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Diffstat (limited to 'src/cython/doc/source/alpha_complex_user.rst')
| -rw-r--r-- | src/cython/doc/source/alpha_complex_user.rst | 43 |
1 files changed, 19 insertions, 24 deletions
diff --git a/src/cython/doc/source/alpha_complex_user.rst b/src/cython/doc/source/alpha_complex_user.rst index 82b99be9..c2a3c5bb 100644 --- a/src/cython/doc/source/alpha_complex_user.rst +++ b/src/cython/doc/source/alpha_complex_user.rst @@ -81,30 +81,25 @@ In order to build the alpha complex, first, a Simplex tree is built from the cel Filtration value computation algorithm ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -.. math:: - \begin{algorithm} - \caption{Filtration value computation algorithm}\label{alpha} - \begin{algorithmic} - \For{i : dimension $\rightarrow$ 0} - \ForAll{$\sigma$ of dimension i} - \If {filtration($\sigma$) is NaN} - \State filtration($\sigma$) = $\alpha^2(\sigma)$ - \EndIf - \ForAll{$\tau$ face of $\sigma$} \Comment{propagate alpha filtration value} - \If {filtration($\tau$) is not NaN} - \State filtration($\tau$) = min (filtration($\tau$), filtration($\sigma$)) - \Else - \If {$\tau$ is not Gabriel for $\sigma$} - \State filtration($\tau$) = filtration($\sigma$) - \EndIf - \EndIf - \EndFor - \EndFor - \EndFor - \State make\_filtration\_non\_decreasing() - \State prune\_above\_filtration() - \end{algorithmic} - \end{algorithm} + **for** i : dimension :math:`\rightarrow` 0 **do** + **for all** :math:`\sigma` of dimension i + **if** filtration(:math:`\sigma`) is NaN **then** + filtration(:math:`\sigma`) = :math:`\alpha^2(\sigma)` + **end if** + + *//propagate alpha filtration value* + + **for all** :math:`\tau` face of :math:`\sigma` + **if** filtration(:math:`\tau`) is not NaN **then** + filtration(:math:`\tau`) = filtration(:math:`\sigma`) + **end if** + **end for** + **end for** + **end for** + + make_filtration_non_decreasing() + + prune_above_filtration() Dimension 2 ^^^^^^^^^^^ |