new_positions)
+
+    # gives a vector of (x,y) vectors
+    stress = stress_function(new_graph, new_pos, n)
+    new_pos = stress
+
+    for i in 1:n
+        #gives the solution vector (x,y)
+        sln = new_pos[i]
+        string_sln = string(sln[1], ",", sln[2])
+
+        push!(new_positions, string_sln)
+    end
+
+
+    return new_positions
+end
+
+
+#======= TESTING =======#
+
+
+#original graph
+
+nv = 4
+
+cat_g = cat_grs.cycle_graph(cat_grs.Graph, nv)
+gv = to_graphviz(cat_g)
+
+g = grs.cycle_graph(nv)
+
+# new graph
+
+#good guess
+#curr = [[1.0, 0.0], [2.0, 1.0], [3.0, 1.0], [4.0, 1.0], [5.0, 0.0]]
+
+curr = []
+#bad guess
+for i in 1:nv
+    push!(curr, [float(rand((1:nv))), float(rand((0:nv)))])
+end
+
+pos_string = stress_majorization(curr, g, nv)
+
+new_G = to_graphviz_property_graph(cat_g; prog="neato", node_attrs=Dict(:pos=>pos_string))
+#new_G = to_graphviz_property_graph(cat_g; prog="neato")
+
+to_graphviz(new_G)
+
diff --git a/experiments/layout/src/Setup.jl b/experiments/layout/src/Setup.jl
new file mode 100644
index 000000000..25000d14a
--- /dev/null
+++ b/experiments/layout/src/Setup.jl
@@ -0,0 +1,68 @@
+module Setup
+export BW, is_mat, is_normal
+
+using AlgebraicRewriting
+using Catlab, Catlab.CategoricalAlgebra, Catlab.Present, Catlab.Theories, Catlab.Graphs
+
+using Catlab.Meta: Expr0
+
+import Base: (*)
+
+@present TheoryWeightedLabeledGraphCospan <: SchGraph begin
+  (Weight, Color)::AttrType
+  weight::Attr(E,Weight)
+  color::Attr(V,Color)
+  (I,O)::Ob
+  i::Hom(I, V)
+  o::Hom(O, V)
+  # Not enforced, but:
+  # i ⋅ color == false
+  # o ⋅ color == true
+end
+
+@abstract_acset_type AbstractWeightedLabeledGraphCospan <: AbstractGraph
+
+@acset_type WeightedLabeledGraphCospan(
+  TheoryWeightedLabeledGraphCospan, index=[:src,:tgt,]
+  ) <: AbstractWeightedLabeledGraphCospan
+
+const BW = WeightedLabeledGraphCospan{Union{Expr0, Var, Int, Rational},
+                                      Union{Expr0, Var, Bool}}
+
+function BW(s,t,color=false,weight=1;i=[],o=[])
+  i = i isa AbstractVector ? i : [i]
+  o = o isa AbstractVector ? o : [o]
+  color = color isa AbstractVector ? color : repeat([color], max(vcat(s,t)))
+  weight = weight isa AbstractVector ? weight : repeat([weight], length(s))
+  @acset BW begin
+      V = length(color); E=length(s); I=length(i); O=length(o);
+      i=i; o=o; color=color; weight=weight; src=s; tgt=t
+  end
+end
+
+function (*)(g::BW, scalar::Union{Int,Rational})
+  g = deepcopy(g)
+  set_subpart!(g, :weight, [a*scalar for a in g[:weight]])
+  return g
+end
+
+(*)(scalar::Union{Int,Rational}, g::BW) = g * scalar
+
+
+function is_normal(g::BW)::Bool
+  for v in vertices(g)
+    if g[v, :color] # white node
+      if !isempty(incident(g, v, :src)) return false end
+    else
+      if !isempty(incident(g, v, :tgt)) return false end
+    end
+  end
+  st = collect(zip(g[:src], g[:tgt])) # at most one edge btw two nodes
+  return length(st) == length(unique(st))
+end
+
+is_mat(g::BW) = (is_normal(g)
+    && sort(g[:i]) == findall((!).(g[:color]))
+    && sort(g[:o]) == findall(g[:color]))
+
+end # module
diff --git a/experiments/layout/src/Visualization.jl b/experiments/layout/src/Visualization.jl
new file mode 100644
index 000000000..b18a61f06
--- /dev/null
+++ b/experiments/layout/src/Visualization.jl
@@ -0,0 +1,153 @@
+module Visualization
+export graphviz, view_window
+
+using Blink
+using Interact
+using AlgebraicRewriting
+using Catlab.CategoricalAlgebra
+
+using Catlab.Graphs
+using Catlab.Graphics.Graphviz: Statement
+import Catlab.Graphics: to_graphviz, to_graphviz_property_graph
+import Catlab.Graphics.GraphvizGraphs: node_label, default_node_attrs
+import Catlab.Graphics.Graphviz: pprint
+import Catlab.Graphics.Graphviz
+import Catlab.Graphics: to_graphviz
+
+using AlgebraicRewriting
+using ..Setup
+
+struct Title <: Statement
+  title::String
+end
+
+function pprint(io, titl::Title, n::Int; directed::Bool=false)
+  print(io, """labelloc="t";
+  label="$(titl.title)";""")
+end
+
+function to_graphviz(g::AbstractPropertyGraph)::Graphviz.Graph
+  gv_name(v::Int) = "n$v"
+  gv_path(e::Int) = [gv_name(src(g,e)), gv_name(tgt(g,e))]
+
+  # Add Graphviz node for each vertex in property graph.
+
+  stmts = Graphviz.Statement[gprops(g)[:stmts]...]
+
+  for v in vertices(g)
+    push!(stmts, Graphviz.Node(gv_name(v), vprops(g, v)))
+  end
+
+  # Add Graphviz edge for each edge in property graph.
+  is_directed = !(g isa SymmetricPropertyGraph)
+  for e in edges(g)
+    # In undirected case, only include one edge from each pair.
+    if is_directed || (e <= inv(g,e))
+      push!(stmts, Graphviz.Edge(gv_path(e), eprops(g, e)))
+    end
+  end
+
+  attrs = gprops(g)
+  ga = Graphviz.as_attributes(get(attrs, :graph, Dict()))
+  na = Graphviz.as_attributes(get(attrs, :node, Dict()))
+  ea = Graphviz.as_attributes(get(attrs, :edge, Dict()))
+  Graphviz.Graph(
+    name = get(attrs, :name, "G"),
+    directed = is_directed,
+    prog = get(attrs, :prog, is_directed ? "dot" : "neato"),
+    stmts = stmts,
+    graph_attrs = ga,
+    node_attrs = na,
+    edge_attrs = ea,
+  )
+end
+function to_graphviz_property_graph(g::AbstractGraph;
+  prog::AbstractString="dot", graph_attrs::AbstractDict=Dict(),
+  node_attrs::AbstractDict=Dict(), edge_attrs::AbstractDict=Dict(),
+  node_labels::Union{Symbol,Bool, Pair{Symbol, <:Function}}=false,
+  edge_labels::Union{Symbol,Bool, Pair{Symbol, <:Function}}=false,
+  title::Union{Nothing, String} = nothing
+  )
+  grph = merge!(Dict{Any,Any}(:rankdir => "LR",), graph_attrs)
+  nde = merge!(Dict{Any,Any}(default_node_attrs(node_labels)),
+                             filter(x->!(x[2] isa AbstractVector), node_attrs))
+
+  edg = merge!(Dict{Any,Any}(:arrowsize => "0.5"),
+                             filter(x->!(x[2] isa AbstractVector),edge_attrs))
+  pg = PropertyGraph{Any}(
+    g,
+    v -> node_label(g, node_labels, v),
+    e -> edge_label(g, edge_labels, e);
+    prog = prog,
+    graph = grph,
+    stmts= [Title(isnothing(title) ? "" : title)],
+    node = nde,
+    edge = edg,
+  )
+for (prop, vec) in filter(x->x[2] isa AbstractVector, node_attrs)
+  length(vec) == nv(g) || error("Bad node attr vector length for prop $prop: $(length(vec))!=$(nv(g))")
+  for (v,val) in zip(vertices(g), vec)
+    set_vprops!(pg, v, Dict([prop=>string(val)]))
+  end
+end
+for (prop, vec) in filter(x->x[2] isa AbstractVector, edge_attrs)
+  length(vec) == ne(g) || error("Bad edge attr vector length for prop $prop")
+  for (e,val) in zip(edges(g), vec)
+    set_eprops!(pg, e, Dict([prop=>string(val)]))
+  end
+end
+
+return pg
+end
+node_label(g, labels::Bool, v::Int) = labels ? Dict(:label => string(v)) : Dict{Symbol,String}()
+node_label(g, namef::Pair{Symbol, <:Function}, e::Int) = node_label(g, namef[1], namef[2], e)
+node_label(g, name::Symbol, f::Function, e::Int) = begin
+lab = string(f(g[e, name]))
+return lab == "" ? Dict() :  Dict(:label => lab, :shape=>"circle")
+end
+
+edge_label(g, labels::Bool, v::Int) = labels ? Dict(:label => string(v)) : Dict{Symbol,String}()
+edge_label(g, namef::Pair{Symbol, <:Function}, e::Int) = edge_label(g, namef[1], namef[2], e)
+edge_label(g, name::Symbol, f::Function, e::Int) = Dict(:label => string(f(g[e, name])))
+function default_node_attrs(labels::Union{Symbol,Bool, Pair{Symbol, <:Function}})
+  shape = labels isa Symbol ? "ellipse" : "point" #((!(labels isa Bool) || labels) ? "circle" : "point")
+  Dict(:shape => shape, :width => "0.05", :height => "0.05", :margin => "0")
+end
+
+
+
+function graphviz(G::BW, pos=nothing; title=nothing)
+  G = deepcopy(G)
+  fc = Any[(!(c isa Bool) || c) ? "white" : "black" for c in G[:color]]
+  n_v, n_e, ni, no = [nparts(G,x) for x in [:V,:E,:I,:O]]
+  if !isnothing(pos)
+    if length(pos) == n_v
+      append!(pos, fill("", ni+no))
+    elseif length(pos)!=n_v+ni+no
+       error("pos $pos not length $n_v nor $(n_v+ni+no)")
+    end
+  end
+  append!(fc, fill(:red, ni), fill(:blue, no))
+  add_parts!(G,:V,ni+no; color=true)
+  add_parts!(G,:E, ni+no; src=vcat(n_v+1:n_v+ni, G[:o]),
+              tgt=vcat(G[:i],n_v+ni+1:nv(G)), weight=1//1)
+  sty = vcat(fill("filled", n_v), fill("dotted", ni+no)) # why doesn't this work?
+  n_a = Dict([:width=>".2", :height=>".2", :penwidth=>"3", :fillcolor=>fc,
+              :style=>sty, :color=>"black"])
+  if !isnothing(pos)
+    n_a[:pos] = pos
+  end
+  esty = vcat(fill("solid", n_e), fill("dotted", ni+no))
+  edir = vcat(fill("forward", n_e+ni), fill("forward", no)) # CHANGED
+  e_a = Dict([:style=>esty, :dir=>edir])
+  to_graphviz(G, title=title, prog=isnothing(pos) ? "dot" : "neato", node_attrs=n_a, edge_attrs=e_a,
+            edge_labels= :weight => (x -> x == 1 ? "" : x),
+            node_labels=:color => (x -> (x isa Var || x isa Expr) ? string(x) : ""))
+end;
+
+function view_window(x,y; positions=nothing)
+  w = Window()
+  body!(w, view_traj(x,y; positions=positions))
+end
+
+end # module
diff --git a/experiments/layout/src/layout.jl b/experiments/layout/src/layout.jl
new file mode 100644
index 000000000..53ae989a2
--- /dev/null
+++ b/experiments/layout/src/layout.jl
@@ -0,0 +1,5 @@
+module layout
+
+greet() = print("Hello World!")
+
+end # module