1 files changed, 60 insertions, 19 deletions

diff --git a/src/Rips_complex/include/gudhi/Sparse_rips_complex.h b/src/Rips_complex/include/gudhi/Sparse_rips_complex.h
index 4dcc08ed..8df6e387 100644
--- a/src/Rips_complex/include/gudhi/Sparse_rips_complex.h
+++ b/src/Rips_complex/include/gudhi/Sparse_rips_complex.h
@@ -47,7 +47,9 @@ namespace rips_complex {
  *
  * \details
  * This class is used to construct a sparse \f$(1+O(\epsilon))\f$-approximation of `Rips_complex`, i.e. a filtered
- * simplicial complex that is multiplicatively \f$(1+O(\epsilon))\f$-interleaved with the Rips filtration.
+ * simplicial complex that is multiplicatively
+ * \f$(1+O(\epsilon))\f$-interleaved with the Rips filtration. More precisely,
+ * this is a \f$(1,\frac{1}{1-\epsilon}\f$-interleaving.
  *
  * \tparam Filtration_value is the type used to store the filtration values of the simplicial complex.
  */
@@ -55,7 +57,7 @@ template <typename Filtration_value>
 class Sparse_rips_complex {
  private:
   // TODO(MG): use a different graph where we know we can safely insert in parallel.
-  typedef typename boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS,
+  typedef typename boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS,
                                          boost::property<vertex_filtration_t, Filtration_value>,
                                          boost::property<edge_filtration_t, Filtration_value>>
       Graph;
@@ -68,32 +70,36 @@ class Sparse_rips_complex {
    * @param[in] points Range of points.
    * @param[in] distance Distance function that returns a `Filtration_value` from 2 given points.
    * @param[in] epsilon Approximation parameter. epsilon must be positive.
+   * @param[in] mini Minimal filtration value. Ignore anything below this scale. This is a less efficient version of `Gudhi::subsampling::sparsify_point_set()`.
+   * @param[in] maxi Maximal filtration value. Ignore anything above this scale.
    *
    */
   template <typename RandomAccessPointRange, typename Distance>
-  Sparse_rips_complex(const RandomAccessPointRange& points, Distance distance, double epsilon) {
+  Sparse_rips_complex(const RandomAccessPointRange& points, Distance distance, double epsilon, Filtration_value mini=-std::numeric_limits<Filtration_value>::infinity(), Filtration_value maxi=std::numeric_limits<Filtration_value>::infinity())
+      : epsilon_(epsilon) {
     GUDHI_CHECK(epsilon > 0, "epsilon must be positive");
-    std::vector<Vertex_handle> sorted_points;
-    std::vector<Filtration_value> params;
     auto dist_fun = [&](Vertex_handle i, Vertex_handle j) { return distance(points[i], points[j]); };
     Ker<decltype(dist_fun)> kernel(dist_fun);
     subsampling::choose_n_farthest_points(kernel, boost::irange<Vertex_handle>(0, boost::size(points)), -1, -1,
                                           std::back_inserter(sorted_points), std::back_inserter(params));
-    compute_sparse_graph(sorted_points, params, dist_fun, epsilon);
+    compute_sparse_graph(dist_fun, epsilon, mini, maxi);
   }
 
   /** \brief Sparse_rips_complex constructor from a distance matrix.
    *
    * @param[in] distance_matrix Range of range of distances.
    * `distance_matrix[i][j]` returns the distance between points \f$i\f$ and
-   * \f$j\f$ as long as \f$ 0 \leqslant i < j \leqslant
+   * \f$j\f$ as long as \f$ 0 \leqslant j < i \leqslant
    * distance\_matrix.size().\f$
    * @param[in] epsilon Approximation parameter. epsilon must be positive.
+   * @param[in] mini Minimal filtration value. Ignore anything below this scale. This is a less efficient version of `Gudhi::subsampling::sparsify_point_set()`.
+   * @param[in] maxi Maximal filtration value. Ignore anything above this scale.
    */
   template <typename DistanceMatrix>
-  Sparse_rips_complex(const DistanceMatrix& distance_matrix, double epsilon)
+  Sparse_rips_complex(const DistanceMatrix& distance_matrix, double epsilon, Filtration_value mini=-std::numeric_limits<Filtration_value>::infinity(), Filtration_value maxi=std::numeric_limits<Filtration_value>::infinity())
       : Sparse_rips_complex(boost::irange<Vertex_handle>(0, boost::size(distance_matrix)),
-                            [&](Vertex_handle i, Vertex_handle j) { return distance_matrix[j][i]; }, epsilon) {}
+                            [&](Vertex_handle i, Vertex_handle j) { return (i==j) ? 0 : (i<j) ? distance_matrix[j][i] : distance_matrix[i][j]; },
+                            epsilon, mini, maxi) {}
 
   /** \brief Fills the simplicial complex with the sparse Rips graph and
    * expands it with all the cliques, stopping at a given maximal dimension.
@@ -111,7 +117,26 @@ class Sparse_rips_complex {
                 std::invalid_argument("Sparse_rips_complex::create_complex - simplicial complex is not empty"));
 
     complex.insert_graph(graph_);
-    complex.expansion(dim_max);
+    if(epsilon_ >= 1) {
+      complex.expansion(dim_max);
+      return;
+    }
+    const int n = boost::size(params);
+    std::vector<Filtration_value> lambda(n);
+    // lambda[original_order]=params[sorted_order]
+    for(int i=0;i<n;++i)
+      lambda[sorted_points[i]] = params[i];
+    double cst = epsilon_ * (1 - epsilon_) / 2;
+    auto block = [cst,&complex,&lambda](typename SimplicialComplexForRips::Simplex_handle sh){
+      auto filt = complex.filtration(sh);
+      auto mini = filt * cst;
+      for(auto v : complex.simplex_vertex_range(sh)){
+        if(lambda[v] < mini)
+          return true; // v died before this simplex could be born
+      }
+      return false;
+    };
+    complex.expansion_with_blockers(dim_max, block);
   }
 
  private:
@@ -127,9 +152,11 @@ class Sparse_rips_complex {
   };
 
   // PointRange must be random access.
-  template <typename PointRange, typename ParamRange, typename Distance>
-  void compute_sparse_graph(const PointRange& points, const ParamRange& params, Distance& dist, double epsilon) {
+  template <typename Distance>
+  void compute_sparse_graph(Distance& dist, double epsilon, Filtration_value mini, Filtration_value maxi) {
+    const auto& points = sorted_points; // convenience alias
     const int n = boost::size(points);
+    double cst = epsilon * (1 - epsilon) / 2;
     graph_.~Graph();
     new (&graph_) Graph(n);
     // for(auto v : vertices(g)) // doesn't work :-(
@@ -143,29 +170,43 @@ class Sparse_rips_complex {
     // TODO(MG):
     // - make it parallel
     // - only test near-enough neighbors
-    for (int i = 0; i < n; ++i)
+    for (int i = 0; i < n; ++i) {
+      auto&& pi = points[i];
+      auto li = params[i];
+      if (li < mini) break;
       for (int j = i + 1; j < n; ++j) {
-        auto&& pi = points[i];
         auto&& pj = points[j];
         auto d = dist(pi, pj);
-        auto li = params[i];
         auto lj = params[j];
+        if (lj < mini) break;
         GUDHI_CHECK(lj <= li, "Bad furthest point sorting");
         Filtration_value alpha;
 
         // The paper has d/2 and d-lj/e to match the Cech, but we use doubles to match the Rips
         if (d * epsilon <= 2 * lj)
           alpha = d;
-        else if (d * epsilon <= li + lj && (epsilon >= 1 || d * epsilon <= lj * (1 + 1 / (1 - epsilon))))
-          alpha = (d - lj / epsilon) * 2;
-        else
+        else if (d * epsilon > li + lj)
           continue;
+        else {
+          alpha = (d - lj / epsilon) * 2;
+          // Keep the test exactly the same as in block to avoid inconsistencies
+          if (epsilon < 1 && alpha * cst > lj)
+            continue;
+        }
 
-        add_edge(pi, pj, alpha, graph_);
+        if (alpha <= maxi)
+          add_edge(pi, pj, alpha, graph_);
       }
+    }
   }
 
   Graph graph_;
+  double epsilon_;
+  // Because of the arbitrary split between constructor and create_complex
+  // sorted_points[sorted_order]=original_order
+  std::vector<Vertex_handle> sorted_points;
+  // params[sorted_order]=distance to previous points
+  std::vector<Filtration_value> params;
 };
 
 }  // namespace rips_complex