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product.hxx

00001 // product.hxx: this file is part of the Vaucanson project.
00002 //
00003 // Vaucanson, a generic library for finite state machines.
00004 //
00005 // Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 The Vaucanson Group.
00006 //
00007 // This program is free software; you can redistribute it and/or
00008 // modify it under the terms of the GNU General Public License
00009 // as published by the Free Software Foundation; either version 2
00010 // of the License, or (at your option) any later version.
00011 //
00012 // The complete GNU General Public Licence Notice can be found as the
00013 // `COPYING' file in the root directory.
00014 //
00015 // The Vaucanson Group consists of people listed in the `AUTHORS' file.
00016 //
00017 #ifndef VCSN_ALGORITHMS_PRODUCT_HXX
00018 # define VCSN_ALGORITHMS_PRODUCT_HXX
00019 
00020 # include <set>
00021 # include <map>
00022 # include <queue>
00023 # include <stack>
00024 
00025 # include <vaucanson/algorithms/product.hh>
00026 
00027 # ifndef VCSN_NDEBUG
00028 #  include <vaucanson/algorithms/realtime.hh>
00029 # endif // ! VCSN_NDEBUG
00030 
00031 # include <vaucanson/automata/concept/automata_base.hh>
00032 # include <vaucanson/misc/usual_macros.hh>
00033 # include <vaucanson/automata/implementation/geometry.hh>
00034 # include <vaucanson/misc/static.hh>
00035 
00036 namespace vcsn
00037 {
00038 
00039 /*--------------------------------.
00040 | Functor for product algorithm.  |
00041 `--------------------------------*/
00042 template<typename A, typename T, typename U>
00043 class Product
00044 {
00045   public:
00046     typedef AutomataBase<A> structure_t;
00047     typedef Element<A, T> lhs_t;
00048     typedef Element<A, U> rhs_t;
00049     typedef lhs_t           output_t;
00050     typedef std::map<typename output_t::hstate_t,
00051               std::pair<typename lhs_t::hstate_t, typename rhs_t::hstate_t> >
00052                           pair_map_t;
00053 
00054     Product (const structure_t& structure,
00055              const bool use_geometry)
00056       : use_geometry_(use_geometry),
00057         series_(structure.series()),
00058         monoid_(series_.monoid()),
00059         semiring_zero_(series_.semiring().zero(SELECT(semiring_elt_value_t)))
00060     {
00061     }
00062 
00063     // returns the product of @c lhs and @c rhs (and put it also in @c output)
00064     output_t&
00065     operator() (output_t& output,
00066                 const lhs_t& lhs,
00067                 const rhs_t& rhs,
00068                 pair_map_t& m)
00069     {
00070       BENCH_TASK_SCOPED("product");
00071       visited_.clear();
00072 
00073       precondition(is_realtime(lhs));
00074       precondition(is_realtime(rhs));
00075 
00076       this->initialize_queue(output, lhs, rhs, m);
00077 
00078       while (not to_process_.empty())
00079       {
00080         const pair_hstate_t current_pair = to_process_.front();
00081         to_process_.pop();
00082 
00083         const hstate_t lhs_s         = current_pair.first;
00084         const hstate_t rhs_s         = current_pair.second;
00085         const hstate_t current_state = visited_[current_pair];
00086 
00087         output.set_initial(current_state,
00088                            lhs.get_initial(lhs_s) * rhs.get_initial(rhs_s));
00089         output.set_final(current_state,
00090                          lhs.get_final(lhs_s) * rhs.get_final(rhs_s));
00091 
00092         for (typename lhs_t::delta_iterator l(lhs.value(), lhs_s);
00093              ! l.done();
00094              l.next())
00095           for (typename rhs_t::delta_iterator r(rhs.value(), rhs_s);
00096                ! r.done();
00097                r.next())
00098           {
00099             series_set_elt_t    prod_series(series_);
00100 
00101             if (is_product_not_null(lhs, rhs, l, r, prod_series))
00102             {
00103               const pair_hstate_t new_pair(lhs.dst_of(*l), rhs.dst_of(*r));
00104               typename visited_t::const_iterator found = visited_.find(new_pair);
00105 
00106               hstate_t dst;
00107               if (found == visited_.end())
00108               {
00109                 dst = output.add_state();
00110 
00111                 this->add_state_to_process(output, lhs, rhs, m, dst, new_pair);
00112               }
00113               else
00114                 dst = found->second;
00115               output.add_series_transition(current_state, dst, prod_series);
00116             }
00117           }
00118       }
00119       return output;
00120     }
00121 
00122   private:
00123     // Some little graphic tools
00124     class grphx
00125     {
00126       public:
00127         template <typename Output, typename Lhs, typename Rhs>
00128         static void
00129         setcoordfrom (Output& a,
00130                       const Lhs& lhs,
00131                       const Rhs& rhs,
00132                       const typename Output::hstate_t state,
00133                       const typename Lhs::hstate_t x_state,
00134                       const typename Rhs::hstate_t y_state)
00135         {
00136           typename std::map<typename Lhs::hstate_t,
00137             typename Lhs::geometry_t::coords_t>::const_iterator iter;
00138           typename std::map<typename Rhs::hstate_t,
00139             typename Rhs::geometry_t::coords_t>::const_iterator iter2;
00140           double x = 0, y = 0;
00141 
00142           iter = lhs.geometry().states().find(x_state);
00143           if (iter != lhs.geometry().states().end())
00144             x = iter->second.first;
00145 
00146           iter2 = rhs.geometry().states().find(y_state);
00147           if (iter2 != rhs.geometry().states().end())
00148             y = iter2->second.second;
00149 
00150           a.geometry().states()[state] = std::make_pair(x, y);
00151         }
00152       private:
00153         // Diagonal alignement with a depth-first traversal
00154         template<typename I>
00155         void
00156         align (const I& a)
00157         {
00158           AUTOMATON_TYPES(I);
00159           std::map<hstate_t,bool> visited;
00160           std::stack<hstate_t> stack;
00161 
00162           for_all_const_states(i, a)
00163             {
00164               visited[*i] = false;
00165               // ensure inaccessible states will be visited
00166               stack.push(*i);
00167             }
00168 
00169           for_all_const_initial_states(i, a)
00170             stack.push(*i);
00171 
00172           int x = 0;
00173           while (!stack.empty())
00174           {
00175             hstate_t i = stack.top();
00176             stack.pop();
00177 
00178             if (!visited[i])
00179             {
00180               visited[i] = true;
00181 
00182               a.geometry()[i] = std::make_pair(x, x);
00183               x++;
00184 
00185               for (delta_iterator j(a.value(), i);
00186                    ! j.done();
00187                    j.next())
00188                 stack.push(a.dst_of(*j));
00189             }
00190           }
00191         }
00192 
00193     };
00194     class no_grphx
00195     {
00196       public:
00197         template <typename Output, typename Lhs, typename Rhs>
00198         static void
00199         setcoordfrom (Output& a,
00200                       const Lhs& lhs,
00201                       const Rhs& rhs,
00202                       const typename Output::hstate_t state,
00203                       const typename Lhs::hstate_t x_state,
00204                       const typename Rhs::hstate_t y_state) {};
00205     };
00206 
00207     // useful typedefs
00208     AUTOMATON_TYPES(output_t);
00209 
00210     typedef std::pair<typename lhs_t::hstate_t, typename rhs_t::hstate_t>
00211                                                       pair_hstate_t;
00212     typedef std::list<htransition_t>                    delta_ret_t;
00213     typedef std::map<pair_hstate_t, hstate_t>           visited_t;
00214     typedef typename series_set_elt_t::support_t        support_t;
00215 
00216     // add a @c new_state in the queue
00217     inline void
00218     add_state_to_process (output_t& output,
00219                           const lhs_t& lhs,
00220                           const rhs_t& rhs,
00221                           pair_map_t& m,
00222                           const hstate_t& new_state,
00223                           const pair_hstate_t& new_pair)
00224     {
00225       m[new_state] = new_pair;
00226       visited_[new_pair] = new_state;
00227       to_process_.push(new_pair);
00228 
00229 # define if_(Cond, ThenClause, ElseClause)                      \
00230 misc::static_if_simple<Cond, ThenClause, ElseClause>::t
00231 # define eq_(Type1, Type2)                      \
00232 misc::static_eq<Type1, Type2>::value
00233 # define DECLARE_GEOMETRY(Type) \
00234   typedef geometry<typename Type::hstate_t, typename Type::htransition_t, typename Type::geometry_coords_t> geometry_ ## Type ;
00235 
00236       DECLARE_GEOMETRY(output_t)
00237       DECLARE_GEOMETRY(lhs_t)
00238       DECLARE_GEOMETRY(rhs_t)
00239       if (use_geometry_)
00240         if_(eq_(typename output_t::geometry_t, geometry_output_t)  and \
00241             eq_(typename rhs_t::geometry_t, geometry_rhs_t) and \
00242             eq_(typename lhs_t::geometry_t, geometry_lhs_t),    \
00243             grphx, no_grphx)
00244           ::setcoordfrom(output, lhs, rhs,
00245                          new_state, new_pair.first, new_pair.second);
00246 # undef if_
00247 # undef eq_
00248     }
00249 
00250     // initialize queue with all pairs of intials states from @c lhs and @c rhs
00251     inline void
00252     initialize_queue (output_t& output,
00253                       const lhs_t& lhs,
00254                       const rhs_t& rhs,
00255                       pair_map_t& m)
00256     {
00257       for_all_const_initial_states(lhs_s, lhs)
00258         for_all_const_initial_states(rhs_s, rhs)
00259         {
00260           const pair_hstate_t   new_pair(*lhs_s, *rhs_s);
00261           const hstate_t        new_state = output.add_state();
00262 
00263           this->add_state_to_process(output, lhs, rhs, m, new_state, new_pair);
00264         }
00265     }
00266 
00267     inline bool
00268     is_product_not_null (const lhs_t& lhs,
00269                          const rhs_t& rhs,
00270                          const typename lhs_t::delta_iterator& l,
00271                          const typename rhs_t::delta_iterator& r,
00272                          series_set_elt_t&  prod_series) const
00273     {
00274       const series_set_elt_t    left_series  = lhs.series_of(*l);
00275       const series_set_elt_t    right_series = rhs.series_of(*r);
00276 
00277       bool                      prod_is_not_null = false;
00278       for_all_(support_t, supp, left_series.supp())
00279         {
00280           const monoid_elt_t     supp_elt (monoid_, *supp);
00281           const semiring_elt_t l = left_series.get(supp_elt);
00282           const semiring_elt_t r = right_series.get(supp_elt);
00283           const semiring_elt_t p = l * r;
00284           if (p != semiring_zero_)
00285           {
00286             prod_series.assoc(*supp, p.value());
00287             prod_is_not_null = true;
00288           }
00289         }
00290       return (prod_is_not_null);
00291     }
00292 
00293     // If set to true, <geometry> tags of the result automaton should be filled
00294     const bool  use_geometry_;
00295 
00296     // keep traces of new states created
00297     visited_t                   visited_;
00298     // @c to_process_ stores all states of output that needs are not
00299     std::queue<pair_hstate_t>   to_process_;
00300 
00301     // frequently used objects in computation
00302     const series_set_t& series_;
00303     const monoid_t&             monoid_;
00304     // This variable's type must not be set to a reference.
00305     const semiring_elt_t        semiring_zero_;
00306 };
00307 
00308 /*-----------.
00309 | Wrappers.  |
00310 `-----------*/
00311 
00312 template<typename A, typename T, typename U>
00313 Element<A, T>
00314 product (const Element<A, T>& lhs, const Element<A, U>& rhs,
00315          std::map<typename T::hstate_t,
00316          std::pair<typename T::hstate_t, typename U::hstate_t> >& m,
00317          const bool use_geometry)
00318 {
00319   Element<A, T> ret(rhs.structure());
00320   Product<A, T, U> do_product(ret.structure(), use_geometry);
00321   return do_product (ret, lhs, rhs, m);
00322 }
00323 
00324 template<typename A, typename T, typename U>
00325 Element<A, T>
00326 product (const Element<A, T>& lhs, const Element<A, U>& rhs,
00327          const bool use_geometry)
00328 {
00329   std::map<typename T::hstate_t,
00330     std::pair<typename T::hstate_t, typename U::hstate_t> > m;
00331   return product (lhs, rhs, m, use_geometry);
00332 }
00333 
00334 } // End of namespace vcsn.
00335 
00336 #endif // ! VCSN_ALGORITHMS_PRODUCT_HXX

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