diff options
| author | glisse <glisse@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-02-02 13:31:23 +0000 |
|---|---|---|
| committer | glisse <glisse@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-02-02 13:31:23 +0000 |
| commit | bae3210f6fb5ef1c498ef669c067b21cd6ddf953 (patch) | |
| tree | fc550c873fe06a7f1edd114f3360f8cd5e9c1a5e /src/Rips_complex | |
| parent | c6957d5b3d8e410b6104a848c793d633fba8990a (diff) | |
epsilon
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/sparserips-glisse@3209 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: c7cac815867c94821d13d8dd972e6505c43b04ba
Diffstat (limited to 'src/Rips_complex')
| -rw-r--r-- | src/Rips_complex/doc/Intro_rips_complex.h | 6 | ||||
| -rw-r--r-- | src/Rips_complex/include/gudhi/Sparse_rips_complex.h | 8 |
2 files changed, 8 insertions, 6 deletions
diff --git a/src/Rips_complex/doc/Intro_rips_complex.h b/src/Rips_complex/doc/Intro_rips_complex.h index f9663315..909735cd 100644 --- a/src/Rips_complex/doc/Intro_rips_complex.h +++ b/src/Rips_complex/doc/Intro_rips_complex.h @@ -82,12 +82,14 @@ namespace rips_complex { * filtered simplicial complex (linear size, with constants that depend on * ε and the doubling dimension of the space) that is * \f$(1+O(\epsilon))-\f$interleaved with it (in particular, their persistence - * diagrams are at log-bottleneck distance at most ε). + * diagrams are at log-bottleneck distance at most \f$O(\epsilon)\f$). * * The sparse Rips filtration was introduced by Don Sheehy * \cite sheehy13linear. We are using the version from \cite buchet16efficient * (except that we multiply all filtration values by 2, to match the usual - * Rips complex). + * Rips complex), which proves a + * \f$\frac{1+\epsilon}{1-\epsilon}\f$-interleaving, although in practice the + * error is usually smaller. * A more intuitive presentation of the idea is available in * \cite cavanna15geometric, and in a video \cite cavanna15visualizing. * diff --git a/src/Rips_complex/include/gudhi/Sparse_rips_complex.h b/src/Rips_complex/include/gudhi/Sparse_rips_complex.h index 44b73930..503a783a 100644 --- a/src/Rips_complex/include/gudhi/Sparse_rips_complex.h +++ b/src/Rips_complex/include/gudhi/Sparse_rips_complex.h @@ -46,7 +46,7 @@ namespace rips_complex { * \ingroup rips_complex * * \details - * This class is used to construct a sparse \f$(1+\epsilon)\f$-approximation of `Rips_complex`, i.e. a filtered simplicial complex that is multiplicatively \f$(1+\epsilon)\f$-interleaved with the Rips filtration. + * 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. * * \tparam Filtration_value is the type used to store the filtration values of the simplicial complex. */ @@ -64,8 +64,8 @@ class Sparse_rips_complex { /** \brief Sparse_rips_complex constructor from a list of points. * * @param[in] points Range of points. - * @param[in] distance distance function that returns a `Filtration_value` from 2 given points. - * @param[in] epsilon (1+epsilon) is the desired approximation factor. epsilon must be positive. + * @param[in] distance Distance function that returns a `Filtration_value` from 2 given points. + * @param[in] epsilon Approximation parameter. epsilon must be positive. * */ template<typename RandomAccessPointRange, typename Distance > @@ -85,7 +85,7 @@ class Sparse_rips_complex { * `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 * distance\_matrix.size().\f$ - * @param[in] epsilon (1+epsilon) is the desired approximation factor. epsilon must be positive. + * @param[in] epsilon Approximation parameter. epsilon must be positive. */ template<typename DistanceMatrix> Sparse_rips_complex(const DistanceMatrix& distance_matrix, double epsilon) |