[translation] boolean expressions, some typos fixes

programming/lecture/programming.tex

@@ -833,11 +833,11 @@ the statements but not both are true. There is no operator for XOR in
 
 Table~\ref{logicalrelationaloperators} show the logical and relational
 operators that are available in \matlab{}. The additional
-\code[Operator!logical!and2@\&\&]{\&\&} und
+\code[Operator!logical!and2@\&\&]{\&\&} and
 \code[Operator!logical!or2@{"|}{"|} {}]{||} operators are the so
-called `\enterm{shorrt-circuit} operators for the logical OR and
+called `\enterm{short-circuit} operators for the logical OR and
-AND. Short-circuit means that \matlab{} stopps to evaluate a Boolean
+AND. Short-circuit means that \matlab{} stops to evaluate a Boolean
-expresssion as soon as it becomes clear that the whole expression
+expression as soon as it becomes clear that the whole expression
 cannot become true. For example assume that the two statements A and B
 are joined using a AND. The whole expression can only be true if A is
 already true. This means, that there is no need to evaluate B if A is
@@ -865,7 +865,7 @@ this saves processing time.
     \varcode{$\sim=$} & unequal\\
     \varcode{$>$} &  greater than \\
     \varcode{$<$} & less than \\
-    \varcode{$>=$} & greateror equal \\
+    \varcode{$>=$} & greater or equal \\
     \varcode{$<=$} & less or equal \\
     \hline
   \end{tabular}
@@ -881,12 +881,12 @@ this saves processing time.
 Previously we have introduced the data types for integer or floating
 point numbers and discussed that there are instances where it is more
 efficient to use a integer data type rather than storing floating
-poing numbers. The result of a Boolean expression can only assume two
+point numbers. The result of a Boolean expression can only assume two
 values (true or false). This implies that we need only a single bit to
 store this information as a 0 (false) and 1 (true). In \matlab{} knows
 a special data type (\codeterm{logical}) to store the result of a
-Boolean expresssion. Every variable can be evaluated to true or false
+Boolean expression. Every variable can be evaluated to true or false
-by just onverting it to the logical data type. When doing so \matlab{}
+by converting it to the logical data type. When doing so \matlab{}
 interprets all values different form zero to be true.  In
 listing~\ref{booleanexpressions} we show several examples for such
 operations. \matlab{} also knows the keywords \code{true} and
@@ -906,6 +906,8 @@ ans = 1
 ans = 0
 >> logical('test')
 ans = 1   1   1   1
+>> logical([1 2 3 4 0 0 10])
+and = 1   1   1   1   0   0   1
 >> 1 > 2
 ans = 0
 >> 1 < 2
@@ -919,83 +921,85 @@ ans = 1  0  1  1  0
 \end{lstlisting}
 
 
-\section{Logisches Indizieren}\label{logicalindexingsec}
+\section{Logical indexing}\label{logicalindexingsec}
-
+We have introduced how one can select certain element of a vector or
-Einer der wichtigsten Einsatzorte f\"ur boolesche Ausdr\"ucke ist das
+matrix by addressing the respective elements by their index. This is
-logische Indizieren. Logisches Indizieren ist eines der
+fine when we know the range of elements we want t select. There are,
-Schl\"usselkonzepte in \matlab{}. Nur mit diesem k\"onnen
+however, many situations in which a selection based on the value of
-Filteroperationen auf Vektoren und Matrizen effizient durchgef\"uhrt
+the stored element is desired. These situations is one of the major
-werden. Es ist sehr m\"achtig und, wenn es einmal verstanden wurde,
+places where we need Boolean expressions. The selection based on the
-sehr intuitiv zu benuzten.
+result of a Boolean expression is called \enterm{logical
-
+  indexing}. With this approach we can easily filter based on the
-Das Grundkonzept hinter der logischen Indizierung ist, dass durch die
+values stored in a vector or matrix. It is very powerful and, once
-Verwendung eines booleschen Ausdrucks auf z.B. einen Vektor ein
+understood, very intuitive.
-logischer Vektor gleicher Gr\"o{\ss}e zur\"uckgegeben wird. Dieser
+
-wird benutzt um die Elemente des urspr\"unglichen Vektors
+The basic concept is that applying a Boolean operation on a vector
-auszuw\"ahlen, bei denen der logische Vektor \codeterm{wahr} ist
+results in a \code{logical} vector of the same size (see
-(Listing \ref{logicalindexing1}).  Zeile 14 kann wie
+listing~\ref{booleanexpressions}. This logical vector is then used to
-folgt gelesen werden: Gib die Elemente von \varcode{x} an den
+select only those values for which the logical vector is true. Line 14
-Stellen, an denen \varcode{x < 0} wahr ist, zur\"uck.
+in listing~\ref{logicalindexing} can be read: ``Give me all those
-
+elements of \varcode{x} where the Boolean expression \varcode{x < 0}
-\begin{lstlisting}[caption={Beispiel logisches Indizieren.}, label=logicalindexing1]
+evaluates to true''.
->> x = randn(1, 6)              % Zeilenvektor mit 6 Zufallszahlen
+
+\begin{lstlisting}[caption={Logical indexing.}, label=logicalindexing1]
+>> x = randn(1, 6)   % a vector with 6 random numbers
 x =
    -1.4023   -1.4224    0.4882   -0.1774   -0.1961    1.4193
 
->> % logisches Indizieren in zwei Schritten:
+>> % logical indexing in two steps
->> x_smaller_zero = x < 0                    % logischer Vektor
+>> x_smaller_zero = x < 0    % create the logical vector
 x_smaller_zero =
      1     1     0     1     1     0
->> elements_smaller_zero = x(x_smaller_zero) % benutzen, um zuzugreifen 
+>> elements_smaller_zero = x(x_smaller_zero) % use it to select
 elements_smaller_zero =
    -1.4023   -1.4224   -0.1774   -0.1961
 
->> % logisches Indizieren in einem Schritten:
+>> % logical indexing with a single command
 >> elements_smaller_zero = x(x < 0)
 elements_smaller_zero =
    -1.4023   -1.4224   -0.1774   -0.1961
 \end{lstlisting}
 
 \begin{exercise}{logicalVector.m}{logicalVector.out}
-  Erstelle einen Vektor \varcode{x} mit den Werten 0--10.
+  Create a vector \varcode{x} containing the values 0--10.
   \begin{enumerate}
-  \item F\"uhre aus: \varcode{y = x < 5}
+  \item Execute: \varcode{y = x < 5}
-  \item Gib den Inhalt von \varcode{y} auf dem Bildschirm aus.
+  \item Display the content of \varcode{y} in the command window.
-  \item  Was ist der Datentyp von \varcode{y}?
+  \item  What is the data type of \varcode{y}?
-  \item  Gibt alle Elemente aus \varcode{x} zur\"uck, die kleiner als 5 sind.
+  \item  Return only those elements \varcode{x} that are less than 5.
   \end{enumerate}
   \pagebreak[4]
 \end{exercise}
 
 \begin{figure}[t]
   \includegraphics[width= 0.9\columnwidth]{logicalIndexingTime}
-  \titlecaption{Beispiel f\"ur logisches Indizieren.}
+  \titlecaption{Example for logical indexing.}  {The highlighted
-    {Der rot markierte Abschnitt aus den Daten wurde indirekt
+    segment of the data was selected using logical indexing on
-    mit logischem Indizieren auf dem Zeitvektor
+    the time vector: (\varcode{x(t > 5 \& t <
-    ausgew\"ahlt (\varcode{x(t > 5 \& t < 6)}).}\label{logicalindexingfig}
+      6)}).}\label{logicalindexingfig}
 \end{figure}
 
-Logisches Indizieren wurde oben so benutzt, dass die Auswahl auf dem
+So far we have used logical indexing to select elements of a vector
-Inhalt desselben Vektors beruhte. Ein weiterer sehr h\"aufiger Fall
+that match a certain condition. When analyzing data we are often
-ist jedoch, dass die Auswahl aus einem Vektor auf dem Inhalt eines
+faced with the problem that we want to select the elements of one
-zweiten Vektors basiert. Ein Beispiel ist, dass \"uber einen
+vector for the case that the elements of a second vector assume a
-gewissen Zeitraum Daten aufgenommen werden und aus diesen die Daten eines
+certain value. One example for such a use-case is the selection of a
-bestimmten Zeitraums ausgew\"ahlt werden sollen (\figref{logicalindexingfig}).
+segment of data of a certain time span (the stimulus was on,
+\figref{logicalindexingfig}).
 
 \begin{exercise}{logicalIndexingTime.m}{}
-  Angenommen es werden \"uber einen bestimmten Zeitraum Messwerte
+  Assume that measurements have been made for a certain time. Usually
-  genommen. Bei solchen Messungen erh\"alt man einen Vektor, der die
+  measured values and the time are stored in two vectors.
-  Zeitpunkte der Messung speichert und einen zweiten mit den
-  jeweiligen Messwerten.
   
   \begin{itemize}
-  \item Erstelle einen Vektor \varcode{t = 0:0.001:10;}, der die Zeit
+  \item Create a vector that represents the recording time \varcode{t
-    repr\"asentiert.
+    = 0:0.001:10;}.
-  \item Erstelle einen zweiten Vektor \varcode{x} mit Zufallszahlen, der
+  \item Create a second vector \varcode{x} filled with random number
-    die gleiche L\"ange hat wie \varcode{t}. Die Werte darin stellen
+    that has the same length as \varcode{t}. The values stored in
-    Messungen zu den Zeitpunkten in \varcode{t} dar.
+    \varcode{x} represent the measured data at the times in
-  \item Benutze logische Indizieren um die Messwerte
+    \varcode{t}.
-    auszuw\"ahlen, die dem zeitlichen Abschnitt 5--6\,s entsprechen.
+  \item Use logical indexing to select those values that have been
+    recorded in the time span form 5--6\,s.
   \end{itemize}
 \end{exercise}