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-rw-r--r-- | src/python/doc/alpha_complex_user.rst | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index a75a0347..bc9fe513 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -26,10 +26,9 @@ Remarks * Using the default :code:`complexity = 'safe'` makes the construction safe. If you pass :code:`complexity = 'exact'` to :func:`~gudhi.AlphaComplex.__init__`, the filtration values are the exact ones converted to float. This can be very slow. - If you pass :code:`complexity = 'safe'` (the default) or :code:`complexity = 'fast'`, the filtration values are only - guaranteed to have a small multiplicative error compared to the exact value, see - `CGAL::Lazy_exact_nt<NT>::set_relative_precision_of_to_double <https://doc.cgal.org/latest/Number_types/classCGAL_1_1Lazy__exact__nt.html>`_ - for details. A drawback, when computing persistence, is that an empty exact interval [10^12,10^12] may become a + If you pass :code:`complexity = 'safe'` (the default), the filtration values are only + guaranteed to have a small multiplicative error compared to the exact value. + A drawback, when computing persistence, is that an empty exact interval [10^12,10^12] may become a non-empty approximate interval [10^12,10^12+10^6]. Using :code:`complexity = 'fast'` makes the computations slightly faster, and the combinatorics are still exact, but the computation of filtration values can exceptionally be arbitrarily bad. In all cases, we still guarantee that the |