work

Author: scheinerman

development/cycling-tries.jl

@@ -0,0 +1,91 @@
+# source: https://web.ist.utl.pt/~mcasquilho/CD_Casquilho/LP2004Comp&OR_GassVinjamuri.pdf
+
+using SimplexTableaux, SimpleGraphs, DrawSimpleGraphs, Plots
+
+
+
+"""
+    find_all_matrix_pivots(T::Tableau)
+
+Return a list of tuples `(i,j)` at which `T` has a good matrix pivot 
+at the `i,j`-entry. 
+"""
+function find_all_matrix_pivots(T::Tableau)
+    top_row = T.M[1, 2:(end - 1)]
+    m, n = size(T.A)
+    col_list = [j for j in 1:n if top_row[j] > 0]
+
+    result = Vector{Tuple{Int,Int}}()
+    for j in col_list
+        a = T.M[2:end, j + 1]
+        b = T.M[2:end, end]
+        rats = b .// a
+
+        for i in 1:m
+            if a[i] < 0 || rats[i] < 0
+                rats[i] = 1//0
+            end
+        end
+
+        min_rat = minimum(rats)
+
+        if min_rat == 1//0
+            continue
+        end
+
+        ilist = [i for i in 1:m if rats[i]==min_rat]
+
+        for i in ilist
+            p = (i, j)
+            push!(result, p)
+        end
+    end
+    return result
+end
+
+"""
+    simplex_graph(T::Tableau)::DirectedGraph{Vector{Int}}
+
+Create a `DirectedGraph` for every possible pivot of `T`.
+"""
+function simplex_graph(T::Tableau)::DirectedGraph{Vector{Int}}
+    G = DirectedGraph{Vector{Int}}()
+
+    blist = find_all_bases(T)
+    for B in blist
+        add!(G, B)
+    end
+
+    for B in blist
+        set_basis!(T, B)
+        plist = find_all_matrix_pivots(T)
+        for ij in plist
+            i, j = ij
+            matrix_pivot!(T, i, j)
+            BB = get_basis(T)
+            add!(G, B, BB)
+            println("$B --> $BB")
+            set_basis!(T, B)
+        end
+    end
+
+    return G
+end
+
+function _one_pass_trim(G::DirectedGraph)::Int
+    kills = 0
+    VV = vlist(G)
+    for v in VV
+        if in_deg(G, v)==0 || out_deg(G, v)==0
+            delete!(G, v)
+            kills+=1
+        end
+    end
+    return kills
+end
+
+import SimpleGraphs.trim
+function trim(G::DirectedGraph)
+    while _one_pass_trim(G) > 0
+    end
+end

development/examples.jl

@@ -150,6 +150,30 @@ function deg_picture()
     finish()
 end
 
+# from the Gass and Vinjamuri paper
 
+function example_kuhn()
+    A = [
+        1 0 0 -2 -9 1 9;
+        0 1 0 1//3 1 -1//3 -2;
+        0 0 1 2 3 -1 -12
+    ]
+    b = [0; 0; 2]
+    c = [0; 0; 0; -2; -3; 1; 12]
+
+    return Tableau(A, b, c, false)
+end
+
+function example_chvatal()
+    c = [10; -57; -9; -24]
+    A = [
+        1//2 -11//2 -5//2 9
+        1//2 -3//2 -1//2 1
+        1 0 0 0
+    ]
+    b = [0; 0; 1]
+    T = Tableau(A, b, -c)
+    return T
+end
 
 nothing