RhodeCode

  }

  return true;

}

// Check the feasibility of the given potentials (dual soluiton)

// using the "Complementary Slackness" optimality condition

template < typename GR, typename LM, typename UM,

           typename CM, typename SM, typename FM, typename PM >

bool checkPotential( const GR& gr, const LM& lower, const UM& upper,

                     const CM& cost, const SM& supply, const FM& flow, 

                     const PM& pi )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);

  bool opt = true;

  for (ArcIt e(gr); opt && e != INVALID; ++e) {

    typename CM::Value red_cost =

      cost[e] + pi[gr.source(e)] - pi[gr.target(e)];

    opt = red_cost == 0 ||

          (red_cost > 0 && flow[e] == lower[e]) ||

          (red_cost < 0 && flow[e] == upper[e]);

  }

  for (NodeIt n(gr); opt && n != INVALID; ++n) {

    typename SM::Value sum = 0;

    for (OutArcIt e(gr, n); e != INVALID; ++e)

      sum += flow[e];

    for (InArcIt e(gr, n); e != INVALID; ++e)

      sum -= flow[e];

    opt = (sum == supply[n]) || (pi[n] == 0);

  }

  return opt;

}

// Run a minimum cost flow algorithm and check the results

template < typename MCF, typename GR,

           typename LM, typename UM,

           typename CM, typename SM >

void checkMcf( const MCF& mcf, bool mcf_result,

               const GR& gr, const LM& lower, const UM& upper,

               const CM& cost, const SM& supply,

               bool result, typename CM::Value total,

               const std::string &test_id = "",

               ProblemType type = EQ )

{

  check(mcf_result == result, "Wrong result " + test_id);

  if (result) {

    check(checkFlow(gr, lower, upper, supply, mcf.flowMap(), type),

          "The flow is not feasible " + test_id);

    check(mcf.totalCost() == total, "The flow is not optimal " + test_id);

    check(checkPotential(gr, lower, upper, cost, supply, mcf.flowMap(),

                         mcf.potentialMap()),

          "Wrong potentials " + test_id);

  }

}

int main()

{

  // Check the interfaces

  {

    typedef int Flow;

    typedef int Cost;

    checkConcept< McfClassConcept<GR, Flow, Cost>,

                  NetworkSimplex<GR, Flow, Cost> >();

  }

  // Run various MCF tests

  typedef ListDigraph Digraph;

  DIGRAPH_TYPEDEFS(ListDigraph);

  // Read the test digraph

  Digraph gr;

  Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);

  Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr);

  ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());

  Node v, w;

  std::istringstream input(test_lgf);

  DigraphReader<Digraph>(gr, input)

    .arcMap("cost", c)

    .arcMap("cap", u)

    .arcMap("low1", l1)

    .arcMap("low2", l2)

    .nodeMap("sup1", s1)

    .nodeMap("sup2", s2)

    .nodeMap("sup3", s3)

    .nodeMap("sup4", s4)

    .nodeMap("sup5", s5)

    .node("source", v)

    .node("target", w)

    .run();

  // A. Test NetworkSimplex with the default pivot rule

  {

    NetworkSimplex<Digraph> mcf(gr);

    // Check the equality form

    mcf.upperMap(u).costMap(c);

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l1, u, c, s1, true,  5240, "#A1");

    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),

             gr, l1, u, c, s2, true,  7620, "#A2");

    mcf.lowerMap(l2);

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l2, u, c, s1, true,  5970, "#A3");

    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),

             gr, l2, u, c, s2, true,  8010, "#A4");

    mcf.reset();

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l1, cu, cc, s1, true,  74, "#A5");

    checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(),

             gr, l2, cu, cc, s2, true,  94, "#A6");

    mcf.reset();

    checkMcf(mcf, mcf.run(),

             gr, l1, cu, cc, s3, true,   0, "#A7");

    checkMcf(mcf, mcf.boundMaps(l2, u).run(),

             gr, l2, u, cc, s3, false,   0, "#A8");

    // Check the GEQ form

    mcf.reset().upperMap(u).costMap(c).supplyMap(s4);

    checkMcf(mcf, mcf.run(),

             gr, l1, u, c, s4, true,  3530, "#A9", GEQ);

    mcf.problemType(mcf.GEQ);

    checkMcf(mcf, mcf.lowerMap(l2).run(),

             gr, l2, u, c, s4, true,  4540, "#A10", GEQ);

    mcf.problemType(mcf.CARRY_SUPPLIES).supplyMap(s5);