first pass at ideal lexico normal form algorithm

src/LocalPolytope/generators.jl

@@ -32,7 +32,7 @@ function generator_facet(BG :: BellGame, PM :: PrepareAndMeasure) :: BellGame
 end
 
 """
-Helper function for `generator_facet`. 
+Helper function for `generator_facet`.
 """
 function _perm_increase_lexico_score(
     game::Matrix{Int64},
@@ -140,3 +140,106 @@ function lexico_score(BG :: BellGame) :: Vector{Int64}
 
     map(row -> QMath.base_n_val(row, base), eachrow(game_copy))
 end
+
+
+# function generator(BG :: BellGame, PM :: PrepareAndMeasure) :: BellGame
+#
+#     _lexico_reduce(m :: Matrix{Int64}, target_row :: Int64,  )
+#
+# end
+
+
+function _lexico_reduce(
+    m :: Matrix{Int64},
+    target_row :: Int64,
+    max_perms ::  Vector{Tuple{Vector{Int64},Vector{Int64}}},
+    allowed_col_perms :: Vector{Vector{Int64}}
+    # allowed_row_perms :: Vector{Int64},
+    # PM :: PrepareAndMeasure
+)
+    num_rows = size(m,2)
+    allowed_row_perms = collect(target_row:num_rows)
+
+    println("m : ", m)
+    println("target_row : ", target_row)
+    println("allowed_col_perms : ", allowed_col_perms)
+
+    current_best_row =  m[max_perms[1][1][target_row], max_perms[1][2]]
+
+    for allowed_col_perm  in allowed_col_perms
+
+        new_max_perms = Vector{Tuple{Vector{Int64},Vector{Int64}}}(undef,0)
+        for perm in max_perms
+
+
+            # find the col permutation ids which maximize each row
+            max_col_perms = map( b -> sort(allowed_col_perm, by=x->m[b,x], rev=true), perm[1][allowed_row_perms])
+
+            # sort row ids by their maximal col permutation
+            sorted_row_perms = sort( allowed_row_perms, by=b -> m[b,max_col_perms[b-target_row+1]], rev=true)
+
+            example_best = m[sorted_row_perms[1],max_col_perms[sorted_row_perms[1]-target_row + 1 ]]
+            example_best_row = copy(current_best_row)
+            example_best_row[allowed_col_perm] = example_best
+
+            # find all row ids which achieve the maximal permutation
+            max_row_perms = filter(b -> isequal(example_best, m[b,max_col_perms[b-target_row+1]]), sorted_row_perms)
+
+            if current_best_row < example_best_row
+                current_best_row = example_best_row
+                new_max_perms = Vector{Tuple{Vector{Int64},Vector{Int64}}}(undef,0)
+            end
+
+            if current_best_row == example_best_row
+                # update and branch the existing permutation
+                for max_row_perm in max_row_perms
+
+                    new_max_perm = copy.(perm)
+
+                    # swap optimal row into its optimal position
+                    new_max_perm[1][target_row] = max_row_perm
+                    new_max_perm[1][max_row_perm] = target_row
+
+                    # update allowed columns with the corresponding permutation ids
+                    new_max_perm[2][allowed_col_perm] = max_col_perms[max_row_perm-target_row+1]
+
+                    push!(new_max_perms, new_max_perm)
+                end
+
+            end
+        end
+
+        if length(new_max_perms) > 0
+            max_perms = new_max_perms
+        end
+    end
+
+    best_row_id = max_perms[1][1][target_row]
+    best_col_ids = max_perms[1][2]
+    best_m_row = m[best_row_id,best_col_ids]
+
+
+    if target_row < PM.B
+        # updating the allowed column permutations
+        new_allowed_col_perms = Vector{Vector{Int64}}(undef,0)
+        for col_perm in allowed_col_perms
+            if length(col_perm) == 1
+                # if we couldn't permute before we still can't
+                push!(new_allowed_col_perms, col_perm)
+            elseif length(unique(best_m_row[col_perm])) == 1
+                # if all elements are the same, we continue to  consider the perm group
+                push!(new_allowed_col_perms, col_perm)
+            else
+                for n in unique(best_m_row[col_perm])
+                    sub_group_ids = findall( el -> el == n, best_m_row[col_perm])
+
+                    push!(new_allowed_col_perms, col_perm[sub_group_ids])
+                end
+            end
+        end
+
+        _lexico_reduce(m, target_row + 1, max_perms, new_allowed_col_perms )
+    end
+
+    max_perms
+end