Using HRepIterator and hyperplane to check binding inequalities.

Author: shizejin

src/vertex_enumeration.jl

@@ -1,4 +1,7 @@
-function vertex_enumeration(g::NormalFormGame{2}; plib=getlibraryfor(2, Float64))
+import Polyhedra: hyperplane
+
+function vertex_enumeration(g::NormalFormGame{2};
+                            plib=getlibraryfor(2, Float64))
 
     c = Channel(0)
     task = vertex_enumeration_task(c, g, plib)
@@ -22,53 +25,73 @@ function vertex_enumeration_task(c::Channel,
 
 end
 
-function _vertex_enumeration_producer(c::Channel,
-                                      g::NormalFormGame{2},
-                                      plib)
+function _vertex_enumeration_producer{T}(c::Channel,
+                                         g::NormalFormGame{2, T},
+                                         plib)
 
     n, m = size(g.players[1].payoff_array)
-    BRSv = [_BRS_vertices(g, opp_idx, plib) for opp_idx in 1:2]
-    ZERO_LABELING = BitArray(vcat(zeros(m), ones(n)))
-    COMPLETE_LABELING = trues(n+m)
 
-    for i in 1:size(BRSv[1][3])[1]
-        v1 = BRSv[1][3][i, :]
-        labeling1 = *(BRSv[1][1], v1) .≈ BRSv[1][2]
+    # create Representation for player 1
+    H1, V1, H2, V2 = construction_BRP(g, plib)
+
+    ZERO_LABELING_BITS = (1 << (n+m)) - (1 << m)
+    COMPLETE_LABELING_BITS = 1 << (n+m) - 1
 
-        if labeling1 == ZERO_LABELING
+    for v1 in vreps(V1)
+        labelings_bits1 = labelings_bits(v1, H1)
+        if labelings_bits1 == ZERO_LABELING_BITS
             continue
         end
-
-        for j in 1:size(BRSv[2][3])[1]
-            v2 = BRSv[2][3][j, :]
-            labeling2 = *(BRSv[2][1], v2) .≈ BRSv[2][2]
-
-            if xor.(labeling1, labeling2) == COMPLETE_LABELING
+        for v2 in vreps(V2)
+            labelings_bits2 = labelings_bits(v2, H2)
+            if xor(labelings_bits1, labelings_bits2) == COMPLETE_LABELING_BITS
                 put!(c, (_get_mixed_action(v1),
                          _get_mixed_action(v2)))
             end
         end
     end
-end
 
-function _BRS_vertices(g::NormalFormGame, idx::Integer, plib)
+end
 
-    opp_idx = idx % 2 + 1
-    B = g.players[opp_idx].payoff_array
-    n, m = size(B)
+function construction_BRP{T}(g::NormalFormGame{2, T}, plib)
 
-    arr = [B, -eye(m)]
-    D = vcat(arr[idx], arr[opp_idx])
-    vec = [ones(Float64, n), zeros(Float64, m)]
-    b = vcat(vec[idx], vec[opp_idx])
+    n, m = size(g.players[1].payoff_array)
 
-    hrep = SimpleHRepresentation(D, b)
-    p = polyhedron(hrep, plib)
-    vertices = SimpleVRepresentation(p).V
+    # create Representation for player 1
+    C = Matrix{T}(n+m, n)
+    C[1:m, :] = g.players[2].payoff_array
+    C[m+1:end, :] = -eye(T, n)
+    b1 = Vector{T}(n+m)
+    b1[1:m] = one(T)
+    b1[m+1:end] = zero(T)
+    H1 = SimpleHRepresentation(C, b1)
+    p1 = polyhedron(H1, plib)
+    V1 = SimpleVRepresentation(p1)
+
+    # create Representation for player 2
+    D = Matrix{T}(n+m, m)
+    D[1:m, :] = -eye(T, m)
+    D[m+1:end, :] = g.players[1].payoff_array
+    b2 = Vector{T}(n+m)
+    b2[1:m] = zero(T)
+    b2[m+1:end] = one(T)
+    H2 = SimpleHRepresentation(D, b2)
+    p2 = polyhedron(H2, plib)
+    V2 = SimpleVRepresentation(p2)
+
+    return H1, V1, H2, V2
+end
 
-    return D, b, vertices
+function labelings_bits(v::VRepElement, p::HRep)
+    b = 0
+    for (i, h) in enumerate(hreps(p))
+        if v in hyperplane(h)
+            b += 1 << (i-1)
+        end
+    end
+    return b
 end
 
-function _get_mixed_action(a)
+function _get_mixed_action(a::Vector)
     return a ./ sum(a)
 end