From 7eca0c81603b433072a5ca86edb2174da9b9490b Mon Sep 17 00:00:00 2001
From: Lionel GUEZ <guez@lmd.ens.fr>
Date: Tue, 23 Mar 2021 23:17:39 +0100
Subject: [PATCH] Polish
---
.../Documentation_texfol/documentation.tex | 36 +++++++++++++++----
1 file changed, 30 insertions(+), 6 deletions(-)
diff --git a/Convert_Matlab/Documentation_texfol/documentation.tex b/Convert_Matlab/Documentation_texfol/documentation.tex
index 013dc21e..85f7c6a1 100644
--- a/Convert_Matlab/Documentation_texfol/documentation.tex
+++ b/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
--
GitLab