Finished the stream of 09-09-2020. Still need to do multidimensional FFTs though...

tex-docs/appendices/vars.tex

@@ -51,4 +51,8 @@ only applies to variables in code, every symbol in equations are explained at th
     \item $p_0$: The pressure of a latitude, longitude, atmospheric layer gridcell from the previous calculation round.
     \item $\alpha_a$: The thermal diffusivity constant for air.
     \item $\alpha_p$: The thermal diffusivity constant for the planet surface.
+    \item $smooth_t$: The smoothing parameter for the temperature.
+    \item $smooth_u$: The smoothing parameter for the $u$ component of the velocity.
+    \item $smooth_v$: The smoothing parameter for the $v$ component of the velocity.
+    \item $smooth_w$: The smoothing parameter for the $w$ component of the velocity.
 \end{itemize}

tex-docs/topics/control_panel.tex

@@ -106,7 +106,10 @@ definitions can be found in \autoref{alg:model constants}. What the $adv$ boolea
     $\delta y \leftarrow \frac{2\pi r}{nlat}$ \Comment*[l]{How far apart the gridpoints in the y direction are (degrees latitude)}
     $\alpha_a \leftarrow 2 \cdot 10^{-5}$ \Comment*[l]{The diffusivity constant for the atmosphere}
     $\alpha_p \leftarrow 1.5 \cdot 10^{-6}$ \Comment*[l]{The diffusivity constant for the planet surface}
-
+    $smooth_t \leftarrow 0.9$ \Comment*[l]{the smoothing parameter for the temperature}
+    $smooth_u \leftarrow 0.8$ \Comment*[l]{The smoothing parameter for the $u$ component of the velocity}
+    $smooth_v \leftarrow 0.8$ \Comment*[l]{The smoothing parameter for the $v$ component of the velocity}
+    $smooth_w \leftarrow 0.3$ \Comment*[l]{The smoothing parameter for the $w$ component of the velocity}
     $count \leftarrow 0$ \;
     \For{$j \in [0, top]$}{
         $heights[j] \leftarrow count$ \Comment*[l]{The height of a layer}

tex-docs/topics/master.tex

@@ -134,3 +134,23 @@ the first valid index to $bla$.
     \label{alg:velocity clamped}
 \end{algorithm}
 
+\subsection{Smoothing all the things}
+On a planet wide scale, you have a lot of variety in the data. To counteract that we filter out the high frequency data. Which means that we filter out the data that occurs sporadically. So we 
+do not consider the data that occurs so infrequently that it means nothing. We do this for the radiation (temperature) and the velocity which is shown in \autoref{alg:smootht} and 
+\autoref{alg:smoothv} respectively. It is worth mentioning that \autoref{alg:smootht} is executed after we do the calculations for $T_a$ (shown in \autoref{alg:optical depth}). 
+\autoref{alg:smoothv} is done after \autoref{alg:velocity} but before \autoref{alg:velocity clamped}. 
+
+
+\begin{algorithm}
+    $T_a \leftarrow \texttt{Smooth}(T_a, smooth_t)$ \;
+    \caption{Smoothing the atmospheric temperature}
+    \label{alg:smootht}
+\end{algorithm}
+
+\begin{algorithm}
+    $u \leftarrow \texttt{Smooth}(u, smooth_u)$ \;
+    $v \leftarrow \texttt{Smooth}(v, smooth_v)$ \;
+    $w \leftarrow \texttt{Smooth}(w, smooth_w)$ \;
+    \caption{Smoothing the velocity}
+    \label{alg:smoothv}
+\end{algorithm}

tex-docs/topics/util_funcs.tex

@@ -282,6 +282,7 @@ This symmetry as it is called can be exploited to produce a divide and conquer a
         }
     }
     \Return{B}
+    \caption{One dimensional Fast Fourier Transformation}
     \label{alg:FFT}
 \end{algorithm}
 
@@ -297,3 +298,24 @@ second dimension. This can of course be extended in the same way for a $p$-dimen
 It is at this point that the algorithm becomes very complicated. Therefore I would like to invite you to use a library for these kinds of calculations, like Numpy \cite{numpy} for Python. If you
 really want to use your own made version, you need to wait for a bit as I try to decode the literature on the algorithm for it. It is one heck of a thing to decode, so I decided to treat that at 
 a later point in the future. It will then be found here, so you will have to stay tuned. Sorry about that, it's quite complex...
+
+With that out of the way (or rather on the TODO list), we need to create a smoothing operation out of it. We do this in \autoref{alg:smooth}. Keep in mind that \texttt{FFT} the call is to the 
+multidimensional Fast Fourier Transform algorithm, \texttt{IFFT} the call to the inverse of the multidimensional Fast Fourier Transform algorithm (also on the TODO list) and that the $int()$ 
+function ensures that the number in brackets is an integer. Also note that the inverse of the FFT might give complex answers, and we only want real answers which the $.real$ ensures. We only 
+take the real part and return that.
+
+\begin{algorithm}
+    \SetKwInOut{Input}{Input}
+    \SetKwInOut{Output}{Output}
+    \Input{Array $a$, smoothing factor $s$}
+    \Output{Array $A$ with less variation}
+    $nlat \leftarrow a.length$ \;
+    $nlon \leftarrow a[0].length$ \;
+    $nlevels \leftarrow a[0][0].length$ \;
+    $temp \leftarrow \texttt{FFT}(a)$ \;
+    $temp[int(nlat s):int(nlat(1 - s)),:,:] \leftarrow 0$ \;
+	$temp[:,int(nlon s):int(nlon(1 - s)),:] \leftarrow 0$ \;
+    \Return $\texttt{IFFT}(temp).real$ \;
+    \caption{Smoothing function}
+    \label{alg:smooth}
+\end{algorithm}