Fix doc and tests

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/cechcomplex_vincent@3262 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: c76eb981f5960938221aa2498cb87b0707391733

11 files changed, 249 insertions, 221 deletions

diff --git a/src/Cech_complex/benchmark/cech_complex_benchmark.cpp b/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
index 71c88982..83ef9dca 100644
--- a/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
+++ b/src/Cech_complex/benchmark/cech_complex_benchmark.cpp
@@ -93,12 +93,12 @@ int main(int argc, char * argv[]) {
                                                                                                Radius_distance());
   std::cout << radius_clock << std::endl;
 
-  Gudhi::Clock squared_radius_clock("Gudhi::Radius_distance()");
+  Gudhi::Clock common_radius_clock("Gudhi::Radius_distance()");
   // Compute the proximity graph of the points
   Proximity_graph sq_radius_prox_graph = Gudhi::compute_proximity_graph<Simplex_tree>(off_reader.get_point_cloud(),
                                                                                                threshold,
                                                                                                Gudhi::Radius_distance());
-  std::cout << squared_radius_clock << std::endl;
+  std::cout << common_radius_clock << std::endl;
 
 
   boost::filesystem::path full_path(boost::filesystem::current_path());
@@ -116,6 +116,7 @@ int main(int argc, char * argv[]) {
       if ( itr->path().extension() == ".off" ) // see below
       {
         Points_off_reader off_reader(itr->path().string());
+        Point p0 = off_reader.get_point_cloud()[0];
 
         for (Filtration_value radius = 0.1; radius < 0.4; radius += 0.1) {
           std::cout << itr->path().stem() << ";";
@@ -123,7 +124,7 @@ int main(int argc, char * argv[]) {
           Gudhi::Clock rips_clock("Rips computation");
           Rips_complex rips_complex_from_points(off_reader.get_point_cloud(), radius, Gudhi::Radius_distance());
           Simplex_tree rips_stree;
-          rips_complex_from_points.create_complex(rips_stree, 2);
+          rips_complex_from_points.create_complex(rips_stree, p0.size() - 1);
           // ------------------------------------------
           // Display information about the Rips complex
           // ------------------------------------------
@@ -133,7 +134,7 @@ int main(int argc, char * argv[]) {
           Gudhi::Clock cech_clock("Cech computation");
           Cech_complex cech_complex_from_points(off_reader.get_point_cloud(), radius);
           Simplex_tree cech_stree;
-          cech_complex_from_points.create_complex(cech_stree, 2);
+          cech_complex_from_points.create_complex(cech_stree, p0.size() - 1);
           // ------------------------------------------
           // Display information about the Cech complex
           // ------------------------------------------
@@ -141,6 +142,7 @@ int main(int argc, char * argv[]) {
           std::cout << cech_sec << ";";
           std::cout << cech_sec / rips_sec << ";";
 
+          assert(rips_stree.num_simplices() >= cech_stree.num_simplices());
           std::cout << rips_stree.num_simplices() << ";";
           std::cout << cech_stree.num_simplices() << ";" << std::endl;
         }
diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h
index f2052763..8b6c7851 100644
--- a/src/Cech_complex/doc/Intro_cech_complex.h
+++ b/src/Cech_complex/doc/Intro_cech_complex.h
@@ -29,7 +29,7 @@ namespace cech_complex {
 
 /**  \defgroup cech_complex Cech complex
  * 
- * \author    Clément Maria, Pawel Dlotko, Vincent Rouvreau
+ * \author    Vincent Rouvreau
  * 
  * @{
  * 
@@ -40,40 +40,54 @@ namespace cech_complex {
  * proximity graph that allows to construct a
  * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a>
  * from it.
- * The input can be a point cloud with a given distance function.
+ * The input shall be a point cloud in an Euclidean space.
  * 
- * The filtration value of each edge is computed from a user-given distance function.
+ * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from `Gudhi::Radius_distance` function.
  * 
- * All edges that have a filtration value strictly greater than a given threshold value are not inserted into
- * the complex.
+ * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$,
+ * are not inserted into the complex.
  * 
- * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the data
- * structure, and then expands the simplicial complex when required.
- *
  * Vertex name correspond to the index of the point in the given range (aka. the point cloud).
  * 
- * \image html "cech_complex_representation.png" "Cech complex proximity graph representation"
- * 
- * On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration
- * value set with \f$max(filtration(4,5), filtration(4,6), filtration(5,6))\f$.
- * And so on for simplex (0,1,2,3).
+ * \image html "cech_one_skeleton.png" "Cech complex proximity graph representation"
  * 
+ * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the simplicial
+ * complex data structure, and then expands the simplicial complex when required.
+ *
+ * On this example, as edges \f$(x,y)\f$, \f$(y,z)\f$ and \f$(z,y)\f$ are in the complex, the minimal ball radius
+ * containing the points \f$(x,y,z)\f$ is computed.
+ *
+ * \f$(x,y,z)\f$ is inserted to the simplicial complex with the filtration value set with
+ * \f$mini\_ball\_radius(x,y,z))\f$ iff \f$mini\_ball\_radius(x,y,z)) \leq max\_radius\f$.
+ *
+ * And so on for higher dimensions.
+ *
+ * \image html "cech_complex_representation.png" "Cech complex expansion"
+ *
+ * The minimal ball radius computation is insured by
+ * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html">
+ * the miniball software (V3.0)</a> - Smallest Enclosing Balls of Points - and distributed with GUDHI.
+ *
+ * Please refer to
+ * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/esa99_final.pdf">
+ * the miniball software design description</a> for more information about this computation.
+ *
  * If the Cech_complex interfaces are not detailed enough for your need, please refer to
- * <a href="_persistent_cohomology_2cech_persistence_step_by_step_8cpp-example.html">
- * cech_persistence_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed.
+ * <a href="_cech_complex_2cech_complex_step_by_step_8cpp-example.html">
+ * cech_complex_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed.
  *
- * \section cechpointsdistance Point cloud and distance function
+ * \section cechpointsdistance Point cloud
  * 
- * \subsection cechpointscloudexample Example from a point cloud and a distance function
+ * \subsection cechpointscloudexample Example from a point cloud
  * 
- * This example builds the proximity graph from the given points, threshold value, and distance function.
+ * This example builds the proximity graph from the given points, and maximal radius values.
  * Then it creates a `Simplex_tree` with it.
  * 
  * Then, it is asked to display information about the simplicial complex.
  * 
  * \include Cech_complex/cech_complex_example_from_points.cpp
  * 
- * When launching (Cech maximal distance between 2 points is 7.1, is expanded until dimension 2):
+ * When launching (Cech maximal distance between 2 points is 1., is expanded until dimension 2):
  * 
  * \code $> ./Cech_complex_example_from_points
  * \endcode
diff --git a/src/Cech_complex/doc/cech_complex_representation.ipe b/src/Cech_complex/doc/cech_complex_representation.ipe
index 7f6028f4..c64d7596 100644
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diff --git a/src/Cech_complex/doc/cech_complex_representation.png b/src/Cech_complex/doc/cech_complex_representation.png
index e901d92e..4d103a56 100644
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diff --git a/src/Cech_complex/doc/cech_one_skeleton.ipe b/src/Cech_complex/doc/cech_one_skeleton.ipe
index 3a35970c..345e6d7b 100644
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diff --git a/src/Cech_complex/doc/cech_one_skeleton.png b/src/Cech_complex/doc/cech_one_skeleton.png
index ffa9c329..807e0936 100644
--- a/src/Cech_complex/doc/cech_one_skeleton.png
+++ b/src/Cech_complex/doc/cech_one_skeleton.png
diff --git a/src/Cech_complex/example/cech_complex_example_from_points.cpp b/src/Cech_complex/example/cech_complex_example_from_points.cpp
index 97327e69..3b889d56 100644
--- a/src/Cech_complex/example/cech_complex_example_from_points.cpp
+++ b/src/Cech_complex/example/cech_complex_example_from_points.cpp
@@ -15,22 +15,26 @@ int main() {
   using Cech_complex = Gudhi::cech_complex::Cech_complex<Simplex_tree, Point_cloud>;
 
   Point_cloud points;
-  points.push_back({0., 0.});
-  points.push_back({0., 2.});
-  points.push_back({std::sqrt(3.), 1.});
-  points.push_back({1., 0.});
-  points.push_back({1., 2.});
-  points.push_back({1. - std::sqrt(3.), 1.});
+  points.push_back({1., 0.});                 // 0
+  points.push_back({0., 1.});                 // 1
+  points.push_back({2., 1.});                 // 2
+  points.push_back({3., 2.});                 // 3
+  points.push_back({0., 3.});                 // 4
+  points.push_back({3. + std::sqrt(3.), 3.}); // 5
+  points.push_back({1., 4.});                 // 6
+  points.push_back({3., 4.});                 // 7
+  points.push_back({2., 4. + std::sqrt(3.)}); // 8
+  points.push_back({0., 4.});                 // 9
+  points.push_back({-0.5, 2.});               // 10
 
   // ----------------------------------------------------------------------------
   // Init of a Cech complex from points
   // ----------------------------------------------------------------------------
-  // 5. is a magic number to force one blocker, and one non-blocker
-  Filtration_value max_radius = 12.;
+  Filtration_value max_radius = 1.;
   Cech_complex cech_complex_from_points(points, max_radius);
 
   Simplex_tree stree;
-  cech_complex_from_points.create_complex(stree, -1);
+  cech_complex_from_points.create_complex(stree, 2);
   // ----------------------------------------------------------------------------
   // Display information about the one skeleton Cech complex
   // ----------------------------------------------------------------------------
diff --git a/src/Cech_complex/example/cech_complex_example_from_points_for_doc.txt b/src/Cech_complex/example/cech_complex_example_from_points_for_doc.txt
index 684e120b..be0afc76 100644
--- a/src/Cech_complex/example/cech_complex_example_from_points_for_doc.txt
+++ b/src/Cech_complex/example/cech_complex_example_from_points_for_doc.txt
@@ -1,16 +1,31 @@
-Cech complex is of dimension 2 - 14 simplices - 7 vertices.
 Iterator on Cech complex simplices in the filtration order, with [filtration value]:
-   ( 0 ) -> [0] 
-   ( 1 ) -> [0] 
-   ( 2 ) -> [0] 
-   ( 3 ) -> [0] 
-   ( 4 ) -> [0] 
-   ( 5 ) -> [0] 
-   ( 6 ) -> [0] 
-   ( 3 2 ) -> [5] 
-   ( 5 4 ) -> [5.38516] 
-   ( 2 0 ) -> [5.83095] 
-   ( 1 0 ) -> [6.08276] 
-   ( 3 1 ) -> [6.32456] 
-   ( 2 1 ) -> [6.7082] 
-   ( 3 2 1 ) -> [7.07107] 
+   ( 0 ) -> [0]
+   ( 1 ) -> [0]
+   ( 2 ) -> [0]
+   ( 3 ) -> [0]
+   ( 4 ) -> [0]
+   ( 5 ) -> [0]
+   ( 6 ) -> [0]
+   ( 7 ) -> [0]
+   ( 8 ) -> [0]
+   ( 9 ) -> [0]
+   ( 10 ) -> [0]
+   ( 9 4 ) -> [0.5]
+   ( 9 6 ) -> [0.5]
+   ( 10 1 ) -> [0.559017]
+   ( 10 4 ) -> [0.559017]
+   ( 1 0 ) -> [0.707107]
+   ( 2 0 ) -> [0.707107]
+   ( 3 2 ) -> [0.707107]
+   ( 6 4 ) -> [0.707107]
+   ( 9 6 4 ) -> [0.707107]
+   ( 2 1 ) -> [1]
+   ( 2 1 0 ) -> [1]
+   ( 4 1 ) -> [1]
+   ( 5 3 ) -> [1]
+   ( 7 3 ) -> [1]
+   ( 7 5 ) -> [1]
+   ( 7 6 ) -> [1]
+   ( 8 6 ) -> [1]
+   ( 8 7 ) -> [1]
+   ( 10 4 1 ) -> [1]
diff --git a/src/Cech_complex/include/gudhi/Cech_complex.h b/src/Cech_complex/include/gudhi/Cech_complex.h
index a50ed9fa..612c73c3 100644
--- a/src/Cech_complex/include/gudhi/Cech_complex.h
+++ b/src/Cech_complex/include/gudhi/Cech_complex.h
@@ -23,7 +23,7 @@
 #ifndef CECH_COMPLEX_H_
 #define CECH_COMPLEX_H_
 
-#include <gudhi/distance_functions.h>        // for Gudhi::Squared_radius
+#include <gudhi/distance_functions.h>        // for Gudhi::Radius_distance
 #include <gudhi/graph_simplicial_complex.h>  // for Gudhi::Proximity_graph
 #include <gudhi/Debug_utils.h>               // for GUDHI_CHECK
 #include <gudhi/Cech_complex_blocker.h>      // for Gudhi::cech_complex::Cech_blocker
@@ -43,7 +43,7 @@ namespace cech_complex {
  * 
  * \details
  * The data structure is a proximity graph, containing edges when the edge length is less or equal
- * to a given max_radius. Edge length is computed from `Gudhi::Squared_radius` distance function.
+ * to a given max_radius. Edge length is computed from `Gudhi::Radius_distance` distance function.
  *
  * \tparam SimplicialComplexForProximityGraph furnishes `Vertex_handle` and `Filtration_value` type definition required
  * by `Gudhi::Proximity_graph`.
diff --git a/src/Cech_complex/include/gudhi/Cech_complex_blocker.h b/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
index d718b56e..5ba17c51 100644
--- a/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
+++ b/src/Cech_complex/include/gudhi/Cech_complex_blocker.h
@@ -24,7 +24,7 @@
 #define CECH_COMPLEX_BLOCKER_H_
 
 #include <gudhi/Cech_complex.h>        // Cech_blocker is using a pointer on Gudhi::cech_complex::Cech_complex
-#include <gudhi/distance_functions.h>  // for Gudhi::Squared_radius
+#include <gudhi/distance_functions.h>  // for Gudhi::Radius_distance
 
 #include <iostream>
 #include <vector>
@@ -75,12 +75,13 @@ class Cech_blocker {
       std::cout << "#(" << vertex << ")#";
 #endif  // DEBUG_TRACES
     }
-    Filtration_value squared_radius = Gudhi::Radius_distance()(points);
+    Filtration_value radius = Gudhi::Radius_distance()(points);
 #ifdef DEBUG_TRACES
-    std::cout << "squared_radius = " << squared_radius << " - " << (squared_radius > cc_ptr_->max_radius()) << std::endl;
+    if (radius > cc_ptr_->max_radius())
+      std::cout << "radius > max_radius => expansion is blocked\n";
 #endif  // DEBUG_TRACES
-    simplicial_complex_.assign_filtration(sh, squared_radius);
-    return (squared_radius > cc_ptr_->max_radius());
+    simplicial_complex_.assign_filtration(sh, radius);
+    return (radius > cc_ptr_->max_radius());
   }
 
   /** \internal \brief Cech complex blocker constructor. */
diff --git a/src/Cech_complex/test/test_cech_complex.cpp b/src/Cech_complex/test/test_cech_complex.cpp
index 626f1d82..eae8778c 100644
--- a/src/Cech_complex/test/test_cech_complex.cpp
+++ b/src/Cech_complex/test/test_cech_complex.cpp
@@ -86,7 +86,7 @@ BOOST_AUTO_TEST_CASE(Cech_complex_from_file) {
   BOOST_CHECK(st.num_vertices() == NUMBER_OF_VERTICES);
 
   std::cout << "st.num_simplices()=" << st.num_simplices() << std::endl;
-  BOOST_CHECK(st.num_simplices() == 18);
+  BOOST_CHECK(st.num_simplices() == 28);
 
   // Check filtration values of vertices is 0.0
   for (auto f_simplex : st.skeleton_simplex_range(0)) {
@@ -119,7 +119,7 @@ BOOST_AUTO_TEST_CASE(Cech_complex_from_file) {
   BOOST_CHECK(st2.num_vertices() == NUMBER_OF_VERTICES);
 
   std::cout << "st2.num_simplices()=" << st2.num_simplices() << std::endl;
-  BOOST_CHECK(st2.num_simplices() == 23);
+  BOOST_CHECK(st2.num_simplices() == 63);
 
   Point_cloud points012;
   for (std::size_t vertex = 0; vertex <= 2; vertex++) {
@@ -156,7 +156,7 @@ BOOST_AUTO_TEST_CASE(Cech_complex_from_file) {
   BOOST_CHECK(st3.num_vertices() == NUMBER_OF_VERTICES);
 
   std::cout << "st3.num_simplices()=" << st3.num_simplices() << std::endl;
-  BOOST_CHECK(st3.num_simplices() == 24);
+  BOOST_CHECK(st3.num_simplices() == 98);
 
   Point_cloud points0123;
   for (std::size_t vertex = 0; vertex <= 3; vertex++) {
@@ -236,13 +236,13 @@ BOOST_AUTO_TEST_CASE(Cech_complex_from_points) {
         GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.0);
         break;
       case 1:
-        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.5);
+        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.707107, .00001);
         break;
       case 2:
-        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.666667, .00001);
+        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.816497, .00001);
         break;
       case 3:
-        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.75);
+        GUDHI_TEST_FLOAT_EQUALITY_CHECK(st.filtration(f_simplex), 0.866025, .00001);
         break;
       default:
         BOOST_CHECK(false);  // Shall not happen