Polish

Convert_Matlab/Documentation_texfol/documentation.tex

@@ -100,16 +100,15 @@ cyclones. Cf. table (\ref{tab:eddy_id_Matlab}).
   \centering
   \begin{tabular}{lll}
     date index 0 & & \\
-           & anticyclones & $1, \dots, e_\mathrm{max,anti}(0)$ \\
-           & cyclones & $1, \dots, e_\mathrm{max,cyclo}(0)$ \\
+           & anticyclones & $n = 1, \dots, e_\mathrm{max,anti}(0)$ \\
+           & cyclones & $n = 1, \dots, e_\mathrm{max,cyclo}(0)$ \\
     date index k & & \\
-           & anticyclones & $k E + 1, \dots, k
+           & anticyclones & $n = k E + 1, \dots, k
                             E + e_\mathrm{max,anti}(k)$ \\
-           & cyclones & $k E + 1, \dots, k E
+           & cyclones & $n = k E + 1, \dots, k E
                         + e_\mathrm{max,cyclo}(k)$
   \end{tabular}
-  \caption{Node indices in the Matlab program. $k$ is the date index,
-    starting at 0.}
+  \caption{Node indices. $k$ is the date index, starting at 0.}
   \label{tab:eddy_id_Matlab}
 \end{table}
 Conversely, from the definition of $E$, knowing $n$ and $E$, we can
@@ -122,6 +121,31 @@ obtain $(k, e)$:
   & = 1 + (n - 1) \bmod E
 \end{align*}
 
+In the Matlab program, the node index $n'$ is different:
+\begin{equation*}
+  n' = k' E + e
+\end{equation*}
+where $k'$ is the index, starting at 0, of the date $d$ in the suite
+of processed dates. So $k' \ne k$ if there is a missing date in the
+suite of processed dates.
+\begin{equation*}
+  k' = \left \lfloor \frac{n' - 1}{E} \right \rfloor
+\end{equation*}
+The suite of processed dates is stored in the array
+\verb+date_num+. For a given date, from $n'$ we can compute $k'$ and
+$e$, and then $d$ from \verb+date_num[k']+, without any search. But
+the reverse conversion needs a search: from $d$ and $e$, we need to
+search \verb+date_num+ to get $k'$, then $n'$.
+
+To convert from $n'$ to $n$, we note that:
+\begin{equation*}
+  k = \mathtt{date\_num[k']} - \mathtt{date\_num[0]}
+\end{equation*}
+and:
+\begin{equation*}
+  n = n' + (k - k') E
+\end{equation*}
+
 \section{Instantaneous eddies}
 
 The data for instantaneous eddies is stored in shapefiles, in the