Moved the doc file + changed notations in Witness_complex.h

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/witness@1023 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 1053d8ac2f833be8086c81b50dbb34c18de07ebb

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+#ifndef WITNESS_COMPLEX_DOC_H_
+#define WITNESS_COMPLEX_DOC_H_
+
+/**
+   \defgroup witness_complex Witness complex
+
+   \author Siargey Kachanovich
+
+   \section Definitions
+
+   Witness complex \f$ Wit(W,L) \f$  is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$:
+
+   \li \f$W\f$ set of **witnesses** and 
+   \li \f$L \subseteq W\f$ set of **landmarks**.
+
+   The simplices are based on landmarks
+   and a simplex belongs to the witness complex if and only if it is witnessed, that is:
+
+   \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that 
+   w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well. 
+      
+   \section Implementation
+
+   The principal class of this module is Gudhi::Witness_complex.
+
+   In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a witness and consists of landmarks sorted by distance to this witness.
+   This table can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module.
+
+   *\image html "bench_Cy8.png" "Running time as function on number of landmarks" width=10cm
+   *\image html "bench_sphere.png" "Running time as function on number of witnesses for |L|=300" width=10cm
+   
+
+   \copyright GNU General Public License v3.
+
+
+ */
+
+#endif  // WITNESS_COMPLEX_DOC_H_