• Home
  • Line#
  • Scopes#
  • Navigate#
  • Raw
  • Download
1 // Copyright 2004 The Trustees of Indiana University.
2 
3 // Distributed under the Boost Software License, Version 1.0.
4 // (See accompanying file LICENSE_1_0.txt or copy at
5 // http://www.boost.org/LICENSE_1_0.txt)
6 
7 //  Authors: Douglas Gregor
8 //           Andrew Lumsdaine
9 #ifndef BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP
10 #define BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP
11 
12 #include <boost/graph/graph_traits.hpp>
13 #include <boost/graph/topology.hpp>
14 #include <boost/graph/iteration_macros.hpp>
15 #include <boost/graph/johnson_all_pairs_shortest.hpp>
16 #include <boost/type_traits/is_convertible.hpp>
17 #include <utility>
18 #include <iterator>
19 #include <vector>
20 #include <iostream>
21 #include <boost/limits.hpp>
22 #include <boost/config/no_tr1/cmath.hpp>
23 
24 namespace boost
25 {
26 namespace detail
27 {
28     namespace graph
29     {
30         /**
31          * Denotes an edge or display area side length used to scale a
32          * Kamada-Kawai drawing.
33          */
34         template < bool Edge, typename T > struct edge_or_side
35         {
edge_or_sideboost::detail::graph::edge_or_side36             explicit edge_or_side(T value) : value(value) {}
37 
38             T value;
39         };
40 
41         /**
42          * Compute the edge length from an edge length. This is trivial.
43          */
44         template < typename Graph, typename DistanceMap, typename IndexMap,
45             typename T >
compute_edge_length(const Graph &,DistanceMap,IndexMap,edge_or_side<true,T> length)46         T compute_edge_length(
47             const Graph&, DistanceMap, IndexMap, edge_or_side< true, T > length)
48         {
49             return length.value;
50         }
51 
52         /**
53          * Compute the edge length based on the display area side
54            length. We do this by dividing the side length by the largest
55            shortest distance between any two vertices in the graph.
56          */
57         template < typename Graph, typename DistanceMap, typename IndexMap,
58             typename T >
compute_edge_length(const Graph & g,DistanceMap distance,IndexMap index,edge_or_side<false,T> length)59         T compute_edge_length(const Graph& g, DistanceMap distance,
60             IndexMap index, edge_or_side< false, T > length)
61         {
62             T result(0);
63 
64             typedef
65                 typename graph_traits< Graph >::vertex_iterator vertex_iterator;
66 
67             for (vertex_iterator ui = vertices(g).first,
68                                  end = vertices(g).second;
69                  ui != end; ++ui)
70             {
71                 vertex_iterator vi = ui;
72                 for (++vi; vi != end; ++vi)
73                 {
74                     T dij = distance[get(index, *ui)][get(index, *vi)];
75                     if (dij > result)
76                         result = dij;
77                 }
78             }
79             return length.value / result;
80         }
81 
82         /**
83          * Dense linear solver for fixed-size matrices.
84          */
85         template < std::size_t Size > struct linear_solver
86         {
87             // Indices in mat are (row, column)
88             // template <typename Vec>
89             // static Vec solve(double mat[Size][Size], Vec rhs);
90         };
91 
92         template <> struct linear_solver< 1 >
93         {
94             template < typename Vec >
solveboost::detail::graph::linear_solver95             static Vec solve(double mat[1][1], Vec rhs)
96             {
97                 return rhs / mat[0][0];
98             }
99         };
100 
101         // These are from http://en.wikipedia.org/wiki/Cramer%27s_rule
102         template <> struct linear_solver< 2 >
103         {
104             template < typename Vec >
solveboost::detail::graph::linear_solver105             static Vec solve(double mat[2][2], Vec rhs)
106             {
107                 double denom = mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1];
108                 double x_num = rhs[0] * mat[1][1] - rhs[1] * mat[0][1];
109                 double y_num = mat[0][0] * rhs[1] - mat[1][0] * rhs[0];
110                 Vec result;
111                 result[0] = x_num / denom;
112                 result[1] = y_num / denom;
113                 return result;
114             }
115         };
116 
117         template <> struct linear_solver< 3 >
118         {
119             template < typename Vec >
solveboost::detail::graph::linear_solver120             static Vec solve(double mat[3][3], Vec rhs)
121             {
122                 double denom = mat[0][0]
123                         * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
124                     - mat[1][0]
125                         * (mat[0][1] * mat[2][2] - mat[2][1] * mat[0][2])
126                     + mat[2][0]
127                         * (mat[0][1] * mat[1][2] - mat[1][1] * mat[0][2]);
128                 double x_num
129                     = rhs[0] * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
130                     - rhs[1] * (mat[0][1] * mat[2][2] - mat[2][1] * mat[0][2])
131                     + rhs[2] * (mat[0][1] * mat[1][2] - mat[1][1] * mat[0][2]);
132                 double y_num
133                     = mat[0][0] * (rhs[1] * mat[2][2] - rhs[2] * mat[1][2])
134                     - mat[1][0] * (rhs[0] * mat[2][2] - rhs[2] * mat[0][2])
135                     + mat[2][0] * (rhs[0] * mat[1][2] - rhs[1] * mat[0][2]);
136                 double z_num
137                     = mat[0][0] * (mat[1][1] * rhs[2] - mat[2][1] * rhs[1])
138                     - mat[1][0] * (mat[0][1] * rhs[2] - mat[2][1] * rhs[0])
139                     + mat[2][0] * (mat[0][1] * rhs[1] - mat[1][1] * rhs[0]);
140                 Vec result;
141                 result[0] = x_num / denom;
142                 result[1] = y_num / denom;
143                 result[2] = z_num / denom;
144                 return result;
145             }
146         };
147 
148         /**
149          * Implementation of the Kamada-Kawai spring layout algorithm.
150          */
151         template < typename Topology, typename Graph, typename PositionMap,
152             typename WeightMap, typename EdgeOrSideLength, typename Done,
153             typename VertexIndexMap, typename DistanceMatrix,
154             typename SpringStrengthMatrix, typename PartialDerivativeMap >
155         struct kamada_kawai_spring_layout_impl
156         {
157             typedef
158                 typename property_traits< WeightMap >::value_type weight_type;
159             typedef typename Topology::point_type Point;
160             typedef
161                 typename Topology::point_difference_type point_difference_type;
162             typedef point_difference_type deriv_type;
163             typedef
164                 typename graph_traits< Graph >::vertex_iterator vertex_iterator;
165             typedef typename graph_traits< Graph >::vertex_descriptor
166                 vertex_descriptor;
167 
kamada_kawai_spring_layout_implboost::detail::graph::kamada_kawai_spring_layout_impl168             kamada_kawai_spring_layout_impl(const Topology& topology,
169                 const Graph& g, PositionMap position, WeightMap weight,
170                 EdgeOrSideLength edge_or_side_length, Done done,
171                 weight_type spring_constant, VertexIndexMap index,
172                 DistanceMatrix distance, SpringStrengthMatrix spring_strength,
173                 PartialDerivativeMap partial_derivatives)
174             : topology(topology)
175             , g(g)
176             , position(position)
177             , weight(weight)
178             , edge_or_side_length(edge_or_side_length)
179             , done(done)
180             , spring_constant(spring_constant)
181             , index(index)
182             , distance(distance)
183             , spring_strength(spring_strength)
184             , partial_derivatives(partial_derivatives)
185             {
186             }
187 
188             // Compute contribution of vertex i to the first partial
189             // derivatives (dE/dx_m, dE/dy_m) (for vertex m)
compute_partial_derivativeboost::detail::graph::kamada_kawai_spring_layout_impl190             deriv_type compute_partial_derivative(
191                 vertex_descriptor m, vertex_descriptor i)
192             {
193 #ifndef BOOST_NO_STDC_NAMESPACE
194                 using std::sqrt;
195 #endif // BOOST_NO_STDC_NAMESPACE
196 
197                 deriv_type result;
198                 if (i != m)
199                 {
200                     point_difference_type diff
201                         = topology.difference(position[m], position[i]);
202                     weight_type dist = topology.norm(diff);
203                     result = spring_strength[get(index, m)][get(index, i)]
204                         * (diff
205                             - distance[get(index, m)][get(index, i)] / dist
206                                 * diff);
207                 }
208 
209                 return result;
210             }
211 
212             // Compute partial derivatives dE/dx_m and dE/dy_m
compute_partial_derivativesboost::detail::graph::kamada_kawai_spring_layout_impl213             deriv_type compute_partial_derivatives(vertex_descriptor m)
214             {
215 #ifndef BOOST_NO_STDC_NAMESPACE
216                 using std::sqrt;
217 #endif // BOOST_NO_STDC_NAMESPACE
218 
219                 deriv_type result;
220 
221                 // TBD: looks like an accumulate to me
222                 BGL_FORALL_VERTICES_T(i, g, Graph)
223                 {
224                     deriv_type deriv = compute_partial_derivative(m, i);
225                     result += deriv;
226                 }
227 
228                 return result;
229             }
230 
231             // The actual Kamada-Kawai spring layout algorithm implementation
runboost::detail::graph::kamada_kawai_spring_layout_impl232             bool run()
233             {
234 #ifndef BOOST_NO_STDC_NAMESPACE
235                 using std::sqrt;
236 #endif // BOOST_NO_STDC_NAMESPACE
237 
238                 // Compute d_{ij} and place it in the distance matrix
239                 if (!johnson_all_pairs_shortest_paths(
240                         g, distance, index, weight, weight_type(0)))
241                     return false;
242 
243                 // Compute L based on side length (if needed), or retrieve L
244                 weight_type edge_length = detail::graph::compute_edge_length(
245                     g, distance, index, edge_or_side_length);
246 
247                 // std::cerr << "edge_length = " << edge_length << std::endl;
248 
249                 // Compute l_{ij} and k_{ij}
250                 const weight_type K = spring_constant;
251                 vertex_iterator ui, end;
252                 for (ui = vertices(g).first, end = vertices(g).second;
253                      ui != end; ++ui)
254                 {
255                     vertex_iterator vi = ui;
256                     for (++vi; vi != end; ++vi)
257                     {
258                         weight_type dij
259                             = distance[get(index, *ui)][get(index, *vi)];
260                         if (dij == (std::numeric_limits< weight_type >::max)())
261                             return false;
262                         distance[get(index, *ui)][get(index, *vi)]
263                             = edge_length * dij;
264                         distance[get(index, *vi)][get(index, *ui)]
265                             = edge_length * dij;
266                         spring_strength[get(index, *ui)][get(index, *vi)]
267                             = K / (dij * dij);
268                         spring_strength[get(index, *vi)][get(index, *ui)]
269                             = K / (dij * dij);
270                     }
271                 }
272 
273                 // Compute Delta_i and find max
274                 vertex_descriptor p = *vertices(g).first;
275                 weight_type delta_p(0);
276 
277                 for (ui = vertices(g).first, end = vertices(g).second;
278                      ui != end; ++ui)
279                 {
280                     deriv_type deriv = compute_partial_derivatives(*ui);
281                     put(partial_derivatives, *ui, deriv);
282 
283                     weight_type delta = topology.norm(deriv);
284 
285                     if (delta > delta_p)
286                     {
287                         p = *ui;
288                         delta_p = delta;
289                     }
290                 }
291 
292                 while (!done(delta_p, p, g, true))
293                 {
294                     // The contribution p makes to the partial derivatives of
295                     // each vertex. Computing this (at O(n) cost) allows us to
296                     // update the delta_i values in O(n) time instead of O(n^2)
297                     // time.
298                     std::vector< deriv_type > p_partials(num_vertices(g));
299                     for (ui = vertices(g).first, end = vertices(g).second;
300                          ui != end; ++ui)
301                     {
302                         vertex_descriptor i = *ui;
303                         p_partials[get(index, i)]
304                             = compute_partial_derivative(i, p);
305                     }
306 
307                     do
308                     {
309                         // For debugging, compute the energy value E
310                         double E = 0.;
311                         for (ui = vertices(g).first, end = vertices(g).second;
312                              ui != end; ++ui)
313                         {
314                             vertex_iterator vi = ui;
315                             for (++vi; vi != end; ++vi)
316                             {
317                                 double dist = topology.distance(
318                                     position[*ui], position[*vi]);
319                                 weight_type k_ij = spring_strength[get(
320                                     index, *ui)][get(index, *vi)];
321                                 weight_type l_ij = distance[get(index, *ui)]
322                                                            [get(index, *vi)];
323                                 E += .5 * k_ij * (dist - l_ij) * (dist - l_ij);
324                             }
325                         }
326                         // std::cerr << "E = " << E << std::endl;
327 
328                         // Compute the elements of the Jacobian
329                         // From
330                         // http://www.cs.panam.edu/~rfowler/papers/1994_kumar_fowler_A_Spring_UTPACSTR.pdf
331                         // with the bugs fixed in the off-diagonal case
332                         weight_type dE_d_d[Point::dimensions]
333                                           [Point::dimensions];
334                         for (std::size_t i = 0; i < Point::dimensions; ++i)
335                             for (std::size_t j = 0; j < Point::dimensions; ++j)
336                                 dE_d_d[i][j] = 0.;
337                         for (ui = vertices(g).first, end = vertices(g).second;
338                              ui != end; ++ui)
339                         {
340                             vertex_descriptor i = *ui;
341                             if (i != p)
342                             {
343                                 point_difference_type diff
344                                     = topology.difference(
345                                         position[p], position[i]);
346                                 weight_type dist = topology.norm(diff);
347                                 weight_type dist_squared = dist * dist;
348                                 weight_type inv_dist_cubed
349                                     = 1. / (dist_squared * dist);
350                                 weight_type k_mi = spring_strength[get(
351                                     index, p)][get(index, i)];
352                                 weight_type l_mi
353                                     = distance[get(index, p)][get(index, i)];
354                                 for (std::size_t i = 0; i < Point::dimensions;
355                                      ++i)
356                                 {
357                                     for (std::size_t j = 0;
358                                          j < Point::dimensions; ++j)
359                                     {
360                                         if (i == j)
361                                         {
362                                             dE_d_d[i][i] += k_mi
363                                                 * (1
364                                                     + (l_mi
365                                                         * (diff[i] * diff[i]
366                                                             - dist_squared)
367                                                         * inv_dist_cubed));
368                                         }
369                                         else
370                                         {
371                                             dE_d_d[i][j] += k_mi * l_mi
372                                                 * diff[i] * diff[j]
373                                                 * inv_dist_cubed;
374                                             // dE_d_d[i][j] += k_mi * l_mi *
375                                             // sqrt(hypot(diff[i], diff[j])) *
376                                             // inv_dist_cubed;
377                                         }
378                                     }
379                                 }
380                             }
381                         }
382 
383                         deriv_type dE_d = get(partial_derivatives, p);
384 
385                         // Solve dE_d_d * delta = -dE_d to get delta
386                         point_difference_type delta
387                             = -linear_solver< Point::dimensions >::solve(
388                                 dE_d_d, dE_d);
389 
390                         // Move p by delta
391                         position[p] = topology.adjust(position[p], delta);
392 
393                         // Recompute partial derivatives and delta_p
394                         deriv_type deriv = compute_partial_derivatives(p);
395                         put(partial_derivatives, p, deriv);
396 
397                         delta_p = topology.norm(deriv);
398                     } while (!done(delta_p, p, g, false));
399 
400                     // Select new p by updating each partial derivative and
401                     // delta
402                     vertex_descriptor old_p = p;
403                     for (ui = vertices(g).first, end = vertices(g).second;
404                          ui != end; ++ui)
405                     {
406                         deriv_type old_deriv_p = p_partials[get(index, *ui)];
407                         deriv_type old_p_partial
408                             = compute_partial_derivative(*ui, old_p);
409                         deriv_type deriv = get(partial_derivatives, *ui);
410 
411                         deriv += old_p_partial - old_deriv_p;
412 
413                         put(partial_derivatives, *ui, deriv);
414                         weight_type delta = topology.norm(deriv);
415 
416                         if (delta > delta_p)
417                         {
418                             p = *ui;
419                             delta_p = delta;
420                         }
421                     }
422                 }
423 
424                 return true;
425             }
426 
427             const Topology& topology;
428             const Graph& g;
429             PositionMap position;
430             WeightMap weight;
431             EdgeOrSideLength edge_or_side_length;
432             Done done;
433             weight_type spring_constant;
434             VertexIndexMap index;
435             DistanceMatrix distance;
436             SpringStrengthMatrix spring_strength;
437             PartialDerivativeMap partial_derivatives;
438         };
439     }
440 } // end namespace detail::graph
441 
442 /// States that the given quantity is an edge length.
443 template < typename T >
edge_length(T x)444 inline detail::graph::edge_or_side< true, T > edge_length(T x)
445 {
446     return detail::graph::edge_or_side< true, T >(x);
447 }
448 
449 /// States that the given quantity is a display area side length.
450 template < typename T >
side_length(T x)451 inline detail::graph::edge_or_side< false, T > side_length(T x)
452 {
453     return detail::graph::edge_or_side< false, T >(x);
454 }
455 
456 /**
457  * \brief Determines when to terminate layout of a particular graph based
458  * on a given relative tolerance.
459  */
460 template < typename T = double > struct layout_tolerance
461 {
layout_toleranceboost::layout_tolerance462     layout_tolerance(const T& tolerance = T(0.001))
463     : tolerance(tolerance)
464     , last_energy((std::numeric_limits< T >::max)())
465     , last_local_energy((std::numeric_limits< T >::max)())
466     {
467     }
468 
469     template < typename Graph >
operator ()boost::layout_tolerance470     bool operator()(T delta_p,
471         typename boost::graph_traits< Graph >::vertex_descriptor p,
472         const Graph& g, bool global)
473     {
474         if (global)
475         {
476             if (last_energy == (std::numeric_limits< T >::max)())
477             {
478                 last_energy = delta_p;
479                 return false;
480             }
481 
482             T diff = last_energy - delta_p;
483             if (diff < T(0))
484                 diff = -diff;
485             bool done = (delta_p == T(0) || diff / last_energy < tolerance);
486             last_energy = delta_p;
487             return done;
488         }
489         else
490         {
491             if (last_local_energy == (std::numeric_limits< T >::max)())
492             {
493                 last_local_energy = delta_p;
494                 return delta_p == T(0);
495             }
496 
497             T diff = last_local_energy - delta_p;
498             bool done
499                 = (delta_p == T(0) || (diff / last_local_energy) < tolerance);
500             last_local_energy = delta_p;
501             return done;
502         }
503     }
504 
505 private:
506     T tolerance;
507     T last_energy;
508     T last_local_energy;
509 };
510 
511 /** \brief Kamada-Kawai spring layout for undirected graphs.
512  *
513  * This algorithm performs graph layout (in two dimensions) for
514  * connected, undirected graphs. It operates by relating the layout
515  * of graphs to a dynamic spring system and minimizing the energy
516  * within that system. The strength of a spring between two vertices
517  * is inversely proportional to the square of the shortest distance
518  * (in graph terms) between those two vertices. Essentially,
519  * vertices that are closer in the graph-theoretic sense (i.e., by
520  * following edges) will have stronger springs and will therefore be
521  * placed closer together.
522  *
523  * Prior to invoking this algorithm, it is recommended that the
524  * vertices be placed along the vertices of a regular n-sided
525  * polygon.
526  *
527  * \param g (IN) must be a model of Vertex List Graph, Edge List
528  * Graph, and Incidence Graph and must be undirected.
529  *
530  * \param position (OUT) must be a model of Lvalue Property Map,
531  * where the value type is a class containing fields @c x and @c y
532  * that will be set to the @c x and @c y coordinates of each vertex.
533  *
534  * \param weight (IN) must be a model of Readable Property Map,
535  * which provides the weight of each edge in the graph @p g.
536  *
537  * \param topology (IN) must be a topology object (see topology.hpp),
538  * which provides operations on points and differences between them.
539  *
540  * \param edge_or_side_length (IN) provides either the unit length
541  * @c e of an edge in the layout or the length of a side @c s of the
542  * display area, and must be either @c boost::edge_length(e) or @c
543  * boost::side_length(s), respectively.
544  *
545  * \param done (IN) is a 4-argument function object that is passed
546  * the current value of delta_p (i.e., the energy of vertex @p p),
547  * the vertex @p p, the graph @p g, and a boolean flag indicating
548  * whether @p delta_p is the maximum energy in the system (when @c
549  * true) or the energy of the vertex being moved. Defaults to @c
550  * layout_tolerance instantiated over the value type of the weight
551  * map.
552  *
553  * \param spring_constant (IN) is the constant multiplied by each
554  * spring's strength. Larger values create systems with more energy
555  * that can take longer to stabilize; smaller values create systems
556  * with less energy that stabilize quickly but do not necessarily
557  * result in pleasing layouts. The default value is 1.
558  *
559  * \param index (IN) is a mapping from vertices to index values
560  * between 0 and @c num_vertices(g). The default is @c
561  * get(vertex_index,g).
562  *
563  * \param distance (UTIL/OUT) will be used to store the distance
564  * from every vertex to every other vertex, which is computed in the
565  * first stages of the algorithm. This value's type must be a model
566  * of BasicMatrix with value type equal to the value type of the
567  * weight map. The default is a vector of vectors.
568  *
569  * \param spring_strength (UTIL/OUT) will be used to store the
570  * strength of the spring between every pair of vertices. This
571  * value's type must be a model of BasicMatrix with value type equal
572  * to the value type of the weight map. The default is a vector of
573  * vectors.
574  *
575  * \param partial_derivatives (UTIL) will be used to store the
576  * partial derivates of each vertex with respect to the @c x and @c
577  * y coordinates. This must be a Read/Write Property Map whose value
578  * type is a pair with both types equivalent to the value type of
579  * the weight map. The default is an iterator property map.
580  *
581  * \returns @c true if layout was successful or @c false if a
582  * negative weight cycle was detected.
583  */
584 template < typename Topology, typename Graph, typename PositionMap,
585     typename WeightMap, typename T, bool EdgeOrSideLength, typename Done,
586     typename VertexIndexMap, typename DistanceMatrix,
587     typename SpringStrengthMatrix, typename PartialDerivativeMap >
kamada_kawai_spring_layout(const Graph & g,PositionMap position,WeightMap weight,const Topology & topology,detail::graph::edge_or_side<EdgeOrSideLength,T> edge_or_side_length,Done done,typename property_traits<WeightMap>::value_type spring_constant,VertexIndexMap index,DistanceMatrix distance,SpringStrengthMatrix spring_strength,PartialDerivativeMap partial_derivatives)588 bool kamada_kawai_spring_layout(const Graph& g, PositionMap position,
589     WeightMap weight, const Topology& topology,
590     detail::graph::edge_or_side< EdgeOrSideLength, T > edge_or_side_length,
591     Done done,
592     typename property_traits< WeightMap >::value_type spring_constant,
593     VertexIndexMap index, DistanceMatrix distance,
594     SpringStrengthMatrix spring_strength,
595     PartialDerivativeMap partial_derivatives)
596 {
597     BOOST_STATIC_ASSERT(
598         (is_convertible< typename graph_traits< Graph >::directed_category*,
599             undirected_tag* >::value));
600 
601     detail::graph::kamada_kawai_spring_layout_impl< Topology, Graph,
602         PositionMap, WeightMap,
603         detail::graph::edge_or_side< EdgeOrSideLength, T >, Done,
604         VertexIndexMap, DistanceMatrix, SpringStrengthMatrix,
605         PartialDerivativeMap >
606         alg(topology, g, position, weight, edge_or_side_length, done,
607             spring_constant, index, distance, spring_strength,
608             partial_derivatives);
609     return alg.run();
610 }
611 
612 /**
613  * \overload
614  */
615 template < typename Topology, typename Graph, typename PositionMap,
616     typename WeightMap, typename T, bool EdgeOrSideLength, typename Done,
617     typename VertexIndexMap >
kamada_kawai_spring_layout(const Graph & g,PositionMap position,WeightMap weight,const Topology & topology,detail::graph::edge_or_side<EdgeOrSideLength,T> edge_or_side_length,Done done,typename property_traits<WeightMap>::value_type spring_constant,VertexIndexMap index)618 bool kamada_kawai_spring_layout(const Graph& g, PositionMap position,
619     WeightMap weight, const Topology& topology,
620     detail::graph::edge_or_side< EdgeOrSideLength, T > edge_or_side_length,
621     Done done,
622     typename property_traits< WeightMap >::value_type spring_constant,
623     VertexIndexMap index)
624 {
625     typedef typename property_traits< WeightMap >::value_type weight_type;
626 
627     typename graph_traits< Graph >::vertices_size_type n = num_vertices(g);
628     typedef std::vector< weight_type > weight_vec;
629 
630     std::vector< weight_vec > distance(n, weight_vec(n));
631     std::vector< weight_vec > spring_strength(n, weight_vec(n));
632     std::vector< typename Topology::point_difference_type > partial_derivatives(
633         n);
634 
635     return kamada_kawai_spring_layout(g, position, weight, topology,
636         edge_or_side_length, done, spring_constant, index, distance.begin(),
637         spring_strength.begin(),
638         make_iterator_property_map(partial_derivatives.begin(), index,
639             typename Topology::point_difference_type()));
640 }
641 
642 /**
643  * \overload
644  */
645 template < typename Topology, typename Graph, typename PositionMap,
646     typename WeightMap, typename T, bool EdgeOrSideLength, typename Done >
kamada_kawai_spring_layout(const Graph & g,PositionMap position,WeightMap weight,const Topology & topology,detail::graph::edge_or_side<EdgeOrSideLength,T> edge_or_side_length,Done done,typename property_traits<WeightMap>::value_type spring_constant)647 bool kamada_kawai_spring_layout(const Graph& g, PositionMap position,
648     WeightMap weight, const Topology& topology,
649     detail::graph::edge_or_side< EdgeOrSideLength, T > edge_or_side_length,
650     Done done,
651     typename property_traits< WeightMap >::value_type spring_constant)
652 {
653     return kamada_kawai_spring_layout(g, position, weight, topology,
654         edge_or_side_length, done, spring_constant, get(vertex_index, g));
655 }
656 
657 /**
658  * \overload
659  */
660 template < typename Topology, typename Graph, typename PositionMap,
661     typename WeightMap, typename T, bool EdgeOrSideLength, typename Done >
kamada_kawai_spring_layout(const Graph & g,PositionMap position,WeightMap weight,const Topology & topology,detail::graph::edge_or_side<EdgeOrSideLength,T> edge_or_side_length,Done done)662 bool kamada_kawai_spring_layout(const Graph& g, PositionMap position,
663     WeightMap weight, const Topology& topology,
664     detail::graph::edge_or_side< EdgeOrSideLength, T > edge_or_side_length,
665     Done done)
666 {
667     typedef typename property_traits< WeightMap >::value_type weight_type;
668     return kamada_kawai_spring_layout(g, position, weight, topology,
669         edge_or_side_length, done, weight_type(1));
670 }
671 
672 /**
673  * \overload
674  */
675 template < typename Topology, typename Graph, typename PositionMap,
676     typename WeightMap, typename T, bool EdgeOrSideLength >
kamada_kawai_spring_layout(const Graph & g,PositionMap position,WeightMap weight,const Topology & topology,detail::graph::edge_or_side<EdgeOrSideLength,T> edge_or_side_length)677 bool kamada_kawai_spring_layout(const Graph& g, PositionMap position,
678     WeightMap weight, const Topology& topology,
679     detail::graph::edge_or_side< EdgeOrSideLength, T > edge_or_side_length)
680 {
681     typedef typename property_traits< WeightMap >::value_type weight_type;
682     return kamada_kawai_spring_layout(g, position, weight, topology,
683         edge_or_side_length, layout_tolerance< weight_type >(),
684         weight_type(1.0), get(vertex_index, g));
685 }
686 } // end namespace boost
687 
688 #endif // BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP
689