Clarify setting.

1 files changed, 11 insertions, 2 deletions

diff --git a/sampling_alg_lac2020/LAC-20.tex b/sampling_alg_lac2020/LAC-20.tex
index 7ee146d..8a56d1f 100644
--- a/sampling_alg_lac2020/LAC-20.tex
+++ b/sampling_alg_lac2020/LAC-20.tex
@@ -335,7 +335,16 @@ To the best of our knowledge, this is the first academic article that deals with
 \todobent{Talk about how the drum kit samples are usually created; very briefly.}
 \todobent{Talk about loudness computation of samples.}
 \todo{Mathematical basics (if there are any important ones).}
+
 \todo{Formalize the setting, i.e.\ what is the input/output of our algorithm?}
+\subsection{Setting}
+We now describe the setting in which we want to choose the samples. We are given:
+\begin{itemize}
+	\item a drum kit consisting of a set of instruments $I$
+	\item for each instrument $i \in I$, we are given an input sample set $S_i$
+	\item each sample $s \in S_i$ is already labeled with a power value $p_s \in \mathbb{R}^+$
+\end{itemize}
+After reading the drum kit, requests of the form $(i, p) \in I \times \mathbb{R}^+$ arrive. We want to answer these requests by choosing the best sample from $S_i$ for the power value $p$.
 
 % \todoandre{Make terminology and notation clear and check for consistency in the document.}
 \subsection{Notation and Terminology}
@@ -398,11 +407,11 @@ just adds some noise to the process to make it non-deterministic and thus avoid
 We already explained the core part of the sample selection algorithm. The remainder is now straight-forward. We simply evaluate the objective function for each sample and then pick the one with the smallest value. For completeness, Algorithm \ref{alg:sampling} shows the pseudo code for the sample selection algorithm.
 \begin{algorithm}
 \begin{algorithmic}
-	\Require Requested power $p$, Instrument $I$, current time step $t$, parameters $\alpha, \beta, \gamma$, and array $\mathit{last}$ with the time points a sample has been played last
+	\Require Requested power $p$, Instrument $i$, current time step $t$, parameters $\alpha, \beta, \gamma$, and array $\mathit{last}$ with the time points a sample has been played last
 	\Ensure Sample $s$
 	\State $s = \text{undefined}$
 	\State $f_{\min} = \infty$
-	\For{$s' \in \{ s'' \mid s'' \text{ is sample of instrument }I\}$}
+	\For{$s' \in S_i$}
 		\State $v \gets \alpha \cdot \left( \frac{p-p_{s'}}{p_{\max} - p_{\min}}\right)^2 + \beta \cdot \left( 1 + \frac{t - \mathit{last}[s']}{S}\right)^{-1} + \gamma \cdot r(s',t)$
 		\If{$v < f_{\min}$}
 			\State $f_{\min} \gets v$