duality fixed

Author: scheinerman

src/Dual.jl

@@ -17,12 +17,12 @@ function dual(T::Tableau)::Tableau
     m = T.n_cons
     n = T.n_vars
 
-    II = -T.M[2:end, (n - 1):(end - 1)]
+      II = -A[:, end-m+1:end]
 
     if II ≠ eye(Int, m)
         error(msg)
     end
-    A = A[:, 1:(n - m)]
+    A = A[:, 1:n-m]
 
     if !iszero(c[(n - m + 1):end])
         error(msg)

test/runtests.jl

@@ -17,3 +17,19 @@ using SimplexTableaux
     set_basis!(T, [3, 4])
     @test !is_feasible(T)
 end
+
+@testset "Duality" begin
+    A = [11 2 11; 8 6 9; 8 8 5; 6 5 8; 4 1 2; 2 -1 4]
+    b = [0, 1, 10, 3, 2, 5]
+    c = [3, 4, 7]
+
+    T = Tableau(A, b, c)
+    dT = dual(T)
+
+    simplex_solve!(T, false)
+    v = value(T)
+
+    simplex_solve!(dT, false)
+    dv = value(dT)
+    @test v == -dv
+end